a student`s handbook of laboratory exercises in astronomy

a student`s handbook of laboratory exercises in astronomy
A
STUDENT’S HANDBOOK
OF
LABORATORY EXERCISES IN ASTRONOMY
(Laboratory Manual for Astronomy 101 and 102)
Second Edition
2010
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ii
Astronomy 101 Lab Report
You MUST pass the labs to pass the course. To pass the labs you must
write up your own lab and hand it in to the slot for your lab section in
the box outside Elliott 403. Write legible full sentences in ink in a “Physics
Notes” lab book. If your writing is indecipherable then type the lab report
on a computer and print it so your instructor can read it. To maximize
your marks you will want to follow this format. Notice that NOT all of the
following components will be in every lab; this outline is more of a guideline.
OBJECTIVE/PURPOSE Write one or two sentences about why you are
doing the lab.
INTRODUCTION/THEORY Outline what the lab is about and give
the historical perspective. You especially want to state what you expect the results to be from previous work. What assumptions are you
making?
EQUIPMENT Often a piece of equipment is introduced which allows you
to make your measurements. Describe the equipment giving pertinent
details.
PROCEDURE In your own words write a brief outline of the steps you
used to do the lab. It must not be a copy of the lab manual but it must
say more than “See the lab manual”. A reasonably knowledgeable
person should be able to follow your procedure, complete the lab and
get similar results. Use third person past tense: “The galaxy was
measured ... ” NOT “I measured the galaxy ... ”.
OBSERVATIONS Some of the labs require you to sketch something astronomical so record the date, time and sky conditions on the sketch.
TABLES/MEASUREMENTS The data you measure should be put in
a table on the white pages of the book with the columns labelled and
underlined. Refer to the table in the procedure.
GRAPHS Sometimes we want to show how one thing is related to another
and we will do that with a graph. Make sure you print a label on both
axes and print a title on the top of the graph. The scale should be
chosen so that the points fill the graph paper.
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CALCULATIONS When you calculate an answer take note of the significant digits. If you have three digits in the divisor and three digits in
the dividend then you should state three digits in the quotient. If you
do the same calculation over and over (i.e. for different stars), then
show one calculation and then put the other results in a table.
RESULTS The result of a lab is often a number. You must remember to
quote an uncertainty for your result. You must also remember to quote
the units (kilometres, light years, etc.).
QUESTIONS Usually there are a few questions at the end of the lab for
you to answer. These should be answered here.
CONCLUSIONS/DISCUSSION Does your result make sense? Did you
get the result you expected within the uncertainty? If not, there is some
error and you might want to check it out with your lab instructor! How
are your results dependent on your assumptions?
REFERENCES List the books and web sites that you used to write up
this lab. Use the text but do not copy it.
EVALUATION Did you like this lab? Did you learn anything?
MARKING In general an average mark is 7 or 8 out of 10. The lab is
due approximately 24 hours after you have finished it and one mark is
deducted per week that a lab is late. Please hand in the lab to the box
in the hall on the fourth floor. It is usually hard but not impossible
to get a 10. You need to show that you are interested and to not hold
back. Read the lab manual, read the text, visit a few of the suggested
web sites and you will learn something to impress the marker and get
a better mark.
CONTENTS
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Contents
1 Visual Observations
1
2 Apparent Positions of the Planets
6
3 Galaxies, Stars and Nebulae
13
4 Spectra of Gases and Solids
20
5 Colour-Magnitude Diagrams
26
6 How Big is Our Galaxy?
32
7 What is the Age and Size of the Universe?
40
8 Search for Extraterrestrial Intelligence
46
9 Lunar Imaging
57
10 Constellation Imaging
71
11 Solar Rotation
78
CONTENTS
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1 VISUAL OBSERVATIONS
1
1
Visual Observations
OBJECTIVE
The objective of this laboratory exercise is to introduce the student to the
essentials of astronomy – planets, stars, galaxies, nebulae, and telescopes –
through the observation of the night sky.
EQUIPMENT
Telescopes
At night the brightness of the faintest star which you can see is limited
by the size of the pupils of your eyes. Your pupils dilate in the dark so that
more photons (bits of light) can get into you eye. In the dark your pupil is
about 1 cm in radius and has an area (πr 2 ) of 3.14 cm2 . If the pupil of your
eye were three centimetres radius you could see stars nine times fainter. For
this lab we will give you a telescope, which concentrates all the light which
falls on a mirror 10 cm in radius into a beam small enough to fit in your eye.
These telescopes also magnify about 45 times and have a field of view of 1
degree.
Your instructor will show you the parts of the telescope and explain their
function. You will be shown how to use the telescope. Make sure you understand the use of the instrument before you use it in the dark.
• Draw a diagram of the telescope showing the essential parts: primary
mirror, secondary mirror, eyepiece, focuser, mount and finder.
• In a sentence or two describe and explain the function of these parts.
• Draw on your diagram the path followed by the incoming light.
• How much brighter will your telescope make the stars appear relative
to your unaided eye?
Our telescopes can moved under computer control. The telescopes must
be told the accurate time and properly aligned on two stars at the beginning
of the night and from then on they will point to any object in the sky. If you
turn the power off or bump them then the telescope will need to be realigned
by the instructor.
1 VISUAL OBSERVATIONS
2
The telescope has a hand control that lets you move the telescope up,
down, left and right with the arrow keys. Above the arrow keys are: [Align]
never push it, [Enter] to accept an answer, [undo] to not accept an answer or
to answer no. Below the arrow keys is the number pad and each number is a
command/list of objects. Use the [6=Up] & [9=down] keys to scroll through
a list of objects. The [5=planet] key to scroll through the planets and the
[8=list] key to see lists of named stars and named objects. The [1=M] key is
for a famous list of objects compiled by Charles Messier. The [info] key will
give you information about the object you are looking at. There is a list of
interesting objects at the end of this lab.
Observations
The Moon
We will start with the Moon since it is the brightest and most easily found
object in the sky. To get the moon in the telescope push [undo] a few times;
then push [5=planet]; then push [6=Up] until the display says “Moon” and
then push [Enter] and the telescope will move to the Moon. Then look into
the small finder telescope and centre the image of the moon on the cross
hairs by pushing the arrow keys. The moon should now appear in the main
eyepiece. Centre the moon in the field of view by pushing on the arrow keys.
DO NOT pull or push on the little FINDER telescope.
• Sketch the moon as seen with your eye. Include the time, the horizon
• Sketch the moon as seen through the telescope.
The Planets
People have looked at the night sky with their unaided eye for centuries
and have made some interesting observations. The most obvious is that
everything in the sky other than the Sun and the Moon seems to be a tiny
pin-prick of light. Also, if you measure the moon’s position relative to some
stars tonight and then do the same thing tomorrow you will find that the
moon has moved relative to the stars. The ancients also noticed that some
of the brightest “stars” moved; these they called the “planets”, which means
“wanderers”.
The planets are also bright and usually easily identified. Five planets can
be seen with the naked eye – Mercury, Venus, Mars, Jupiter, and Saturn.
1 VISUAL OBSERVATIONS
3
Depending on their position along their orbit and our position in our orbit
around the Sun, some planets may or may not be visible, i.e. above or below
the horizon, at the time you are doing this lab.
• Note also the time and date of your observation.
• Use the telescope to observe each visible planet.
– What colour is the planet?
– Can you see markings on its surface?
– Can you see its moons?
– Is the planet crescent-shape, round, or gibbous (nearly full)?
• Sketch each planet (and its moons, if any) as seen through the telescope.
• If the moons are visible, label them on your sketch.
The Stars
Even if the moon and the planets are below the horizon during the night,
there are many very interesting stars to look at.
• Point your telescope at any bright star in the sky. What do you see? In
the list of named stars: Vega, Deneb, Altair or Arcturus are probably
good choices.
Hopefully you have seen a tiny pin-prick of light that twinkles. Stars look
the same through a telescope as they do to your eye, but brighter. They are
so far away that they appear to us as dots of light – no matter how many
times you magnify them, you will always see them as dots. The stars are
many light years from us (1 ly = 9.46 × 1012 km, the distance a photon of
light travels during one year). For comparison, the Moon is about 2 light
seconds from us, and the planets are about 20 light minutes from us, the
bright stars are about 20 light years from us and the nearby galaxies are
about 20 million light years from us.
Some stars have close companions which orbit them, similar to the way
our Earth orbits the Sun. These stars are called double stars or binary stars.
The star named Albireo (β Cygni) in the constellation Cygnus is a beautiful
double star.
1 VISUAL OBSERVATIONS
4
• Point your telescope at Albireo.
• Sketch Albireo.
• What is the colour of each star?
• Which star is the hottest of the two? Explain.
• Note the time and date of your observation.
The Constellations
When you look at the night sky you will probably notice that the stars
seem to form lines or simple geometrical shapes. These asterisms are the
basis for the constellations. While the origin of our names of the stars and
constellations is for most part lost, generally we use names derived from the
Arabic names for the stars and the Greek names for the constellations.
constellations of stars. Your instructor will point out the more obvious
constellations and bright stars.
• Sketch at least three (3) new Constellations that you learnt tonight.
• What is the mythology associated with them.
• Note their approximate positions in the sky, and the time and date of
the observations.
• Learn the names of at least three stars and mark them on your constellation sketch.
Deep-Sky Objects : Star Clusters, Nebulae, Galaxies
Plenty of other astronomical objects can be observed such as clusters of
stars, gaseous nebulae and galaxies. These objects are generally very distant
and thus are quite dim, and therefore harder to see with a small telescope
than the planets are. The list of objects compiled by Charles Messier is
stored as key [1=M] and you can use this key to move to any of the Messier
objects in the table.
• Observe and sketch one of each of these four types of objects :
– Globular Cluster
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1 VISUAL OBSERVATIONS
– Open Cluster
– Planetary Nebula
– Galaxy
• Describe in a few sentences what these objects are. Do not copy the
info button!
• Again, note the time and date of your observations.
If you do not get a chance to see one of these nebulous object due to
clouds etc., look them up in your text book or the Internet and write a few
sentences about them.
Web Sites
http://skyandtelescope.com/
http://www.heavens-above.com/
INTERESTING FALL OBJECTS
Objects
Vega
Arcturus
Albireo
Mizar
NGC 869/884
M11
M27
M57
M31
M13
M15
R. A.
18:36:56
14:15:40
19:30:44
13:24
02:20
18:51:06
19:59:24
18:53:24
00:42:42
16:41:42
21:30:00
Declination
38◦ 470
19◦ 110
27◦ 570
54◦ 560
57◦ 080
−6◦ 160
22◦ 430
33◦ 020
41◦ 160
36◦ 280
12◦ 100
Mag.
0.0
0.0
3.1
2.3
6.6
5.8
7.6
9.7
3.5
5.9
6.3
Comments
25 ly A0V
36 ly K2III
K3II+B8V
78 ly, Double Star
6000 ly, Double Open Cluster
6000 ly, Open Cluster
900 ly, Dumbbell Planetary Nebula
1600 ly, Ring Planetary Nebula
2 000 000 ly, Andromeda Galaxy
20 000 ly, Globular Cluster
30 000 ly, Globular Cluster
2 APPARENT POSITIONS OF THE PLANETS
2
6
Apparent Positions of the Planets
OBJECTIVE
This exercise is intended to familiarize you with the apparent motions of the
bright planets and enable you to predict where and when you might expect
to find them in the sky.
INTRODUCTION
In Table 1. you are provided with the heliocentric longitudes of the planets
(helio=sun, centric=centred) Venus, Earth, Mars, Jupiter and Saturn. These
longitudes, and the radii of the planets’ orbits, are used to produce orbits on
the graph paper and indicate where the planets are in their orbits for a given
time of year.
Materials
• large sheet of polar coordinate graph paper
• protractor
• SC001 constellation chart
• coloured pencils
• planisphere
The Planets’ Longitudes
The sun’s annual path, through the stars, defines the great circle called the
ecliptic. This represents the plane of the earth’s orbit projected into space.
Since the bright planets are observed to move in paths which closely follow
the ecliptic, it follows that all the orbits lie approximately in the same plane
(i.e. the plane of the ecliptic). For this lab, we will assume that the orbits
are circular, and draw them on a flat sheet of paper.
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2 APPARENT POSITIONS OF THE PLANETS
Table 1. Heliocentric Longitudes from Astronomical Almanac
Date
Venus
2010-Sep-22
338
2010-Oct-22
026
2010-Nov-21
074
2010-Dec-21
122
2011-Jan-19
170
2011-Feb-18
218
2011-Mar-20
266
2011-Apr-19
314
2011-May-20
003
2011-Jun-21
054
2011-Jul-22
104
2011-Aug-22
154
2011-Sep-22
204
Earth
000
030
060
090
120
150
180
210
240
270
300
330
360
Mars
238
254
270
288
306
325
343
003
022
040
058
074
090
Jupiter
358
001
004
007
009
012
015
018
021
023
026
029
032
Saturn
187
188
189
190
191
192
193
194
195
196
197
199
200
Plot the Planets’ Positions
Before you plot the positions of the planets for the given time frame, there
are some things you need to know. Table 2 gives the radii of the orbits of
the planets in question, in astronomical units (AU). The radius of the earth’s
orbit is defined to be 1 AU (=150 million km).
In order to plot the positions of the planets, the point of zero longitude
must be defined. Both heliocentric and geocentric longitudes are measured
counterclockwise from 0◦ − 360◦ the First Point of Aries as zero. The First
Point of Aries, assigned the symbol Υ , is at the vernal equinox, which is
the point at which the sun crosses the celestial equator moving north. This
is the point in the sky which lies behind the sun at the time of the March
equinox.
