lab astro mannual (outdoor and indoor labs)
TRANSCRIPT
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Table ofContents
Outdoor Exercises
N u m b e r Title
0 1
Observations of
Bright
Stars
O-2 Imp act Features
on the
Waxing Moon
0 3
Maria
on the
Waxing Moon
0 4
Observations
of a
Total Lunar Eclipse
O-5 Observations of a Part ial Lunar Eclipse
O-6
Visual Observa tions
of the
Planet
Mercury
0-7 Visual Observations of the Planet Venus
0 8 Visual Observations of thePlanet Mars
O-9
Visual Obse rvations
of the
Planet Jupiter
0-10 Visual Observationsof the Planet Saturn
0 11
Visual Obs ervations of a Comet
0-12 Observations of Messier Ob jects
0-13 The Field ofView of the Telescope
0-14 Aligninga telescope with the polar axis
0-15
A
Planetary Posit ion
O-16
The
Magnitude Limit
O 17
The Seeing Angle
0-18
The
Visual Magnitude
of a
Variable Star
0-19 The
Distance
to aGlobular Cluster
0-20 Observations of the Sun
Indoor
Exercises
N u m b e r Title
1 1
Math Review
and
Scaling
1-2 Unit transformations, and Calculators
1 3
Web Based Lab Excercises
1-4
Introduction to the
Telescope
1-5
Th e
Height
of a
Lunar Feature
1 6
A
Volcano
on
lo
1-7
Planetary Storms
1 8
The RA and DEC of M4
1-9
The Jupiter-Comet Collision of 1994
1 10
The
Solar Rotation
1 11
The
Mass
of
Jupiter
1-12
Photographic Photometry
1 13
SomePhysical
Characteristicsof a Distant
Star
1-14 Magnification
1 15
Coordinate
System of the
Telescope
1 16 The Distance Betweenan Interior Planet and the Sun
1 17
Th e
Distance
and
Proper Motion
of
Barnard sStar
1 18
Th e
Radial Velocity
of
Barnard sStar
1 19 Masses in the Earth-Mo on System
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Extended
Exercises
N u m b e r Title Pages
E-l
Celestial Motion
of the Sun 119->120
E-2
Observations
of the Sunset
Point
121
E-3
Extended Observations
of the Moon 123-> 128
E-4
Celestial Motion
of the Moon
129-4
1 30
E-5
Planetary Motions
131->
132
E-6
Observations of a Meteor
Shower 133-
134
Appendicies
Number
Title Pages
A-l How to
Build
A
SimpleQuadrant 137-4
1 41
A-2
Constants
Unit Conversions an d Formulae 143-4144
A-3
Finding
the
radius
o f a circle given an arc
145-4
1 46
A-4
Planetary Data
14 7
A- 5
Major Moons
of the
Solar System
149
A-6
Star Charts 151-4164
Roger Culver
Sean
Roberts
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Outdoor xcercises
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Exercise 0 1
Observations of B right Stars
Introduction:
In to night s exercise you w i l l locate w ith your telescope ten of the b righte ststars currently visible
in the sky, and careful ly record yo ur observations o f
each.
Measurements
and
Observations:
Using your telescope, locate each
of the stars
l isted
in Table
O l l
on
page
4 for the
appropriate
season. Star chartsaregiven inAp pendix A-6.The 88 constellation namesand their abbreviations are
given
in Table 0-1-2 on page 5. Onc e the given star is set at the center of the tel escope s field of view,
sketch
the field of
view, including
any and all
additionalstarsw h ich
are in the field.
Note also
th e
color
of
the bright star being observed. Record your observations in the fo l lowing format:
Star: Observed Color:
Field
of
View
As
much as possible, arrange the stars you observed in order of decreasing brightness.
Questions:
1.
Which color(s)
are
absent
in
your survey
o f
bright stars?
2.
Which color (s) w ere
t he
most common
in
your survey?
3. What fraction of the stars in your sample appear to have companion stars? How do the colors of the
companion
stars
compare w ith those
of the
primary stars?
4.
Can you suggest tw o reasonsthat stars might have different colors?