To plot the positions of the planets, place the sun at the centre of the
paper, and use the concentric circles as the orbits. There are 10 heavy black
circles; and since the orbit of Saturn is 9.54 AU, each circle can represent 1
AU. Take the large zero at the bottom of the paper to be the First Point in
Aries, and read off the longitudes of the planets, moving counterclockwise.
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2 APPARENT POSITIONS OF THE PLANETS
Table 2. Radii and Period of Orbits
Planet
Orbit Radius (A.U.)
Period (years)
Symbol
qi
Sun
Mercury
0.387
0.24
g
Venus
0.72
0.62
i
Earth
1.00
1.00
i
Mars
1.52
1.88
i
Jupiter
5.20
11.86
Saturn
9.54
29.46
Uranus
19.218
83.75
Neptune
30.110
163.73
6
qi
66
6
Mark the planet’s positions with a coloured pencil, and label each position
with the date. Plot the planet positions for three months.
Conjunctions, Elongations and Oppositions
Figure 1 is a diagram of the sun, earth, an inner planet (like Venus, for
example) and an outer planet (like Saturn, for example). On this diagram
are labeled various interesting alignments of the planets. Conjunction is
when the planet is in line with the sun and generally hard to see like a new
moon. Opposition is when the planet is opposite the sun and will stay up
all night like a full moon. Greatest Elongation is when an inferior planet
is at its greatest distance from the sun as seen in the sky and most easily
seen. Quadrature is when the planet is ninety degrees from the sun like a
first or third quarter moon. Referring to this diagram and your orbit diagram
drawn earlier, for each outer planet state whether it is closest to conjunction,
opposition or quadrature. For Venus, state whether it is closest to inferior
2 APPARENT POSITIONS OF THE PLANETS
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conjunction, superior conjunction, or greatest eastern or western elongation.
Why does Venus go through phases?
C
S=Sun
E=Earth
Inferior Planet is closer to Sun
SC
C=Conjunction
IC=Inferior Conjunction
S
SC=Superior Conjunction
EW
EE
EE=Greatest Eastern Elongation
IC
EW=Greatest Western Elongation
Q
E
Q
Q=Quadrature
Op
Op=Opposition
Figure 1. Planetary Configurations
The Planets as Seen from Earth
Now where would Venus, Mars, Jupiter and Saturn be in the sky, as seen
from Victoria? You can predict this using your orbit diagram. We know
that the earth rotates on its axis counterclockwise, as seen on your diagram.
Noon at a particular place on the earth occurs when that place fully faces the
sun, midnight is when the earth is turned such that the sun is on the other
side of the earth, dusk and dawn are halfway in between. At dusk the sun
will be on the western horizon and at dawn the sun will be on the eastern
horizon. From Victoria if the sun is “overhead” at noon it is really in the
southern part of the sky.
Just like the sun will rise and set once each day so do the planets. For
each of the four planets, state whether you would see them at dawn, dusk,
noon and midnight and in the eastern or western or southern part of the sky.
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2 APPARENT POSITIONS OF THE PLANETS
Table 3. Planets as seen from the Earth
Planet
Venus
Mars
Jupiter
Saturn
Noon Sunset
Midnight
Sunrise
The Geocentric Coordinates of the Planets
Recall that the geocentric ecliptic longitude is the longitude of the planets as
measured from the earth (geo=earth). In this part you will be determining
the geocentric ecliptic longitude of each of the four planets in question and
thus the constellation in which the planet appears.
First measure the geocentric ecliptic longitude of each planet. Note you
will have to move your origin from the Sun to the Earth (since we want
earth-centred longitudes, not sun-centred ones), and draw a line straight
down from the earth to establish a new First Point in Aries from which
to measure. This line should be parallel to the original line to the First
Point in Aries. Remember to measure from the First Point in Aries around
counterclockwise to the planet’s location.
Using these geocentric longitudes, plot the positions of the planets and
the sun on the ecliptic on the SC001 constellation chart. The zodiac constellations are the 12 constellations which form a band around the celestial
sphere, along the ecliptic.
• In which zodiacal constellation is each planet located?
• In which zodiacal constellation is the sun located?
• In which zodiacal constellation was the sun located when you were
born? What is your astrological sign? Check with your partners and
discuss any discrepancy.
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2 APPARENT POSITIONS OF THE PLANETS
Table 4. Geocentric Equatorial Position of the Planets
Planet
Sun
Venus
Mars
Jupiter
Saturn
Ecliptic Long. Constellation
Right Ascension
Declination
The Geocentric Equatorial Coordinates of the Planets
When we want to move our telescope to see a star or a planet we generally
use what are called the equatorial coordinates, called Declination (latitude)
and Right Ascension (longitude). The Declination is measured from the
equator going north (+) or south (−) in degrees. Right Ascension is measured
around the equator in hours and minutes from the First Point in Aries.
These coordinates scales are on the constellation chart. What are the Right
Ascension and Declination of the planets?
The Use of a Planisphere
A planisphere is a device which displays the stars and sky depending on the
time of day and the date in the year. The sky visible from any location of
Earth depends on the latitude of the observer so the planisphere has a cutout
set for a certain latitude. Here are a number of exercises for you to do which
will illustrate how to use the planisphere.
1. Fold and tape together your planisphere as per the instructions on it
2. Turn the dial round and round and round. Which star seems to stay
in the middle of the visible area.
3. Along the top dial find the 12 arrow. Turn the inside star dial until the
12 matches up with 01 July.
2 APPARENT POSITIONS OF THE PLANETS
12
4. The star in the middle of the visible part of the dial will be the one
passing overhead )in the Zenith). What is the name of the star in the
Zenith? What constellation is it in?
5. On the right hand side of the planisphere is the “Western Horizon”.
Which star is on the Western Horizon?
6. Turn the star dial to 15 July at 11pm. Which star is in the Zenith?
Which star is on the western horizon?
7. Turn the star dial to 15 August at 11pm. Which star is in the Zenith?
Which star is on the western horizon?
8. We can turn the dial until the star Antares is setting on the western
horizon. What time will Antares set on the 22 September? What day
and month will Antares set at 1am.
9. Turn the dial to 11pm on 01January and find the star Sirius. At what
time will Sirius rise on 01 January? At what time will Sirius set on
01Jan? For how many hours will Sirius be above the horizon on 01Jan?
Web Sites
http://www.jpl.nasa.gov/
http://ssd.jpl.nasa.gov/
3 GALAXIES, STARS AND NEBULAE
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Galaxies, Stars and Nebulae
INTRODUCTION
The photographs that we will be using are reproductions of plates taken by
the 1.2 m (48 in) Schmidt telescope on Mount Palomar. Schmidt telescopes
are designed specifically for photographing relatively large (by astronomical standards) areas of the sky with very good definition. This particular
Schmidt telescope is the largest one in the world and was designed, at least
in part, with the idea of compiling an atlas of the entire sky visible from
southern California. The atlas took about 10 years to complete, under the
auspices of the National Geographic Society, and the Hale Observatories
which are run by the Carnegie Institution and California Institute of Technology. It has since been invaluable to astronomers. The telescope was large
enough that the pictures include the most distant objects known, and yet
the field of view was wide enough (In a large telescope the field of view is
usually quite small) that the entire sky is covered by a reasonable number of
photographs. Astronomers use the photographs both for survey work in determining the numbers and kinds of different classes of astronomical objects
and for discovering and identifying objects that need to be studied further
with other types of telescopes.
The original photographs were made on glass, as are most astronomical
photographs, because glass is less subject to the stretching, shrinking and
warping that can occur with the acetate and other bases used for ordinary
photographic film. The original photographs are stored in a vault, but many
copies have been made and sold to various observatories and astronomical
institutions around the world. All the copies (ours are prints but transparencies are also available) are negative contact copies because, as a matter of
practical experience, these preserve more of the details of the original than
do any other types of copies. Each print is about 35 cm square and covers
an area of the sky of 6o x 6o giving a scale of roughly one degree per 6 cm.
(The full moon would thus be about 3 cm in diameter.) For each position
on the sky, there are two different photographs, one taken originally in blue
light and one taken in red light. This lets us estimate the colors of different
objects and even, in extreme cases, see objects in one color that are nearly
or totally invisible in the other.
These prints are of extremely high quality and are the same ones that
3 GALAXIES, STARS AND NEBULAE
14
astronomers use. They are very difficult to replace so please be extremely
careful. Please NO PENS OR PENCILS ANYWHERE NEAR THE PHOTOGRAPHS! DO NOT WRITE ON PAPER THAT IS ON TOP OF THE
PHOTOGRAPHS!
BASIC DATA
In the upper left hand corner of each photograph (which corresponds to
the northeast corner on the sky) is a block containing the basic information about the photograph. This information includes the plate sensitivity
(whether it was sensitive to blue light=O or to red light=E), plate number
(the red and blue photographs of the same piece of sky will have the same
number), the date on which the original photograph was taken, and the astronomical coordinates (right ascension and declination, which are analogous
to latitude and longitude on the earth) which indicate the exact position in
the sky of the center of the photograph.
OBJECT
1. To recognize the importance of practice in looking at photographs of
astronomical objects.
2. To be able to recognize visually spiral and elliptical galaxies in both
face-on and edge-on orientations.
3. To estimate the distance to one cluster of galaxies given the distance
to another.
4. To appreciate the usefulness of photographs of more than one color.
5. To recognize the variety of objects visible in the sky.
GALAXIES
INTRODUCTION
The upper left corner of each print has a number which identifies the
area of sky it covers. In this exercise you will be using prints 0-83 and 01563. Remember that these are negatives, so that light from a star or galaxy
appears black on the prints. The spikes and circles around the images of
bright stars are an artifact of the telescope structure. All stars, except of
course the sun, appear as points of light to even the largest telescopes. The
3 GALAXIES, STARS AND NEBULAE
15
faint circular images which appear here and there are “ghost” images of stars
which arise when light from a bright star bounces off the photograph, then
gets reflected somewhere inside the telescope and finally returns somewhere
else on the photograph.
PROCEDURE
1. Hercules Field
Inspect the print labeled 0-83 for a while. Most of the dots in the print
are foreground stars in our Milky Way. This print also shows hundreds of
galaxies which are not immediately apparent until you have achieved some
experience with the other print.
2. Virgo Cluster
Now study the print 0-1563. You will notice many objects here that are
clearly not stars. They are galaxies, mostly belonging to a cluster of galaxies
in the constellation Virgo, called the Virgo Cluster of Galaxies. It is the
nearest cluster of galaxies to us. We can say that these galaxies are all at
approximately the same distance from us (about 51 million light years) and,
therefore, any differences we find in the size or brightness between different
galaxies are an indication of the intrinsic properties of these galaxies and not
due to differences in their distance from us.
Study the print with a magnifier long enough to be able to distinguish:
a) elliptical galaxies (they show no structure, but get fainter from the
center out) from spiral galaxies.
b) spiral arms of spiral galaxies that are smooth bands of light from those
that are clumpy.
c) spiral galaxies seen edge-on from those seen face-on.
d) spiral galaxies which show a distinct bar across the nucleus (barred
spirals).
e) irregular galaxies or peculiar systems like pairs of galaxies which might
be colliding or orbiting each other. One of the best ways to look at galaxies
carefully is to try to sketch some of them. Sketch at least 6 different galaxies
(one from each of the above groups) in boxes about 3 cm square. Classify
each galaxy as to which of the above groups it belongs.
3. Dust Lane
Near the upper right corner of 0-1563, just above the giant elliptical
galaxy M86, is an elongated galaxy with a white lane across it NGC 4402.
Sketch this system. What do you think the white lane is? Why are no stars
visible where the white lane is?
3 GALAXIES, STARS AND NEBULAE
16
Can you see white lanes or patches in any other galaxies? In what type
of galaxy is there a tendency for white lanes and patches to occur?
4. Hercules Cluster
Now return to print 0-83. With your new experience, you will be able
to find a group of several hundred galaxies clumped in a part of this print.
Make a rough sketch of the features in the print showing location and outline
of the cluster of galaxies (not the individual galaxies). This is the Hercules
Cluster of Galaxies, in the constellation Hercules. Use a magnifier to check
whether the Hercules Cluster contains spiral and elliptical galaxies like the
Virgo Cluster. What do you find?
5. Distance to Hercules Cluster
Astronomers assume that the larger galaxies in each cluster are in fact
very similar in size.
a) Why do the galaxies in the Hercules Cluster look so much smaller than
those in the Virgo Cluster?
b) Estimate the distance of the Hercules Cluster, given that the Virgo
Cluster is 51 million light years away. (Freedman et al., 1994). To do this,
use your magnifier to measure the sizes of the approximately largest galaxies
in each cluster, noting the type of galaxy beside each measurement (elliptical,
E, or spiral, S). Then use the average size of the brightest galaxies as an
indicator of relative distance.
Notes:
i) You will need to think carefully about the criterion you use for measuring size and then try to apply the same criterion to all your measurements.
ii) Estimate roughly the accuracy of your result.
iii) Compare the sizes you measured for the elliptical and spiral galaxies
separately and discuss any differences you notice.
STARS AND NEBULAE
INTRODUCTION
The upper left corner of each print has a number which identifies the area
of sky it covers. There is a red (E) print and a blue (O) print for each area.
Prints 1099 and 754 cover adjacent areas of sky and you can arrange them
as shown in the diagram. The area covered is 6o x 12o , in the constellation
Cygnus, where we are looking along a spiral arm of our galaxy. The very
17
3 GALAXIES, STARS AND NEBULAE
bright star Deneb is at the line of overlap as shown in the diagram and the
direction of the Milky Way is marked.
The spikes and circles around the images of bright stars are an artifact
of the telescope structure. All stars, except of course the sun, appear as
points of light to even the largest telescopes. The faint circular images which
appear here and there are “ghost” images of stars which arise when light from
a bright star bounces off the photograph, then gets reflected somewhere inside
the telescope and finally hits somewhere else on the photograph.
Figure 1. The Stars and Nebulae Prints
1099
51 Cygni
ω Cygni
30 Cygni
754
31 Cygni
Deneb
56 Cygni
Milky Way
γ Cygni
PROCEDURE
Make a sketch similar to figure 1. in your lab book. Show the outline of
the POSS print and mark on a few of the bright stars. Mark the position of
the following objects on it.
1. Stars
a) The brighter a star is in the sky, the larger its image on the photograph
will be. Would you expect, therefore, the image of a blue star to be larger
or smaller on the blue prints than on the red prints?
b) Near the lower right part of the print 1099 there are two fairly bright
stars that appear near each other in the sky. 30 Cygni is the star to the
north and 31 Cygni is to the south. Which is the bluer of these stars?
c) Find and mark the location of another very blue and another very red
star.
2. Planetary Nebula
3 GALAXIES, STARS AND NEBULAE
18
A planetary nebula appears on print 1099. It contains ionized hydrogen
ejected by a dying star, so you would expect its color to be red.
Search on the print of the appropriate color and give its position. Clue:
it is small and round, with a sharp boundary.
Search for it on the print of the other color. What do you find? Explain
how it is formed.
3. Globule
A globule is a very thick dust cloud, so small that it may soon collapse to
form a new star. Since dust absorbs all light emitted by more distant stars
and nebulae behind it what color will the globule appear on the prints?
Search on print E-754 for the tiniest dust cloud you can find and mark its
position. The globule may look like a speck of dust on the print or a flaw in
the film. How can you check that it is a real globule and not merely a flaw?
4. Reflection Nebula
A reflection nebula occurs when dust scatters light from a nearby star.
This makes the star redder and the scattered light seems to come from an
extended region surrounding the star. The same thing happens in our atmosphere, making our sky blue.
A reflection nebula appears in the right half of 0-754. Search for this
reflection nebula, mark its position, and explain how it is formed.
5. Milky Way
The diagram given earlier shows roughly where the Milky Way is located.
Now look on the red prints and compare the number of stars in the Milky
Way (per square mm) with the number in the upper right part of print 1099.
What do you find?
We believe that our Galaxy is a disk of billions of stars, and that most of
these are situated in the direction of the Milky Way. Why, then do we not
see the greatest number of stars along its central line?
We can make a very rough estimate of the number of stars in our galaxy
by counting how many stars there are in a small area and then multiplying
by how many small areas there are in the sky. Count the stars in a millimeter
by a millimeter square and then multiply by 150 Million to find roughly how
many stars there are in the Milky Way galaxy.
6. Dust Clouds
Two dust clouds appear on E-754 at the lower left and lower right. Each
is a thick, opaque cloud. Given this information, which cloud is farther away?
Explain your reasoning.
3 GALAXIES, STARS AND NEBULAE
19
7. Bonus
Other things to do if you have time: (no write-up required).
a) Look at E-1099 and E-754 together and notice how the long filamentary
structures tend to curve and suggest they may be part of a circular structure
with its center on the lower part of E-754. Although it is hard to see on the
print, near the center is a group of stars known as the OB association Cygnus
OB2. They are very strongly reddened by the interstellar dust between us
and them and this dust has also dimmed their light. If this dust were absent,
some of the stars would be among the brightest stars visible in the sky. Can
you see this association? It is also interesting because there is a source of
X-rays as well as a large, strong source of radio waves in the same directions
which may have been left by a supernova.
b) Examine anything else that looks interesting and see what you can
deduce about it from a comparison of the two prints or from a comparison
with other nearby regions.
c) Imagine trying to give a name to each star in the upper right part of
print 1099.
Web Site
http://www.stsci.edu/resources/
20
4 SPECTRA OF GASES AND SOLIDS
4
Spectra of Gases and Solids
OBJECTIVE
Our objective is to observe three kinds of spectra, including continuous spectra of opaque filaments, the emission lines of transparent gases, and the solar
absorption spectrum. Then we will photograph the spectrum of a gas and
identify the lines of Hydrogen and measure the wavelength of the lines.
INTRODUCTION
Wave Nature of Light
In many respects light exhibits a wave-like behaviour. Light has an electric component which undulates up and down, and a magnetic component
that oscillates side to side. The distance from one wave crest to the next
wave crest is the wave length usually denoted by λ. If you stand in one place
and count the wave crests as they go by, the number you count in one second
is called the frequency and is denoted by “f” or sometimes ν. See Figure 1.
The velocity c of a light wave is the distance it travels in one second. That
distance will equal the number of waves passing a point in one second “f”
times the length of each wave (λ). Therefore we have a fundamental relation
between these three quantities:
c = λf
(1)
λ
c
Wavelength
Velocity
Figure 1. Light Waves
Wavelengths of light waves are often measured in nanometres (1 nm =
10 m) or Angstroms (1 Å= 10−10 m). The wavelength of a light wave
−9
21
4 SPECTRA OF GASES AND SOLIDS
determines its colour. Red light has a wavelength of around 6500 Å; green
light has a wavelength of 5000 Å; and blue light has a wavelength of 4500 Å.
The human eye responds to the wavelength range of around 4000 Å−7000 Å.
Sometimes when it rains you can see a rainbow. The rainbow is formed
from sunlight coming over your shoulder and going into the rain drops in
front of you. Inside the rain drops the light is broken up into its component
colours, red, orange, yellow, green, blue, and violet. The relative brightness
of the red to the blue and the yellow to the blue is always the same for
rainbows on the earth.
A prism can also form a rainbow, but in this case we call it a spectrum.
If we have more than one spectrum then we call them spectra. A spectrum
of the sun will have all the colours of the rainbow and in the same relative
brightness.
A transmission grating is a piece of transparent glass or plastic ruled with
many finely spaced lines. A grating will break up light into a spectrum just
like a prism only it will form many little spectra. Some light will go straight
through the grating, this is the zero order image. See figure 2. The spectrum
formed beside the zero order image is the first order image, and the next is
the second order image, et cetera.
Second Order
First Order
Zero Order
First Order
Light Bulb
Second Order
Grating
Spectra
Figure 2. Spectral Orders
EQUIPMENT
We will use a diffraction grating, which is ruled with very fine lines spaced
about 600 lines per millimetre.
An ordinary light bulb contains a very thin wire or filament made from
solid tungsten. An electric current is forced through the filament making it
hot, about 2800 K (=2527 ◦ C). The hotter the solid filament, the brighter it
4 SPECTRA OF GASES AND SOLIDS
22
is and the more white its colour. This is an example of Wein’s Law and the
Stefan-Boltzmann Law.
To make light from various gases we will use gas discharge tubes. These
are glass tubes filled with Helium, Hydrogen, Neon, Mercury, and Argon. A
high voltage power supply is used to pass an electric current through the
gas making it glow. The internal structure of the atoms of the gas make the
colour of the light different for each of the different elements. The spectrum
of each of the elements is composed of discrete lines of colour. The intensity
and position or wavelength of the lines serve as a fingerprint to identify each
element.
PROCEDURE
Observe
• Hold the glass grating close to your eye. Look a little to the left or
the right of the light source to see the spectrum, which will look like a
rainbow.
• Look at the light bulb which is powered through the dimmer switch. As
we turn the power to the light bulb up and down, it is the temperature
of the filament of the bulb which changes. Is the brightness of the bulb
the same with the high and low temperature? Is the bulb’s colour the
same? Is the spectrum the same with the high and low temperature?
Sketch the spectrum at both high and low temperatures. How does
this apply to stars?
• Observe the gas discharge tubes. These are tubes of glass where the
air has been pumped out and a sample of an element has been put
in the tube before it is sealed. A high voltage current is run through
the tube to excite the gas and the gas in turn emits light. Turn the
box to Neon and look at the first order image. Do you see a lot of
red and yellow lines? Make a sketch of the spectra that you see from
the gases in the gas discharge tube box (Argon is probably too faint).
Colour the lines and comment on the similarity of the different spectra.
What is the unknown? Explain two observations about the unknown’s
spectra, which lead you to this belief. Check your sketches with your
neighbour’s. Does everyone agree? Explain.
4 SPECTRA OF GASES AND SOLIDS
23
• We can also observe the spectrum of the nearest star, our sun. One
of the windows is covered with a board with a slit cut in it. If you
stand across the room from that board and look at the spectrum of
the slit you will see a continuous spectrum similar to the light bulb.
If you look closely in the yellow part of the spectrum you will see a
dark line crossing the spectrum. This line is an absorption line due to
the element sodium in the sun’s atmosphere. What does this tell you
about the sun? Can you see other absorption lines? Sketch the sun’s
spectrum identifying as many lines as you can.
Photograph Helium and Hydrogen Spectra
To make a record of your observations of the spectra of the gases we can
replace your eye with a web camera. To start the web cam program, click
on [3Com HomeConnect] in the Start menu. Click on [Video Gear] and then
[HomeConnect ViViewer]. A window will pop up and the camera will begin
taking pictures. We probably need more control over the camera so click on
[Controls], [Camera control], and [More] so a camera control window pops
up. Set the “Auto Brightness Mode” to “AGC Avg Mode” for good results.
You may be able to improve the picture by trying the other options.
Set the gas discharge tube box to Helium. Set up the camera so it is
about one meter from the gas discharge box. Focus the camera on the box.
Put the grating in front of the lens of the camera so it will make a spectrum
to the left and the right of the gas discharge tube. Aim the camera to the
right of the gas discharge tube by about 15 degrees, so that the zero order
image and the first order image will both be near the centre of the picture.
Tilt the camera until the spectrum lines are not tilted and the spectrum runs
left to right. Click on [Still Image] and the image will freeze. Save the image.
Without disturbing anything, switch the gas discharge tube box to the
Hydrogen gas tube and take another picture. Save the picture.
Measure
The lines of Helium are shown in figure 3 and included is a table of
wavelengths of each of the lines. Notice that the red lines have the long
wavelengths (6678 Å) and the violet lines have short wavelengths (3889 Å).
We want to measure the distance from the zero order image to each of the
known lines in the Helium spectrum. Open the Helium picture. Click on
the middle of the zero order image and drag the cursor to the middle of the
4 SPECTRA OF GASES AND SOLIDS
24
Helium line. A box will form on the picture and the size of the box will be
displayed in the bottom left corner of the window. These “x” values are in
pixels. Record these measurements “x” in a table in your lab book along
with the known wavelengths.
Reload the Hydrogen picture. Measure the distance from the zero order
line to each Hydrogen line. The Hydrogen lines are known by the Greek
letters alpha (α), beta (β) and gamma (γ).
Plotting the Graph
Plot the wavelengths of the Helium lines against the “x” measurements
of the Helium lines. Draw the best fitting straight line through the Helium
measurements. This shows that there is a good relationship between the
wavelengths of the lines and the position or “x” values of the lines. We can
use this calibration line to find the wavelength of the Hydrogen lines for the
“x” values for the Hydrogen lines.
On your graph to find the “x” value for the Hydrogen Alpha line, go up
to the calibration line and then across to the wavelength axis to find the
wavelength of the line. Repeat this for the other Hydrogen lines.
To find the uncertainty in our measurements of the wavelengths of the
Hydrogen lines, we must first estimate how precisely we found the centres
of the Hydrogen emission lines. Remeasure a Hydrogen line and find a box
that is believable but not identical to the one you found before. Is it a pixel
or two different? To what wavelength would it correspond? The accepted
wavelengths of the Hydrogen lines are 6563 Å for α, 4861 Å for β, and
4340 Å for γ.
25
4 SPECTRA OF GASES AND SOLIDS
Table 1: TABLE OF HELIUM WAVELENGTHS
Line Number
1
2
3
4
5
6
7
“x” Wavelength
6678
5875
5016
4922
4713
4471
3889
Description
Faint red
Bright yellowish/green
Bright green
Faint Green
Faint green
Bright blue-violet
Faint deep violet
Table 2: TABLE OF HYDROGEN WAVELENGTHS
Line Number
α
β
γ
“x”
Wavelength
Violet
Green
#7
3000
Description
Bright red
Blue
faint blue
4000
#6
5
4 3
Red
#2
5000
6000
Helium Wavelength in Angstroms
Figure 3. Helium Lamp Spectrum (scale only approximate)
#1
7000
5 COLOUR-MAGNITUDE DIAGRAMS
5
26
Colour-Magnitude Diagrams
OBJECTIVE
To find the distance to and age of both open and globular clusters of stars,
using colour-magnitude diagrams.
INTRODUCTION
Stars form from the dust and gas clouds we see silhouetted against the background stars and nebulosity. When one of these clouds collapses, it will form
stars in groups or clusters. Therefore the stars in the cluster will all be the
same age, same composition and at the same distance from the Earth. Generally a cluster of stars contains a few bright ones and lots of faint ones. If we
examine the light from the stars carefully we find they are different colours.
The bright ones are generally blue and the faint ones are generally red. Traditionally we measure the brightness through a yellow filter which we denote
“V” for visual light and then through the blue or “B” filter. We find the
colour by taking the difference of the B and V magnitudes denoted “(B−V)”.
We then plot the brightness “V” against the color “(B-V)” to make variation
of the Hertzsprung-Russell Diagram called the Color-Magnitude Diagram.
To finish the lab on time.