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Table O-l-l
Bright Stars
BF*
aTau
a Ori
Aur
aUMi
Gem
G em
a CMi
/30ri
a CMa
T a u
a CrB
a Her
a Sco
a Boo
C r v
7 Leo
(UMa
a U M i
Leo
a Vir
a Lyr
a
A ql
a Cyg
a U M i
a Aqr
/ ? A q r
aPsA
a Peg
/ 3 P e g
/3
An d
N a m e
Spring
Aldebaran
Betelgeuse
Capella
Polaris
Castor
Pollux
Procyon
Rigel
Sirius
Alcyonne
S u m m e r
Antares
Arcturus
Mizar
Polaris
Regulus
Spica
A u t u m n
Vega
Altair
Deneb
Polaris
Fomalhaut
R A
4
h
35
m
55
s
5h55m10s
5ft16m41s
2
h
31
m
13
s
7ft34m36s
7/'45m19s
7
ft
39
m
18
s
5 ft 14 m 3 2 s
6/l45m9s
3 ft 47m 29 s
15
ft
34
m
41
s
17
h
14
m
40
s
16''29
m
25
s
14h15m40s
12
h
29
m
51
s
10
h
19
m
59
s
13''23m56s
2
/l
31
m
13
10 ft8m 22 s
13/l25mlls
18/'36ra56s
19''50
m
47
s
20 h41m 26 8
2h31m13s
22''5m47s
21/'31m34s
22ft57m39s
23 /l4m 46
23h3m47s
I 9m44'
D EC
16.30
7.24
46.0
89.15
31.53
28.1
5.14
-8.12
-16.43
24.7
26.43
14.23
-26.26
19.11
-16.31
19.51
54.56
89.15
11.58
-11.9
38.47
8.52
45.16
89.15
-0.19
-5.35
-29.37
15.12
28.5
5.36
Mag
0.9
0.8
0.1
2.5
2.0
1.2
0.3
0.1
-1.5
2.9
2.2
3.1
1.1
0.1
3.0
2.6
2.4
2.5
1.4
1.0
+0.0
0.8
1.3
2.5
2.9
2.9
1.2
2.5
2.6
2.0
Distf
68
652
45
1087
45
35
11
>1100
9
652
76
>1100
172
36
181
172
88
1087
84
155
27
17
?
1087
1087
>1100
23
109
217
76
Am*
10.2
10.1
8.0
7.0
1.0
7.7
11.2
7.0
10.1
3.3
3.1
5.5
4. 5
1.5
2.1
7.0
6.5
-
9.5
8.7
10.4
7.0
-
7.9
-
7.0
9.7
Sep*
121.7
175.8
484.6
18.8
7.0
201.1
80.7
9.9
11.9
117.0
5.3
3.4
_
24.4
4.4
14.8
18.8
176.9
-
57.2
165.4
75.5
18.8
-
35.7
264.2
90.8
CIass
K 5
M2
G 8
F8
Al
KO
F5
B8
Al
B7
AO
MS
Ml
K 2
B9
KO
A2
F8
B7
Bl
AO
A 7
A 2
F8
G 2
G O
A 3
B9
M2
MO
Bayer an d Flam steed designation. Agreek letter followed by the constellation abbreviation.
Distance to thestar in Light Years.
Calculated from
the
stars' parallax angle. D =^p. Where j> is
in
arcseconds.
f For
m ultiple star system s.
Am
=
Th e
difference
in
m agni tude between
the two
brightest
stars
in the
system.
Se p
= >
m axim um separation between the two brightest stars in the system.
3 Spectral C lass of the star. The brightest star'sclass is listed in the case of a m ultiplestar sys
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Table
O 1 2
The Constellation Names
Abbr.
And
Ant
Aps
Aqr
Aql
A ra
Ari
Aur
Boo
Cae
Cam
Cnc
CVn
CMa
CM i
Cap
Car
Cas
Cen
Cep
Cet
Cha
Cir
Col
Com
C rA
CrB
Crv
Crt
Cru
Cy g
Del
Dor
Dra
Equ
Eri
For
Gem
Gru
Her
Hor
Hya
Hy i
Ind
Name
ndromeda
ntlia
pus
quarius
quila
Ara
Ar ie s
uriga
Bootes
Caelum
Camelopardalis
Cancer
Canes Venatici
Canis Major
CanisMinor
Capricornus
Carina
Cassiopeia
Centaurus
Cepheu s
Cetus
Chameleon
Circinus
Columba
Coma Berenices
Corona ustralis
Corona Borealis
Corvu s
Crater
Cr u x
C y g n u s
Delph inu s
Dorado
Draco
Equuleus
Eridanus
Fornax
Gemin i
Grua
Hercules
Horologium
Hydra
Hyd r u s
Indus
Abbr.
Lac
Leo
LM i
Lep
Li b
Lup
Ly n
Ly r
Men
M ic
Mon
M us
Nor
Oct
Oph
O ri
Pav
Peg
Pe r
Phe
Pi c
Psc
PsA
Pu p
Py x
Ret
Sge
Sg r
Sco
Scl
Se t
Se r
Sex
Tau
Tel
Tr i
TrA
Tu c
UM a
UM i
Vel
Vi r
Vol
Vu l
Name
Lacerta
Leo
Leo
Minor
Lepus
Libra
Lupu s
Lynx
Lyra
Mensa
Microscopium
Monoceros
Musca
Norma
Octans
Oph iuchu s
Or ion
Pavo
Pegasus
Perseus
Phoenix
Pictor
Pisces
Piscis ustrinus
Puppis
Pyxis
Reticulum
Sagitta
Sagittarius
Scorp ius
Scu lp tor
Sc u t um
Serpens
Sextans
Taurus
Teles copium
Triangulum
Triangulum ustrale
Tucana
Ursa Major
Ursa Minor
Vela
Vi r go
Volans
Vulpecu la
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Exercise
0 2
ImpactFeatures on the Waxing Moon
Introduction:
In this
lab you
will explore
t he
craters
on the
moon.