Your instructor will log you into the a120 computers, but the operating
system is NOT MS-WINDOWS. It is LINUX-XWINDOWS and so many of
the icons and commands, you may be used to, are either nonexistent or will
not work the same. Please do not try random commands. They will mostly
have no effect, but may lock the terminal and then YOU will have difficulty
finishing the lab in a reasonable length of time.
MORPHOLOGY
The program “isochrone” written by James Clem, who was one of our graduate students at the time. It plots the Colour Magnitude Diagram for each
cluster on the computer screen. Plotted on the y-axis is the brightness V
of each star and the x-axis is the colour of each star (B−V). An example
5 COLOUR-MAGNITUDE DIAGRAMS
27
is shown in figure 1. You can see a “Main Sequence” of stars from top left
(bright blue) to bottom right (faint red). This is where most of the stars are
found.
Figure 1. The Morphology of Colour-Magnitude Diagrams
When the cluster stars have burned enough hydrogen in their core, their
internal structure changes and as a consequence their brightness and colour
change and they will move brighter and redder in the Colour-Magnitude
Diagram. The highest mass stars ( 10 Solar Masses) become Supergiants,
then the average sized stars become Red Giants and are found on the Giant
Branch. The most massive stars are the hottest in their core so they burn
their Hydrogen in millions of years and become Supergiants. The less massive
stars, like the sun, burn their Hydrogen in billions of years and become Red
Giant stars latter. Since all the stars in a cluster were formed at the same
time all the high mass/blue stars will move off the Main Sequence first and
the lower mass/redder stars will move off later. Therefore we can tell how
long it has been since the cluster formed by how massive/blue the last few
stars are that are still on the Main Sequence. The bluest stars still on the
Main Sequence are at the “Turn-off Point”. Occasionally in very populous
5 COLOUR-MAGNITUDE DIAGRAMS
28
clusters a few stars are a bit bluer and brighter than the Turn-off point so
they are called “Blue Stragglers”. These stars should have evolved off the
Main-Sequence to be come Red Giants, but for some reason(s) they have not.
The “Horizontal Branch” is where we find stars which are burning Helium in
their core. We can tell they are not foreground or background stars, which
we call “Field Stars” because field stars are found randomly sprinkled across
the diagram.
Click on “New Cluster” and examine each cluster in turn. Which of
the clusters has a “Main-Sequence”, a “Red Giant Branch”, a “Horizontal
Branch”, “Field Stars”, “Blue Stragglers”?
THE SUN
Let’s find where the sun would be if it was on this plot. The sun has a
(B−V) colour of 0.62 and would lie on the Main Sequence of stars. Put the
cursor on the Colour Magnitude Diagram at a (B−V) of 0.62 and on the
Main Sequence and click the left button. The V and (B−V) of the clicked
point are given on the screen. Load each of the clusters and record what the
apparent magnitude V of the sun would be if the sun were in the cluster.
Would the sun be visible to the unaided eye, assuming the limit for your eye
is V=6?
The absolute magnitude (brightness at 10 parsecs) of the sun is about
V=5. Are any of your clusters closer than 10 parsecs?
ISOCHRONE FITTING
The hot bright stars have a larger mass than the small faint red stars. We can
calculate the temperature and pressure of the interior of a star and estimate
the rate at which it is burning Hydrogen into Helium. When it has burnt a
certain fraction of its Hydrogen then it swells and becomes a Red Giant star.
The larger the star’s mass the higher its core temperature and the quicker it
burns its Hydrogen and the sooner it becomes a Red Giant. Some people at
the University of Victoria are world experts in calculating how long it takes
a star to burn its Hydrogen etc. They calculate the brightness V and colour
(B−V) for a number of stars of various masses for a certain age and plot a
line connecting them called an isochrone. Iso means same and chron means
5 COLOUR-MAGNITUDE DIAGRAMS
29
time. Since all the stars in the cluster were formed at the same time, we can
determine the age of the cluster using the isochrones.
Figure 1. The fitting window
Click on the “Older” button a few times to get an isochrone (red line) for
stars of a different age. The age is given in “Gyr”, which means Gigayears,
which means billions of years. The isochrone is called the Zero Age Main
Sequence (ZAMS) if the stars on it have just formed and not had enough
time to evolve significantly. Remember that small, low mass, faint red stars
evolve slowly so the isochrone should fit them better than the bright hot blue
stars.
Even ignoring evolution the isochrone line will not fit your cluster points
because it is set for the wrong distance. Move the isochrone up=closer and
down=further by clicking on the “Closer” and “Further” buttons. This
changes the distance modulous (m-M) which is the difference between the
apparent m and absolute M magnitudes of the stars.
5 COLOUR-MAGNITUDE DIAGRAMS
30
Just like the dust in our atmosphere makes the sun look red at sunset,
there is a little dust in space which will make the stars seem redder. The
farther the light travels through space the redder it becomes. The amount
the stars seem to be reddened by the dust is called the “E(B−V)”. The
isochrone will move left and right when you click on “Less Dust” and “More
Dust”.
The fourth parameter is the amount of heavy elements in the star [Fe/H].
The first stars formed were made of only hydrogen and helium, but stars
born later were formed from dust enriched in elements other than hydrogen
and helium by supernovae. Because the stars in each cluster were all formed
from the same dust cloud they will all have the same [Fe/H] We have set this
parameter to the currently accepted value for each cluster.
There is some interdependency between these three variables so you will
need to do some experimenting to get the range of values which will fit the
data. For instance, if you change the age of the cluster you may be able to
get nearly as good a fit by changing the distance and reddening. You will
need to spend some time varying the parameters to make a good estimate of
the uncertainty in each of these parameters.
Make sure you explain in your write up how the Age, Distance and Dust
buttons move the isochrone.
DISTANCE
The distance D to the cluster can be found from the distance modulus (m −
M ) and the formula
(m−M +5)
D = 10 5
parsecs
Find the distance to each cluster. From your estimate of the uncertainty
in the distance modulus estimate the uncertainty in the distance.
Questions
1. Are any of the clusters older than the earth (4.5 billion years), or the
universe (13.7 billion years)? Comment.
2. What will be the age of the sun when it reaches the turn-off point?
What will happen to the Earth?
5 COLOUR-MAGNITUDE DIAGRAMS
31
3. Two of the clusters - M15 and NGC 104 - are globular clusters (Population II) and look very different from the open clusters (Population
I). Compare their distance, age, and [Fe/H] to the open clusters. Why
is the [Fe/H] different for the two kinds of clusters?
Web Sites
http://antwrp.gsfc.nasa.gov/apod/ap010223.html
6 HOW BIG IS OUR GALAXY?
6
32
How Big is Our Galaxy?
OBJECTIVES
First: using variable stars in the globular cluster M15, determine its distance. Second: find the size of a dozen other globular clusters. Third: find
the weighted mean distance to the centre of our galaxy. Fourth: using the
distance to the centre of the galaxy and Kepler’s Law estimate the mass of
the galaxy.
PART ONE
Globular clusters are spherical, compact stellar systems containing between
tens of thousands and millions of stars. Of the more than one hundred
globular clusters known in the Milky Way, many appear very small (far
away) and cannot be resolved into individual stars.
Figure 1. The globular cluster M15
In 1895 Bailey, working at Harvard College Observatory, noticed that
three nearby globular clusters contained variable stars. The shape of their
light curves identified them as pulsating variables, which was interesting,
since it related stars in these unusual objects to stars in the solar neighbourhood.
33
6 HOW BIG IS OUR GALAXY?
Figure 2. Example light curve of an RR Lyrae star discovered at UVic
The RR Lyrae variable stars all have a period of about half a day and
an amplitude of about 0.5 magnitudes. Their light curves usually have the
sawtooth shape shown in figure 2, but sometimes the variations will be more
sinusoidal.
-4
Classical
-3
Cepheids
Absolute
-2
Magnitude
Type II
-1
Cepheids
RR Lyrae
0
.3
1
3
10
30
Period in Days
Figure 3. Period Luminosity Relation for RR Lyrae and Cepheid Variables
What makes the RR Lyrae stars very interesting is that within a particular globular cluster all these stars seem to have the same apparent magnitude.
This means that all RR Lyrae stars are the same absolute magnitude. After
a great deal of effort, which is still continuing, the absolute magnitude of
the RR Lyrae and their bigger cousins the Cepheid variable stars have been
measured. It is a bit more complicated for the Cepheids, since their intrinsic
6 HOW BIG IS OUR GALAXY?
34
brightness depends on the period of the brightness variation as plotted in
figure 3.
Procedure
Eight photographs of the globular cluster M15 are provided; all taken on
a single night. Six RR Lyrae variables in the cluster are identified by letters,
and on most of the photographs apparent magnitudes of some non-variable
stars are indicated by numbers with the decimal points omitted (i.e. 153
means apparent magnitude 15.3 . The decimal point could be confused with
a stellar image.) By comparison to these non-variable stars the magnitudes
of the variables are to be estimated on each plate.
The best accuracy is obtained if the comparison stars used are close to the
variable, rather than on the other side of the photo, since the emulsion may
vary in sensitivity across the plate. Because of different exposure conditions,
as well as emulsion differences, it is never possible to use comparison stars on
a photograph different from the one on which the variable is recorded. On
some plates a variable may be invisible. In that case it is useful to indicate
the faintest star in the vicinity of the variable which is recorded, since it
then can be said that the variable was fainter than that magnitude. This
information may help in drawing a light curve.
Plot a light curve for each star: apparent magnitude (bright at the top)
versus the times in fractions of a day as given on the last page of the handout.
Now we want to estimate the mean magnitude of each star’s light curve. If
a star goes through a complete cycle, the mean magnitude may be determined
as the average between extreme values read from the graph. Note: Even
though you may not have an observation exactly at, say, maximum light you
can estimate the reading from your sketched-in light curve. Are the mean
magnitudes similar? If not, check with your instructor.
Using the accepted absolute magnitude of RR Lyrae stars (M=0.7 for this
filter), find the distance D to each of these variable stars using the distance
modulus formula.
(m−M +5)
D = 10 5
parsecs
Find the average distance to the stars and thus the distance to the cluster.
Estimate the uncertainty in the distance by finding reasonable upper and
lower bounds?
35
6 HOW BIG IS OUR GALAXY?
Winter Sky
70
70
Cas
60
UMa
50
60
50
Capella
40
Aur
And
Algol
Per
40
30
20
Can
Leo
10
Tau
Gem
Regulus
20
Ari
Aldebaran
Betelgeuse
Procyon
0
−10
Sirius
−20
10
Psc
Ori
0
−10
Rigel
−20
CMa
−30
−30
−40
−40
−50
12
11
10
9
8
Declination
Declination
30
7
6
5
Right Ascension
4
3
2
1
0
−50
Summer Sky
70
70
60
60
UMa
40
Declination
Cyg
Peg
Alberio
Boo
20
10
Altair
Psc
0
Vir
Aqr
−10
−10
Spica
Lib
−20
−20
Cap
−30
−30
Sco
Sgr
−40
−50
30
Her
Arcturus
10
0
40
Vega
30
20
50
Deneb
24
23
22
21
20
19
18
17
Right Ascension
Declination
50
−40
16
15
14
13
12
−50
Figure 4. Winter skies above and summer skies below with globular clusters
marked as *’s.
6 HOW BIG IS OUR GALAXY?
36
PART TWO
The System of the Globular Clusters
In the years 1916-1917, Harlow Shapley had been taking photographs
of globular clusters at Mt. Wilson with the 60” reflector. He noticed the
marked concentration of these clusters toward the region of the sky near the
constellation Sagittarius (Sgr). Can you see a concentration of the globular
clusters plotted in figure 4?
Because of the calibration of the Cepheid period-luminosity relation,
Shapley was now in a good position to estimate the distances to those clusters
in which he could detect Cepheids and measure their periods. This he did
for the brighter clusters. In the fainter clusters the Cepheids are below the
threshold of detection. But these faint clusters also appeared smaller, thus
supporting the hunch that they were of similar construction to the brighter
ones but simply at greater distances. The assumption of similar essence could
be used to convert the brightness and size data into distance data.
Finally, Shapley accumulated sufficient data to construct a picture of the
distribution of the globular clusters with respect to the Milky Way band.
The model comprised a more or less spherical distribution of clusters centred
far off in the direction of Sagittarius, at a distance estimated by Shapley to
be about 16 kpc. The fact that most clusters appear to be in one region of
the sky demonstrates that we are outside most of the spherical distribution.
This was a real revolution in conception of the size of our stellar system.
Supposing the clusters to be symmetrically situated with respect to the Milky
Way stars, we would be in a flat, circular system at least thousands of parsecs
in diameter.
The Distance to the Centre of the Globular Cluster System
In this exercise we shall carry out a computation of the distance to the
centre of the globular cluster system very similar to that done by Shapley.
Instead of the 86 clusters Shapley used, we shall use only about a dozen,
but that is enough to give a reasonable estimate of the distance. Since, in
Shapley’s words, “it appears to be a tenable hypothesis that the supersystem
of globular clusters is coextensive with the Galaxy itself,” by finding the
distance to the centre of the cluster system, we shall also find the distance
to the centre of the galaxy.
We shall choose a section of sky near to the direction of the apparent
6 HOW BIG IS OUR GALAXY?
37
centre of the globular cluster system in Sagittarius. In this area of about
15◦ × 15◦ (centred on right ascension 19h 00m and declination −30◦ ) there are
a dozen globular clusters. We shall find the distance to each one, and then
find the distance to the centre of the group by averaging them. In doing so
we must make several assumptions:
a) The angular size of a cluster is inversely proportional to its distance.
This is tantamount to presuming that all clusters are of more or less the same
intrinsic size.
b) We see in this limited region a representative selection of globular
clusters, both near and far.
Procedure
We want to measure the apparent diameter of each globular cluster on the
photo of (19h 00m , −30◦ ). We have downloaded pictures of each of the clusters
and we can view them with the skycat program using the lab computers.
Click on [File] [Open] and then double click on each cluster. Choose a suitable
criterion for measuring size, such as the diameter of the brightest part of the
image. Use the same criterion when measuring all the clusters. Right click
and drag the cursor across the cluster from side to side or top to bottom.
The numbers displayed are distance across the cluster in arc minutes and
seconds. Convert the minutes to seconds by multiplying the minutes by 60.
Go back and measure M15 a second time and make certain you get the
same answer. If you do not get nearly the same measurement you may want
to continue measuring the globular clusters until you are consistent.
PART THREE
Volume Correction
When we take a photograph of a section of sky, the volume of space
recorded on the picture increases very rapidly with distance (see figure 5).
The first kiloparsec of distance from us a narrow wedge of space (volume A)
is photographed. At a great distance away, however, an extra kiloparsec of
distance includes a much larger slice of space (volume B).
Clearly we should expect to see more clusters in volume B than in volume
A just because of its greater size. That means we shall see an anomalously
great number of distant clusters and an anomalously small number of nearby
clusters.
38
6 HOW BIG IS OUR GALAXY?
We must account for this effect before averaging cluster distances, or else
the preponderance of distant clusters will yield a lopsided result. The area of
the beam covered by the photograph increases as the square of the distance,
and this is the correction factor needed.
Volume B
Volume A
Earth
Figure 5. Globular Cluster Distribution about the Galaxy. The wedge
represents the region of clusters seen on one photographic plate.
Procedure
A computer program has been written to solve the weighted mean equation, correcting for the increasing volume observed. Enter your measurements
to find the distance to the centre of the galaxy. The computer can be used
to estimate the uncertainty in this distance by modifying your measurements
and running the program again.
39
6 HOW BIG IS OUR GALAXY?
PART FOUR
1. To try and get feel for how far it is to the centre of our galaxy, calculate
how long it takes for light to get to the sun from the centre of the galaxy.
There are 3.26 light years in one parsec.
2. The sun orbits the centre of the galaxy just like the earth orbits the
sun. Now that we have found the distance to the centre of the galaxy
we know the radius of the orbit. Calculate the distance the Sun travels
around the centre of the galaxy. (the circumference= 2πr).
3. From observations of other galaxies we measure that the sun travels
around the centre of the galaxy at a speed of ∼ 220 km
= 0.00021 parsec
.
sec
year
How long does it take the sun to orbit the centre of the galaxy?
4. Kepler’s Third Law relates the period P and the distance A separating
two orbiting bodies to the sum of the masses of the bodies. Since we
have the sun orbiting the centre of the galaxy, find the mass of the
galaxy. If we use years for the period and parsecs for the radius of the
orbit, the mass will be:
M ass in Solar M asses = 8.8 × 1015 ×
A3
P eriod2
(2)
5. Assuming each star has a mass the same as the sun (one solar mass),
how many stars are in our galaxy?
If you are looking for life in our galaxy, and you spend 1 second looking
at each star, how many years would it take to check out our galaxy? 1
year = 3 × 107 seconds
An interesting URL concerning the great debate is:
http://antwrp.gsfc.nasa.gov/diamond jubilee/debate.html
7 WHAT IS THE AGE AND SIZE OF THE UNIVERSE?
7
40
What is the Age and Size of the Universe?
“With the 200-inch,” Hubble said in a BBC broadcast in London,“ we may grasp what now we can scarcely brush with our
fingertips.” “What do you expect to find with the 200-inch?” he
was asked, and he replied, “We hope to find something we hadn’t
expected.”
OBJECTIVE
To determine the size and age of the observable universe, by measuring the
distance and recession velocity of some galaxies.
INTRODUCTION
The lab uses one of the “Contemporary Laboratory Experiences in Astronomy” developed by Larry Marshall’s group at the Department of Physics, at
Gettysburg College. This exercise simulates the operation of a telescope and
an electronic spectrometer which adds up (or integrates) the light it receives
from faint objects until a measurable signal has been recorded. We will use
the spectrometer to record the spectra of the brightest galaxies in a number
of clusters of galaxies. Using two prominent spectral lines in the galaxy’s
spectrum, we will calculate the amount each spectrum has been redshifted,
and from this calculate the recession velocity of the galaxy.
Brightest cluster galaxies have been chosen because they can be assumed
to all have approximately the same absolute magnitude, M=−22.0. We shall
use this information and the apparent magnitude of each galaxy to determine
the distance to each galaxy. A plot of Recession Speed vs. the Distance will
give us the value of the Hubble constant.
Making Observations
Begin by selecting Log In on the main menu, and fill in the requested information. After completing the log-in, select Start from the main menu.
A control panel window will appear as in Figure 1. The telescope controls
and readouts are positioned to the left, the spectrometer control is on the
right, and the sky field will be displayed in the centre.
7 WHAT IS THE AGE AND SIZE OF THE UNIVERSE?
41
Figure 1. Control Panel
At the beginning of the exercise, the telescope dome is closed and the sky
cannot be seen. Click on the button labelled Dome to open the telescope
dome slit. You will be able to see stars and galaxies through the open door.
Before observations can made, you must start the telescope tracking motor
by clicking on the Tracking button.
The Slew Rate button adjusts how fast you can move the telescope. The
four buttons below it indicate the directions to move the telescope. Use these
buttons to put one of the galaxies in the telescope cross-hairs.
Once a galaxy is within the cross hairs, you must switch on the Monitor of
the Spectrometer. Click on the Monitor button to get a magnified view of the
telescope’s field of view, and a pair of red lines, simulating the spectrometer
“slit” will appear in the new view. The “slit” is a small hole which lets light
from the galaxy into the spectrograph. The “slit” is surrounded by a mirror
which reflects the light from the surrounding galaxies into the TV monitor.
Use the four slewing buttons to position the centre of the galaxy on the slit.
Click on the Take Reading button.
7 WHAT IS THE AGE AND SIZE OF THE UNIVERSE?
42
Figure 2. Spectrometer Control Window
The Reticon Spectrometer window will appear as in Figure 2. Click on
Start Resume on the menu bar. If the galaxy has been correctly centred
on the slit, you will see the counts build up and a spectrum will begin to
appear on the Relative Intensity vs. Wavelength plot of the spectrometer.
You will notice that for the brighter galaxies the spectrum builds up quite
quickly, and two absorption lines, the K and H lines of ionized calcium, are
apparent very soon after the integration begins. The spectra of the fainter
galaxies build up more slowly and the spectral lines cannot be distinguished
from noise for some time.
You may select Stop/Count from the menu at any time. This causes the
integration to pause and the spectrum which has been collected up to this
point to be displayed. Click on Start/Resume to continue the integration.
You should integrate each spectrum until the Signal/Noise ratio is at least
15.0, click on Stop/Count and measure the spectrum. If the left mouse
button is pressed when the cursor is on the graph, the cursor will change to
cross-hairs. While still pressing the left mouse button, carefully position the
cross-hairs at the centre of the K line, and record the wavelength of the line
position shown on the screen. Repeat for the H line. Record the Signal/Noise
value.
When you have finished measuring a galaxy spectrum, select Return from
the tool bar menu. You can then continue to another galaxy. Be sure you
have recorded all the information you require before returning from the spectrometer window - the information is not saved by the program
7 WHAT IS THE AGE AND SIZE OF THE UNIVERSE?
Galaxy
ID
43
Table 3: Hubble Redshift Distance Relation
Apparent Distance
λ’ in Å
Recession Speed
Mag
(Mpc)
K Line H Line K Line H Line
Measure two or three galaxies from each cluster of galaxies. To move to a
different cluster of galaxies, you first need to return to the telescope monitor
by clicking on it. Then select Change Field from the toolbar menu, select
a new cluster and click on OK.The telescope will move to that field and
you can select the galaxies to measure as above. Continue until you have
completed five clusters of galaxies.
When you have finished your observing, turn off the tracking, close the
dome, and quit the program.
Analysis
Using the following steps complete table 3.
1. If the galaxies were not receding, the K and H lines would be at their
rest wavelengths, λ. The rest wavelength for the K line is 3934 Å and
for the H line it is 3968 Å. Calculate the wavelength difference for each
of the K and H lines for each galaxy, ∆λ = λ0 − λ, where λ0 is the
redshifted wavelength you measured.
Find the Recession Speed v by multiplying the change in wavelength
∆λ for each galaxy by the speed of light, c = 300,000km/sec and
then dividing by the rest wavelength for the line λ.
v=c
∆λ
λ
(3)
7 WHAT IS THE AGE AND SIZE OF THE UNIVERSE?
44
2. Determine the distance, D to each galaxy using its recorded apparent magnitude, m and the assumed absolute magnitude, M=−22.0 We
want the distance to be in Megaparsecs so we modify the usual distance
modulus formula to be:
D = 10
m−M −25
5
(4)
If you are not certain how to use this equation be sure to ask.
3. Plot the Recession Speed=V (km/sec) vs. Distance=D (Mpc) for each
of the galaxies on graph paper in your lab book. Draw a best-fit straight
line through the points including the origin and determine the slope of
this line. The slope is the Hubble Constant=H. If there is time try to
find the uncertainty in the slope by fitting another line which is as flat
as is reasonable, but still goes through the points. Find the slope of this
second line and compare it to the best line. The equation describing
this is :
V = HD
(5)
There is still a great debate over the “real” value of the Hubble Constant. Generally astronomers are finding near 70 km/sec/Mpc, but
values from 40 to 100 km/sec/Mpc have also been reported. More
recently the WMAP satellite (see website below) has confirmed that
H=71 km/sec/Mpc
4. As the galaxies become more distant, the observed speeds of the galaxies can not increase without bound. As the speeds increase towards the
speed of light, the redshift increases to the point where the galaxies are
no longer visible. Nothing can be seen past this horizon. Neglecting
some subtleties we can estimate this distance to the edge of the observable universe by asking at what distance will the velocity of a galaxy
be equal to the speed of light. Convert this distance to billions of light
years, knowing there is 3.26 light years in a parsec.
5. Since we know how far it is to one of these galaxies, and we know
how fast the galaxy is going, we can estimate where it was last year,
7 WHAT IS THE AGE AND SIZE OF THE UNIVERSE?
45
a thousand years ago or a billion years ago. In fact by dividing the
distance to a galaxy by the speed with which it is moving, we can find
how long it took to get there.
T ime =
Distance
.
V elocity
(6)
If we rearrange the Hubble Constant equation V = HD to be D
= H1
V
and change the km to Mpc and the seconds into billions of years to get
more convenient units we find that the age of the universe in billions
of years is:
T =
D
1000
=
.
V
H
(7)
Divide 1000 by your Hubble constant to get the number of Billions of
Years since the galaxies started moving apart due to the Big Bang.
Compare it to the age of the earth (4.5 Billion Years) and the oldest
stars (13 Billion Years). What is your estimate of the uncertainty in
the age of the universe?
Web Sites
http://map.gsfc.nasa.gov/ (WMAP website)
8 SEARCH FOR EXTRATERRESTRIAL INTELLIGENCE
8
46
Search for Extraterrestrial Intelligence
OBJECTIVE
An important part of science is to look for phenomena which are expected,
but have not yet been observed. Here we can use a very simple theory, a little
astronomical knowledge and a few reasonable(?) assumptions to estimate the
chances we will find evidence of extraterrestrial intelligent beings.
Drake Equation
The first person to set out the parameters used to estimate the number
of civilizations in a galaxy was Frank Drake, when he was preparing for a
conference on SETI in 1961. Obviously the number of civilizations Nc will
depend on the number of stars in the galaxy N∗ ; the more stars, the more
places for aliens to live. It also depends on the fraction of stars that have
planets fp , since the aliens probably do not live right on the stars. The
planets have to be warm; not too hot or too cold like the Earth ne . Life
must evolve on the planet fL and it must then produce intelligent beings fi ,
who broadcast their presence in some manner we can detect. Lastly, for us
to know about the alien civilization, they must last long enough to exist at
the same time as us FS .
Our version of the Drake equation is:
N c = N ∗ f p ne f L f i F S
Let’s estimate Nc by examining each of these parameters in more detail.
N∗ = Number of Stars in Our Galaxy
We found the number of stars in our galaxy in the “Size of the Galaxy” lab
from the mass of the galaxy. Look back in your lab book and see what number
you measured. Check with your partners and see if they found approximately
the same number. This number of stars in the galaxy is too large because it
includes dust and gas which has not formed into stars. It also includes the
“Dark Matter” and no one knows what that is.
A second way of estimating the number of stars is by counting the number
in a small area of the sky and scaling it to the whole sky. More than half the
sky was photographed by the Palomar Sky Survey project and we have copies
8 SEARCH FOR EXTRATERRESTRIAL INTELLIGENCE
47
of one of these pictures for you to use. The scale of the pictures is one minute
of arc per millimetre. Count the stars you see in a square a millimetre on a
side and multiply it by 150 million to get another estimate of the number of
stars in our galaxy. This number is probably too small since lots of stars will
be too faint and lots more will be obscured by dust.
From these two methods estimate the number of stars in our
galaxy, N∗ = 2.
Discovering Planets
The first extrasolar planet discovered was in 1995, when Mayor et al. announced the discovery of a planet orbiting the star 51 Peg. Mayor very
precisely measured the spectra of 51 Peg and found that the star moved
towards us and then away from us. He found that its movement was very
predictable and varied in a sinusoidal shape with a period of 4.2293 days.
The fact that the period was constant and the shape of the variations was
a sine curve led him to conclude that something was orbiting 51 Peg. The
amplitude of the star’s motion gave him an estimate of the mass of the orbiting body, which was so small that he concluded that the orbiting body
was a planet.
Characterization of Extrasolar Planets
A spectrum of the star HD209458 shows that it is slightly bigger in radius and
slightly more massive than our sun. The Hipparcos satellite has measured
its parallax and found the distance to HD209458 to be 47 parsecs. Geoff
Marcy discovered a planet orbiting HD209458 with an orbit which is tilted
just right for the planet to pass in front of the star. When the planet blocks
part of the light from the star we see the star become a bit fainter.
A modeling program has been written by J. Clem to help us visualize
the situation and find the mass and radius of the planet orbiting the star
HD209458. The modeling program allows us to simulate the planet orbiting
the star, the eclipse of the star by the planet, and also the variations in the
radial velocity of the star. We can change the planet’s mass, period, radius
and the orbital inclination by clicking on the buttons in the button panel
seen in Figure 1.
8 SEARCH FOR EXTRATERRESTRIAL INTELLIGENCE
48
Figure 1. The modeling program.
The second panel shows the blue planet orbiting the red star. The ellipse
is the path of the planet around the star. Click on the [Orbital Inclination]
button to change how much the orbit is inclined to the line of sight. If the
inclination is just right, the planet will pass in front of the star and block
out part of the star’s light making the star appear fainter.
The third panel shows a plot of how the brightness of HD209458 changes
as a function of time. Every 3.525 days the star becomes very slightly fainter.
We watched the dimming of HD209458 one summer with our 20 inch telescope and our observations are the points plotted in the third panel. The
depth of the eclipse depends on the size of the planet; the bigger the planet,
the more light it blocks and the deeper the eclipse. We can find the radius of
the planet from the depth of the eclipse. Change the radius of the planet using the [Planet Radius] buttons so that the line agrees with the data. Change
the inclination of the orbit to get the observations of the edges of the eclipse
to agree with the model.
Record the radius of the planet and the inclination of the orbit.
8 SEARCH FOR EXTRATERRESTRIAL INTELLIGENCE
49
The bottom panel is a plot of the radial velocities of HD209458 as observed by Geoff Marcy with the world’s largest telescope. A sine curve has
been drawn through the data points, but it does not quite agree with them.
The more massive the planet the larger the reflex motion of the star and the
larger the amplitude of the radial velocities. So we can measure the mass
of the planet by measuring the amplitude of the radial velocity variations.
Change the amplitude of the radial velocity curve by clicking on the [Planet
Mass] button.
We can also change the position of the data points along the graph by
changing our guess of the period of the planet’s orbit around the star. Change
the period by clicking on the [Period] buttons and you will find that the
observed points move left or right a little bit. From Kepler’s Law we know
the semimajor axis of the orbit of the planet around the star depends on the
period of the orbit. Change the period and see that the Radius of the Orbit
changes as well. Change the planet mass and the period to best fit the data
points.
Record your best estimate of the mass, period, and semimajor
axis of the orbit of the planet.
Would you be able to detect a Jupiter mass planet in a one year orbit?
Click on the [Stop] animation box and then click on the Period value and
change it from 3.52 to 365 days. Click [Start] twice and the animation will
start again with the planet at about 1 Astronomical Unit from the star.
Increase the mass of the planet until it is at 1 Jupiter mass. Increase the
radius of the planet until it is at 1 Jupiter radius. Set the Inclination to 90
degrees so that eclipses must occur.
Would you be able to observe radial velocity variations (uncerm
tainty of ±4 sec
) or eclipses for a Jupiter sized planet in an Earth
like orbit?
Would it be possible to detect planets like the Earth? Set the Period in
the simulator to 365 days and the radius of the planet to 0.1 Jupiter and the
mass of the planet to 0.01 Jupiter Masses.
fp = Fraction of Stars with Planets
A few groups are now surveying the bright stars in the sky looking for stars
with the tell-tale small amplitude, periodic variations in their radial velocities. At the present time there are about 500 extra-solar planets that have
8 SEARCH FOR EXTRATERRESTRIAL INTELLIGENCE
50
been found after surveying about 4000 F, G, and K main sequence stars. The
latest results can be found at the last two web sites listed at the end the end
of this lab, or we can use the diagram:
Figure 2. Number of extrasolar planets as a function of their distance from
their star (Jean Schneider and Cyril Dedieu 2010).
Remember these surveys are only sensitive to planets of Jupiter’s mass
or greater and are more sensitive to planets that are orbiting close to their
stars, so there will be lots of planets like the Earth that will be missed.
What is your best guess as to the Fraction of Stars with Planets?
fp = 2
ne = Number of Habitable Planets in Each Solar System
The number of Earth-like planets is a difficult question. While it is possible
to imagine, alien life which does not need liquid water to exist, it is probably
more interesting to look for life which has more in common with us. In
order for life as we know it to exist there must be liquid water, therefore the
temperature of the planet must lie between 273 K=0 ◦ C and 373 K=100 ◦ C
for a pressure at sea level. One planet (Gliese 581c) has already been found
which is about 5 times the mass of the Earth and probably at the correct
distance for liquid water to be found on its surface.
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51
Figure 3. Limits to the habitable zone.
http://www.astro.sunysb.edu/fwalter/AST101/habzone.html
Let’s investigate how these temperature limits are found. A planet orbiting a star will intercept some light and become warm. The warm planet
must radiate this heat away or it will become hotter and hotter. Thus the
planet will need to radiate all the energy it receives to be in equilibrium.
Energy Absorbed = Energy Radiated
The “Energy Absorbed” will depend on the planet-star distance D and
the luminosity of the star L and the radius of the planet r. The “Energy
Radiated” by the planet will depend on the temperature T of the planet and
the radius of the planet r.
Lr 2
∝ r2T 4
D2
We can can see that the radius of the planet r will cancel and if we solve
for L we get:
L ∝ T 4 D2
For another planet orbiting the same star we have the same luminosity
of the star and a different distance D and temperature T .
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52
L ∝ TP4 DP2 = TE4 DE2
For a star with the same luminosity as the sun we can find the temperature
TP of any planet once we know the distance DP of the planet from the star,
assuming that the temperature TE of the Earth is 288 K(15 ◦ C) and its
distance DE is 1 AU.
TP4 DP2 = (288)4 (1.0)2
Square Root of both sides:
TP2 DP = 82944
What would be the temperature of the planet orbiting the star
HD209458, assuming the star has the same luminosity as the Sun
and that the planet is at the distance you found in the last section?
Find the distances a planet would need to be from a star like
the sun to have a surface temperature of 373 K and 273 K.
In our Solar System the Earth orbits in the habitable zone with an orbital radius of 1 Astronomical Unit. The orbital radius for Mercury is 0.387
AU, Venus is 0.723 AU, Mars is 1.524 and Jupiter is 5.203 AU. In the Ups
Andromedae system the planets are at distances of 0.06, 0.83 and 2.51 AU.
In the 55 Cancri system the planets are found at 0.04, 0.11, 0.24, 0.78 and
5.77 AU. In the HD160691 system the planets semimajor axes are 0.09, 0.92,
1.5 and 4.17 AU.
What is your estimate of ne , the number of habitable planets in
each solar system? ne = 2
fL = Fraction of Habitable Planets with Life
The fraction of planets which do have life given that they are in the habitable
zone is difficult to estimate since we have only our Solar System to use for
data. How long it took for life to form on the earth gives us some indication
of how likely it is for life to form given the right conditions. If it is easy for
life to start then generally it will form right away and if it is very difficult for
life to start then it will take a long time for life to form. It is about 4.5 Billion
years since the Earth first formed and during the first few million years the
8 SEARCH FOR EXTRATERRESTRIAL INTELLIGENCE
53
Earth was continually bombarded with asteroids which heated the surface to
incandescence. The Earth did not cool enough to allow liquid water on its
surface until about 4 Billion years ago. The oldest fossils of living organisms
are 3.9 Billion years old so life must have originated almost as soon as it was
possible.
Since it originated, life has spread to cover the surface of the earth and
even thrives far underground and deep in the ocean. There even exist life
forms which do not need light. They live near “black smokers” on the ocean
floor.
What is your best guess as to the fraction of habitable planets
on which life originates?fL = 2
fi = Fraction of Life Systems with Intelligence
Assuming that there is a habitable planet and life originates on it, we need
to guess whether or not intelligent life will evolve. Frank Drake originally defined intelligent life, as life which built radio telescopes, but this is debatable
definition. In the competition for food and habitat mankind has managed
to spread across the Earth, eliminating many of the animals inhabiting our
ecological niche or preying upon us. This is probably mostly due to our intelligence, but also due to our ability to pass our knowledge on to successive
generations. Humans have only existed for the last few million years so at
least for the Earth intelligence has taken a long time to evolve.
If you think intelligence has a large survival value guess 1.0 and
if you think intelligence is not likely to evolve guess something
closer to 0.0.fi = 2
FS = Lifetime fraction
Civilizations will ultimately have a great deal of difficulty lasting longer than
their home star. The sun will become warmer as it evolves and in a billion
years the Earth will not be habitable. Astronomical disasters like comet
impact, supernova or Gamma Ray Bursts will set limits of millions of years.
Historically the civilizations of the Egyptians, Greeks, Romans, Mayans,
Incas and Aztecs have all come and gone. Some lasted a few hundred years
and some lasted a few thousand. If civilizations last only a few years, there
will be fewer in the galaxy at any one time than if civilizations generally last
8 SEARCH FOR EXTRATERRESTRIAL INTELLIGENCE
54
a long time. Of course, if you are pessimistic, humankind could be wiped
out by nuclear war, plague, etc at any time.
Choose an average Lifetime for a Civilization.
To find the civilization lifetime as a fraction of a star lifetime we need to
estimate how long a star like the sun exists. Eventually the sun will become
a red giant and swell so that the Earth will be orbiting at its surface. In
the Colour-Magnitude Diagram lab, we estimated the ages of the clusters of
stars so check back and see how old a star like the sun is when it leaves the
Main Sequence.
Divide the civilization lifetime by the age of a star like the sun
and you have the lifetime fraction.FS = 2
The Number of Civilizations in Our Galaxy
From your previous answers (best guesses) find the number Nc of
intelligent life forms in our galaxy.
Obviously this is a very crude answer so round it off to one significant
figure.
The Distance to the Nearest Civilizations in Our Galaxy
Even if there is a lot of civilizations, the galaxy is so large we may never
detect them. The distance to the next alien civilization depends not only on
how many civilizations there are but also on how big the galaxy is. In the
“Size of the Galaxy” lab you found the distance from us to the centre of the
Milky Way galaxy to be approximately 30,000 light years.
If the sun is two thirds of the way to the edge of the galaxy
what is the radius of the disk of the galaxy?
Find the area of the galaxy (Area = πR2 ).
If the civilizations are evenly distributed across the disk of the galaxy,
each will have its own neighbourhood surrounding its star.
To find the average area of the neighbourhood occupied by a
civilization divide the area of the galaxy by the number of civilizations.
If we imagine the neighbourhood of a civilization to be a square then we
can find the length of a side of the neighbourhood by taking the square root
of the area of the neighbourhood.
8 SEARCH FOR EXTRATERRESTRIAL INTELLIGENCE
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Find the length of the side of a square with the area of the
average neighbourhood.
The length of the side of a square will be the average distance to the next
civilization. Obviously if the next civilization is 100 light years distant, and
we say “Hello” today then they will not hear it until 100 years from now. If
they answer right away we will not receive the answer until another hundred
years have elapsed. So a conversation will have to be between civilizations,
assuming the civilization lasts for a much longer time than the light time
between the two civilizations.
Compare the average distance between civilizations to the lifetime of a civilization.
Detecting the Message
We have been broadcasting our presence to the universe for more than 50
years. Every radio, TV, RADAR, and cell phone signal has leaked a little
radio noise into space. These signals would not be easy to detect because
they are at many different frequencies and both AM and FM coding.
Would our earliest radio signals have made it to the nearest
civilization yet?
Astronomers are looking for these stray signals by listening to “random”
locations in the sky and analyzing the radio noise to look for periodic signals.
This is very computing intensive and so some astronomers have appealed to
the people of the world to become involved in the Search for Extraterrestrial
Intelligence. These astronomers have written a screen saver which will analyze the radio data whenever the computer owner is not using it. More than
a million people are helping with the search. For more info:
http://setiathome.berkeley.edu/
Over the next decade the Allen Radio Telescope array will scan the sky
looking for radio emissions produced by intelligent extraterrestrial creatures.
The array will cost approximately the same as our new science building
(∼60million) and has been made possible by a donation to UC Berkeley by
Paul Allen. One million stars within 1000 light years will be surveyed and
a radar transmitter as powerful as the most powerful on Earth should be
detected. If the Allen radio telescope array can detect civilizations emitting
powerful radio signals out to about 1000 light years:
Do you expect it to detect any civilizations?
8 SEARCH FOR EXTRATERRESTRIAL INTELLIGENCE
56
Decoding the Message
Figure 5. The Pioneer 10 and 11 plaques.
In 1976 the USA launched the spaceships Pioneer 10 and 11. Their main
mission was to photograph Jupiter and Saturn, but they are now on a trajectory which will take them out of the Solar System never to return. A message
was engraved on a plaque attached to the space craft. This spaceship and
plaque will probably outlast not only our civilization but also the Earth. The
plaque has been reproduced in Figure 5 with the numbers added to aid you
in referring to different parts.
What can you decipher about the creatures that made this
plaque? Explain what you base it on.
to find the answer see: http://en.wikipedia.org/wiki/Pioneer plaque
Web Sites
http://www.seti-inst.edu/
http://exoplanet.eu/
http://exoplanets.org/index.html
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9
Lunar Imaging
“The Moon certainly isn’t pretty. It was exotic and it was different and it was challenging...I don’t think it’s forbidding” Gene
Cernan
“nothing but a ball of rocks and dirt” Paul O’Neil
OBJECTIVE
To image the moon using a telescope and to study the craters on its surface.
INTRODUCTION
Early civilizations regarded the Moon with wonder and awe. It was a source
of light, and its changing phases provided a convenient method of tracking
time. Figure 1 shows the different phases of the Moon, and where the Moon
is in relation to the Sun. The lunar cycle of 29.53 days is the basis for the
size of our months.
Figure 1. Lunar Phases
First Quarter
Cresent
Gibbous
Lunar Phase
Full
Earth
New
Sun’s Rays
Lunar Orbit
Third Quarter
The amount of illuminated lunar surface visible from Earth changes from
none at New Moon to 100% at Full Moon. The small lunar figures show
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58
what the Moon looks like from the Earth at that time. The direction of the
Earth’s rotation in this diagram is counter-clockwise, from which it follows
that the First Quarter is visible in the early evening and the Third Quarter
in the early morning.
The Moon had other strange properties, in particular, it would occasionally block out the Sun in a solar eclipse, and at times it would be eclipsed
by the Earth (a lunar eclipse). As these events were taken as being powerful
portends, being able to predict when an eclipse would occur was considered
very important, and was a driving force in the development of early astronomy. The Babylonians were able to make lunar eclipse predictions by the
seventh century BC. The first recorded prediction of a solar eclipse was by
the Greek Thales in 585 BC, and was only accurate to within a year. Thales
also determined that moonlight is actually reflected sunlight.
While the Moon itself would change, first waxing and then waning, the
patterns on the Moon’s surface did not change. In these patterns many early
cultures saw the images of people (the Man in the Moon), the face of a god
or goddess, or animals. Aristotle thought that the markings seen on the
Moon were actually reflections of the Earth, and that the Moon itself was
a perfect crystal sphere. Further determinations as to what these markings
were would have to await the development of the telescope.
Galileo may not have been the first person to use a telescope to look at the
moon, but he was the first to record what he observed. Far from being the
perfect sphere that Aristotle had claimed, Galileo saw a rough surface with
varying terrain. He saw mountain ranges (by measuring the lengths of the
shadows they cast he found that these mountains were similar in height to
mountains on Earth), craters, and large areas of darker material that seemed
to be fairly level which he called maria (Latin for seas). His observations
of the Moon as well as other astronomical observations were published as
Siderius Nuncius (Messenger from the Skies) in 1610.
The fact that the Moon’s features do not change implies that we can only
see one side of the Moon from the Earth. For this to be the case, the Moon’s
rotation must be locked to the Earth, so that the Moon rotates exactly once
on its axis during each complete orbit of the Earth. This can be seen in
Figure 1. If the same side of the Moon is facing the Earth at both first and
third quarter, the Moon must have rotated by 180o . The Moon’s rotation
being locked to the Earth is a consequence of the gravitational interaction of
the Earth and the Moon.
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59
Johanes Hewelcke published the first map of the Moon in 1647. He gave
mountain ranges the names of terrestrial mountain ranges, and named craters
after cities and countries. While his names for the mountain ranges were
adopted, the crater names were changed by Giovanni Riccioli and his student Francesco Grimaldi in Grimaldi’s map which appeared in Almagestum
Novum in 1651. They named craters after famous scientists and Philosophers
(the craters Riccioli and Grimaldi are among the largest).
These names are still in use, although Johann Schrvter and later J. Heinrich von Middler extended the naming system to include subsidiary craters
labeled with capital letters.
The development of photography allowed the production of even more
accurate maps. The first photograph was a daguerreotype taken by Louis
Daguerre in 1839, but it was of poor quality. The first true photograph was
obtained in 1857, and a photographic lunar atlas was published by the Paris
Observatory in 1896. The Photographic Atlas of the Moon, published in
1903 by the Harvard College Observatory, used photographs taken at different phases. This is important, because the different light angles highlight
different features. For example, craters and mountains are best seen when
they are near the terminator (the line separating the light and dark sides of
the Moon), where they cast the largest shadows. Shadowless features, like
the maria and rays extending from craters, are seen most easily at full Moon
as this provides more contrast.
Photography from ground based telescopes remained the best way to
examine the Moon until the development of rockets allowed missions to the
moon. The Luna program of the Soviet Union was the first to send rockets
to the Moon. In 1959 Luna 1 passed within 6000 km of the Moon, Luna 2
successfully crash landed and Luna 3 provided the first pictures of the Far
side of the Moon. While the Soviets also had the first soft lunar landing and
the first spacecraft to orbit the Moon, the American Apollo program landed
the first astronauts on the Moon. On July 20, 1969 the Command Module
Eagle landed on the Sea of Tranquillity, and Neil Armstrong became the
first person to stand on the Moon. There were a total of six manned space
craft that landed on the Moon between 1969 and 1972, vastly increasing our
knowledge of the Moon.
When looking at the Moon, perhaps the most striking feature is the large
number of craters on its surface. The craters range in size from centimetres
to hundreds of kilometres, and are all over the Moon’s surface. Even in
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60
areas that have few craters, evidence of cratering abounds in the form of
mixed dust, small rocks and glass beads that result from impact events.
Early observers believed that the craters were volcanic in origin, but the
craters do not look like terrestrial volcanoes. Volcano’s on the Earth consist
of a cone rising above the surroundings with a bowl-like indentation at the
centre while the craters on the Moon have elevated rim walls surrounding the
crater depression and a small peak in the middle. In 1873 Richard Proctor
suggested that the craters on the Moon were the results of impacts rather
than volcano’s. This idea gained strength with the discovery of the Barringer
impact crater in Arizona, which looks similar to craters on the Moon.
The question then arises, if the Moon is covered with impact craters, why
do we see so few of them on Earth? There are three reasons for this:
1. The Earth is geologically active while the Moon is not. Material on
the Earth’s surface is constantly being replaced by new material.
2. Surface features on the Earth are subject to erosion and mountains are
worn down by wind and rain, while depressions are filled in by sediments. As
the Moon lacks an atmosphere, only solar wind and meteorites cause erosion,
and they are much slower processes.
3. The Earth’s atmosphere protects it from some cratering events.
The Earth’s atmosphere has two effects on objects falling onto the Earth.
The first is that, due to the high speeds with which objects fall, the atmosphere acts somewhat like a sandblaster. The friction with the air strips away
the outermost layers of the object. If it is small, nothing will be left, and it
will have ‘burned up’. For larger meteorites, only the outer few millimetres
are lost, and from reports of people who have seen a meteorite strike, it was
immediately cool to the touch. The second effect of the atmosphere is that
the atmosphere can act like a solid wall. Small meteorites pass fairly easily
through the air, but for larger objects (the size of the Elliott Building, for
example) the air builds up in front of it, while there is no time for the atmosphere to flow in behind it. The resulting pressure difference can cause a
massive explosion, in which the meteor is totally destroyed. This happened
over Revelstoke in 1965 and the explosion had as much energy as the first
atomic bombs.
Meteorites that are even bigger, or that are made of iron rather than rock,
do not get destroyed in the atmosphere. The atmosphere is only a very thin
covering over the Earth; about two-thirds of the atmosphere lies below the
height of the peak of Mt. Everest. As meteorites travel very fast (about 40
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61
km/s), they are only in the atmosphere for about one second. If you imagine
a large asteroid, say ten times the size of Mt. Everest, hitting the Earth,
the first part of it would hit the ground before the last had even entered the
atmosphere. Fortunately, such large meteorites are very rare. For example,
over the land area of the Earth it is predicted that about 6000 meteorites of
0.1 kg or larger will fall in a given year, but only about 250 objects of 10 kg
or more will hit. For even larger objects, such as the asteroid or comet that
presumably killed off the dinosaurs, tens or hundreds of millions of years can
pass between impacts.
PROCEDURE
The 0.5 meter telescope on the roof will be used to take the pictures of the
Moon. Your instructor will help you to find the Moon in the telescope and
take the picture. The telescope does not use film, but a CCD (Charged
Couple Device) that records the image electronically. The image is sent to
a computer, and then printed out. The image of the Moon projected by
the telescope is too large to fit on the CCD, so it is necessary to get several
images if all of the Moon’s visible surface is to be recorded. After all of the
images have been obtained, you will combine them by taping them together,
cutting out anything not needed. With the aid of a Lunar map, you will then
examine your picture and note interesting features.
EXERCISES
1. Combine all the different pictures of the moon into a mosaic.
2. Identify on your picture of the moon three craters, three Maria, and
three landing sites of spacecraft. Note whether or not there are central
peaks in the middle of the crater.
3. Craters which come later are going to overlay craters, which were there
originally. Find and indicate an example of a crater, which was formed
after another crater. We know that the dark Maria are about 3.5 Billion
years old. Find a crater which formed after this. Find one that formed
before 3.5 Billion years ago. Mark these on your mosaic and explain
your reasoning.
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Table 4: Selected Meteorite Impact Craters
Name, Location
Barringer, Arizona
Manicouagan, Quebec
Chicxulub, Mexico
Diameter
(km)
1.2
100
180
Age in
Million years
0.049
214
64.98
Features
shocked sandstone
circular lake
dinosaur killer
The sun produces a wind, which blows continuously against the moon
and turns the lunar rock very black. When new craters form the explosion blasts the underlying lighter coloured rock across the surface.
Can you find some lighter coloured craters? Can you find some lines
(rays) of lighter coloured material emanating from a crater? or an
ejecta blanket?
4. Are the craters on the moon like craters found on the earth? Measure
the diameter of a big and a little crater and convert them to kilometres
assuming a diameter of the moon of 3476 km. Compare them to the
craters listed in the table. The diameter of a crater is about 10 to 50
times the diameter of the meteorite depending on the mass and velocity
of the meteorite. How big was the meteorite, which made these lunar
craters, assuming the craters are 25 times bigger than the meteorite?
5. The dinosaurs became extinct 65 million years ago at the CretaceousTertiary boundary, probably due to an impact by a comet or asteroid.
From the high concentration of Iridium found world wide at this strata,
it has been estimated that the asteroid was 10 km. in diameter. In the
Yucatan peninsula a crater has now been identified which is 180 km in
diameter and 65 million years old. Is this crater about the right size?
This impact is roughly the equivalent of an explosion of 100 million
megatons of TNT or 10,000 times the combined arsenals of the U.S.
and Russia.
It has been estimated that most of the people on the earth would be
killed by the impact of a much smaller 1 km. diameter object. This
is the equivalent of a 1 million megaton explosion and would make a
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Table 5: Crater and Tsunami Size for Various Impact Energies
Crater Diameter (km)
Energy (ergs)
Distance (km)
10000
3000
1000
300
150
1 × 1030
Tsunami Height (meters)
100 m
250 m
540 m
1300 m
50
6 × 1028
10
2.6 × 1026
15 m
40 m
90 m
200 m
1m
3m
5m
15 m
crater about 25 km. across. To estimate how often this happens we
can examine our nearest neighbour, the moon. There are 29 ± 5 craters
bigger than 25 km in diameter on the lunar Maria. The maria are 3.5
billion years old, so how often do craters of this size form on the maria?
To estimate how often this happens on the earth we need to know how
much bigger the earth is compared to the lunar maria. If the area of
the maria is about 5 million sq. km, and if the area of the earth is 500
million sq. km, how often would you expect a crater of this size to be
formed on the earth and end civilization.
6. Every year on the 12 August the Perseid Meteor shower occurs. This
meteor shower is caused by bits of gravel lost from comet Swift-Tuttle,
but still traveling in almost the same orbit. The Earth’s orbit intersects
the comet’s orbit at the place that the Earth is on 12 August. If the
date of perihelion of the periodic comet Swift-Tuttle changes by +15
days (it changed by several years in its last orbit), it will hit the earth
on August 14, 2126. It has a diameter of about 2 km, and would hit
the earth with a speed of about 50 km/s. How big a crater would it
make? There would be a 75% chance that it would land in an ocean.
From the table, how large would the tidal wave be 300 km from the
impact sight? Would you be safe on Mt. Doug (altitude=210 m)?
Web Sites
http://impact.arc.nasa.gov/
http://www.nineplanets.org/
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Figure 2a. Lunar Photo 1
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67
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Figure 2b. Lunar Photo 2
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69
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Figure 2c. Lunar Photo 3
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10
71
Constellation Imaging
“Plato thought that God, after having created the heavenly bodies, assigned them the proper and uniform speeds with which they
were forever to revolve; and that He made them start from rest
and move over definite distances under a natural and rectilinear
acceleration such as governs the motion of terrestrial bodies. He
added that once these bodies had gained their proper and permanent speed, their rectilinear motion was converted into a circular
one, the only motion capable of maintaining uniformity, a motion in which the body revolves without either receding from or
approaching its desired goal.”
. . . Galileo Galilei, 1629, Dialogues
Concerning Two New Sciences, P.283
OBJECTIVE
To photograph your favourite constellation and to learn about some of the
constituent stars.
TAKING THE PICTURE
Generally you will take the picture one night and analyze it on another lab
period a couple of weeks later.
The camera will be mounted so you can point the camera to the constellation you are interested in. Your instructor will help you check that the
camera is focused at infinity.
The camera is controlled by a computer, which will allow you to set the
exposure to about 10 seconds and to name the file etc. Note the date, time,
length of exposure, focal length of the camera, and constellation name in the
log book.
EQUIPMENT
We will use a Santa Barbara Instruments Group - ST8 CCD camera with a
fisheye lens of 15 mm focal length and a sturdy tripod to hold the camera
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10 CONSTELLATION IMAGING
during the time exposure. This camera is a very sensitive digital camera,
which is cooled to decrease the noise inherent in this equipment. The detector
is a Charge Coupled Device (CCD), which is composed of 1530×1020 pixels
each 9 microns in size. The picture elements or pixels can be binned or added
together to make pictures with 2 or 3 times less elements but still cover the
same area on the sky. Generally we use it binned 2×2. The pictures can be
enhanced and stored in a computer.
Field of View
In order to identify stars on the picture we need to know how much of
the sky is included in our picture. This is called the field of view “FOV”
and is usually measured in degrees. The field of view depends on the size
of the picture (s) and the focal length (f ) of the lens. See figure 1. The
bigger the picture, the more sky you will see. A short focal lens length has
a small radius of curvature and will make a small picture. Using the small
angle formula, the distance (s) on the picture is equal to the focal length of
the lens (f ) times the angle (θ), on the sky measured in radians:
s = f θ,
and for an angle θ in arc seconds we get the familiar:
s
θ
=
.
f
206265
θ
θ
Image Size s
Image
Object
Lens
focal length f
Figure 1. The focal length, image size and angular diameter relationship
There are 57.3 degrees in one radian so if you measure θ in degrees the
relation becomes:
10 CONSTELLATION IMAGING
73
s = f θ/57.3,
θ = 57.3s/f.
The focal length (f ) of the camera’s lens is 15 mm and the CCD has a length
(s) 13.77 mm and width 9.18 mm. What is the length and width (θ) of the
picture in degrees?
Theoretical Scale
Closely related to the “field of view” is the scale of the picture. This
term refers to the number of degrees per millimetre on the picture. The
illuminated region of the CCD does not quite go to the edge of many of our
pictures, but usually the width is about 206 mm. To find the scale, divide
the number of degrees your picture is on a side by the length of that side in
millimetres as measured on your print.
Resolution
If you look very closely at your picture with a magnifier you can see that
the picture is made up of tiny pixels. The smallest detail you can see in your
picture is called the “resolution” and depends on the size of these pixels. The
pixels on our CCD are 9 microns on a side, but usually we bin the data by 2
or 3 times so the pixels are effectively 2 or 3 times larger. If two stars appear
very close together on the sky, then the light from both stars may land on
a single pixel and we will record them as one star. Such a star is β Cygni
(=Albireo), which appears to have a separation of 0.01 degrees (= 30 arc
seconds) in the sky.
• Using our lens of 15 mm focal length, how far apart will the two images
of the stars be? Will this angle be resolved by our CCD if the pixels
are 9 microns (0.009 mm) on a side?
• What would you need to change to enable us to resolve the star into
its two components?
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Table 6: Greek Letters
α
β
γ
δ
ζ
Alpha
Beta
Gamma
Delta
Epsilon
Zeta
η
Eta
θ
Theta
ι
Iota
κ Kappa
λ Lambda
µ
Mu
ν
ξ
o
π
ρ
σ
Nu
Xi
Omicron
Pi
Rho
Sigma
τ
υ
φ
χ
ψ
ω
Tau
Upsilon
Phi
Chi
Psi
Omega
OBSERVATIONS
Constellations
Of the 88 constellations in the sky only a few will be visible in your picture.
Some of these constellations such as those of the Zodiac are very ancient and
have referred to the same stars since the time of the Babylonians. Some of
the constellations are rather recent inventions of the 1700’s by Lacaille and
Hevelius.
Sketch on your picture, connecting the bright stars to show the constellation(s) visible in your picture. What mythological figure does your constellation(s) represent?
Star Data
Only the brightest stars such as Betelgeuse were named by the Arabs and
the Greeks. To include fainter stars Bayer introduced in 1603 the system of
identifying each star by a Greek letter and the name of the constellation so
Betelgeuse = α Orion. These designations generally go in order of brightness
with the brightest star designated α and the second brightest designated β
etc.
To include even fainter stars, in 1725 the Astronomer Royal John Flamsteed introduced a system of numbering the stars from West to East in a
constellation. Therefore the bright star Betelgeuse is also called α Orion or
58 Orion. The Henry Draper Catalogue (HD) was compiled in about 1900
and was the first big catalogue to include the spectral types of the 359,000
stars to 9 magnitude. The Smithsonian Astrophysical Observatory (SAO)
catalogue was made in about 1950 and it included accurate positions and
spectral types for 300,000 stars brighter than 9 magnitude. The Guide Star
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75
Catalogue (GSC) was compiled for the the Hubble Space Telescope contains
19 million “stars” to about 15 magnitude. The Hipparcos catalogue (HIP)
was made from data from the Hipparcos satellite which measured the accurate positions and brightnesses of 118,218 nearby stars. The problem of
naming stars continues today as we want to refer to more and more, fainter
and fainter stars, galaxies and other objects.
The “Sky” computer program has been included with your textbook and
we have installed it on the lab computers. Click on the icon and the program
should show you the sky with the constellations and stars named. If not
check with the instructor.
To find your constellation, right click and choose [Find]. Choose Constellation labels and then choose your constellation. Click on [Centre and Frame]
and the program will zoom to your constellation. Click on the magnifying
glass to see more or less sky.
Click on a star to see more about the star. Record the name, magnitude/brightness, distance in light years and spectral class of a few bright
stars.
You will learn much more about spectral classes in later labs and lectures
but for now all you need to know is that it tells us the temperature and size
of a star. The spectral class of a star tells us its temperature - from hottest to
coolest the spectral classes go O,B,A,F,G,K,M. Each spectral class is divided
into ten subclasses so they go B8, B9, A0, A1, A2, A3 ... A8, A9, F0, F1, ...
M9. Usually then there is a Roman numeral to tell whether a star is a dwarf
(=V), a giant (=III) or a supergiant (=I or II). Our sun is a G2V type star
and has a temperature of 5000 degrees. Vega is an A0V type star and has a
temperature of 10000 degrees.
The distance to a star is measured in parsecs or light years and 3.26 light
years equals a parsec. The brightness of a star is measured in magnitudes.
Astronomers use blue (B) and yellow (visual = V) filters to measure the
brightness and colour of a star. Remember that the small magnitudes 0, 1,
2 ... are bright and big magnitudes 5, 6, 7, ... are faint.
Nebulae
Charles Messier was the first to catalogue some nebulae in 1771 and we
still use his list today, M1, M2, M3, etc. Are there any fuzzy objects in your
picture? Can you find any clusters, emission nebulae, or galaxies? If you
find a fuzzy spot, check another picture of the same region to see if it is a
10 CONSTELLATION IMAGING
76
real object or if it is a plate flaw such as scattered light from the moon or a
bright star.
Limiting Magnitude
Astronomers love to talk about “Who can ‘see’ the faintest star?”. In
the star atlas the brightness of a star is indicated by the size of the dot
representing the star. The faintest star in the atlas that you can detect on
your picture is the limiting magnitude. What is the limiting magnitude of
your picture? How could you get a picture with a fainter limiting magnitude?
Right Ascension and Declination
Just as the Earth is divided into a grid of latitude and longitude lines, the
sky is divided into Declination and Right Ascension. Declination measures
North and South of the equator in degrees just like latitude and is given by the
numbers going up the side of the star chart. Right Ascension measures east
and west in hours, minutes and seconds and is given by the numbers on your
star atlas going across the top of the chart. Note that the Right Ascension
increases towards the East. Find the Right Ascension and Declination of the
Centre of your picture. Use the “Sky” program and click a few times to see
how precisely you can measure this quantity.
Observed Plate Scale
We can now confirm the theoretical plate scale. Find two stars which are
quite far apart in the picture and which you can identify unambiguously in
the star atlas or SKY program. On the picture measure with your ruler the
distance between the stars in millimetres. Using the SKY program, left click
on the first star and then left click on the second. Scroll down to the bottom
of the data window and it will tell you how many degrees separate the two
stars.
Find the scale of your picture in degrees per millimetre by dividing the
distance between the stars that you measured on the picture into the number
of degrees from the SKY program. Does this agree with the theoretical scale
you calculated from the focal length of the camera lens? Comment on the
accuracy of this procedure.
Alternatively we can use the atlas to measure the distance between the
same two stars in degrees. The easiest way to do this is to align the edge of
a piece of paper with the two stars and mark their positions on the paper.
Then align the paper with the Declination scale on the edge of the atlas and
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77
just read off the number of degrees between the marks.
Star Counts
The limiting magnitude of your picture is approximately what you would
see from a very dark place with your unaided eyes. Many people think that
the number of stars you can see is uncountable, but we can estimate it from
your picture. You can count the number of stars in a small square and then
multiply it by the number of small squares in the whole sky.
Draw a small square on your picture 25 mm by 25 mm and count the
stars in it. Draw a couple of similar squares in other parts of the picture and
count the stars in the square to measure the uncertainty. Use your observed
scale to find the area of the square in square degrees. It should be close to 41
square degrees. If there are 41,253 square degrees on a sphere, roughly how
many stars are there in the sky that you could photograph with this camera?
Web Sites
http://www.astro.uiuc.edu/∼ kaler/sow
http://en.wikipedia.org/wiki/Constellation
11 SOLAR ROTATION
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78
Solar Rotation
OBJECT
To observe the rotation of the sun as evidenced by sunspot motion, and to
determine the period of rotation.
INTRODUCTION
Would we expect the sun to rotate? There are several reasons which lead us
to anticipate a positive answer to that question.
a) The general dynamical state of the solar system as exemplified by planets and satellites is one of rotation. We should therefore not be particularly
surprised to find similar behaviour on the part of the sun.
b) The condition of zero rotation is unique among all possible rotational
states. If rotational states were randomly chosen, the chances of obtaining
precisely zero are vanishingly small.
c) If a body as massive as the sun is initially endowed with a certain
amount of rotation, astrophysicists are quite hard put to think of ways in
which that rotation might be entirely lost. Cosmogonists do not offer any
help, since most models for the formation of stars include rotation as an
intimate part of the process.
How might we go about determining the rotation of the sun? In 1611
Galileo Galilei, in the course of examining the heavens with his newly invented telescope, noticed sunspots and detected their motion across the solar
disk. Assuming them to be part of the solar surface, Galileo cited this as
evidence proving the sun rotates in about 27 days.
It was established in about 1861 by an English amateur astronomer, Carrington, that the period of solar rotation determined from a sunspot varied
with the latitude of the spot; at higher latitude the period was greater. This
was the first indication that the sun, or at least its surface, does not rotate
as a solid body.
PROCEDURE
1. To find the period of rotation of the sun from the sunspots you need
observations of the sun every day or two for a week. A sketch of the sun
11 SOLAR ROTATION
79
can be made by projecting an image of the sun onto a piece of paper using
a telescope and a projection screen. Carefully mark the edge of the sun and
the positions of all the sunspots. Turn off the drive for the telescope and the
image of the sun and the spots will drift across the field of view. The spots
are drifting across the field of view because the Earth keeps turning and the
telescope is not moving to follow the apparent westward motion of the sun.
Mark on your sheet an arrow showing the direction that one of the spots has
moved. The sun seems to be moving to the West so mark the end of the
arrow with a W. Record the date and time that you made the sketch.
2. Back in the lab you will be given observations of the sun made on a few
other days. To easily see the motion of the spots from day to day trace your
diagram onto a sheet of lined paper. Make the lines of the paper parallel to
the arrow, i.e. the motion of the spot when the drive was turned off. Trace
the other days’ diagrams onto the same paper to form a composite diagram.
Be very careful to align each arrow with the lines on the paper. Label each
of the spots with the date it was observed.
3. To help clarify the situation we will make a three dimensional diagram showing the surface of the sun and the spots. Connect the different
observations/days of the same spot with a line of latitude going east-west
across the sun. Tape a piece of paper along the latitude line. This piece of
paper will be a cross-section of the sun. On the paper draw a semi-circle
with a radius equal to half the length of your latitude line. If you now draw
lines perpendicular to the latitude line from the spots to the semi-circle, you
can see where the spots were on the curved surface of the sun. Draw lines
connecting the centre of the semi-circle with the spots.
4. With a protractor you can now measure the angle that the spot moved
through from observation to observation. Make a table with all the angle
and time differences for each pair of observations of a spot.
5. From the differences calculate the period of rotation for each pair of
observations and average the periods.
80
11 SOLAR ROTATION
Face On View of Sun
B
Line of Latitude
A
Cross-sectional view of sun
θ
B
A
Figure 1. Face-on and Cross-sectional views of the sun.
11 SOLAR ROTATION
81
QUESTIONS
1. The accepted value of the observed rotation period of the sun is 27
days at the equator and 28 days at 30 degrees latitude. Compare your
determination of the period with these values, giving your best estimate
of the uncertainty in your determination.
2. What are we assuming about sunspots, which is fundamental to determining the rotation of the sun by this method? How might you
investigate the validity of this assumption?
3. In a paragraph describe how the sunspots change in size, shape and
number over the few days of observation.
4. Assuming the diameter of the sun is 1,392,500 km, how big is a sunspot?
Compare it to the diameter of the Earth (12,756 km).
Web Sites
http://www.bbso.njit.edu/
http://sohowww.nascom.nasa.gov/
http://www.spaceweather.com/
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