Measurements
and Observations:
Center the
moon s image
i n
y our telescope s
field of
view. Using
the
photographs
on
pages
11 and
12 ,a nd
table O-2-1
on
page
8,
locate
an d identify
three lunar craters which
are
located
at or
near
the
moon s
terminator. Using a higher magnification eyepiece, focus in on each of the craters you identified
an d
make
a
sketch
of
each
one in
your
lab
book, noting
a s
many characteristics (central peaks,
ra y
systems, etc.)
as you
can. Repeat this process
f or
three craters which
a re
located away from
the
moon s
terminator .
Indicate
the
t ime
an d
date
of
your observations
i n
your
l ab
book.
Questions:
1.
Compare
a nd
contrast
th e
structures
of the
craters
yo u
observed along
th e
moon s terminator.
2. Compare and contrast th e s t ructures of the craters yo u observed away from th e moon s terminator.
3. How
does
the
general appearance
of
craters observed along
the
moon s terminator compare with that
of the craters away
from
the moon s terminator.
4. Sketch the approxim ate configuration of the Ear th, Sun, and M oon at the time y ou made your obser-
vations. This diagram should
be as
though
you are
looking down
on the
three objects
from
above
th e
north pole of the Earth.
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Table 0-2-1
ImpactFeatures
N a m e
Phase*
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
Aristoteles
Eudoxus
Mortis
Hercules
Atlas
E n d y m o n
Cassini
Aristillus
Aut o l ycus
Archimedes
Poisonius
Geminus
R omer
Macrobius
Bessel
Jul ius
Caesar
Plinius
Manilus
Agrippa
Delambre
Triesnecker
Ptolemaeus
F
F
F
F
F
F
B
B
B
B
F
F
F
F
F
F
F
B
F
F
B
B
In
table
O-2-1
the
F=First
Quar ter
L=Last Quar ter
phase
phase
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
4 0
41
4 2
43
44
phase
page
N a m e
Alphonsis
Arzachel
Hipparchus
Albategnius
Herschel
Purbach
Abulfeda
Werner
Aliacensis
Geber
Theophilus
Cyril lus
Catharina
Piccolomini
Maginus
Walter
Pitiscus
Langrenus
Plato
LeVerrier
Helicon
Delisle
columns
refer
11
Phase*
B
B
B
B
B
B
F
B
B
F
F
F
F
F
B
B
F
F
L
L
L
L
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
Na me Phase*
Aristarchus
Timocharis
Lambert
Copernicus
Kepler
Eratosthenes
Lansberg
Euclides
Parry
Mosting
Bullialdus
Campanus
Hainzel
Pitatus
Tycho
Wilhelm
Longomontanus
Clavius
Grimaldi
Billy
Deslandres
Pytheas
to
w hich pic ture
that
particular
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
feature can be found on.
page 12
B=Both
these features
are
near
th e
terminator
in
both pictures
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Exercise
O-3
Maria on the
Waxing
Moon
Introduction:
In this lab you
will
explore the maria (dark areas) on the moon.
Measurements
and
Observations:
Center
the
moon s image
in
yo ur telescope s
field of v iew. As
accurately
as
possible
sketch-tile
image of the moon in your lab book and label the maria using the photograph s on pages 11 and 12 and
table
0^}_-_l_at
the bottom of this page.
Indicate^ w hich
of the lunar maria (dark areas) are (a) totally
visible
and (b)
partlaTIjTvisible. Record your observational results
in
your
la b
book. Estimate
th e
total
fraction of the mo on s visible
surface
covered by the maria, and record this estimate in your lab book.
Also
note the
difference
in crater density (nu mb er of craters per unit area) betw een the maria and the
areas outside of the maria. Record this observation in your lab book.
Questions:
1.
Which
of the
visible maria
has the
largest surface area? Which
has the
smallest? Estimate
the
ratio
of
th e
sizes
of the largest
maria
to the
smallest.
2.
Discuss any differences yo u observed betw een the maria located at the m oon s termin ator an d
those
located away
from
the terminator.
3. Propose an explanation for the differences between the crater density
wi thin
the maria and that outside
th e
maria.
4. Discuss the medieval view that the maria are bodies of water.
T a b l e 0 3 1
Maria
A
B
c
D
E
F
G
H
I
J
K
L
M
N
O
P
Name (Lat in)
Mare Crisium
Mare Serenitatis
Mare
Tranquillitatis
Mare Vaporum
Mare Fecunditatis
Mare N ectaris
Mare
Frigoris
Mare Marginis
Mare
Smythii
Mare Australe
Mare Imbrium
Oceanus
Procellarum
Mare Hu morum
Mare N ubium
Mare Insularum
Mare Cognitum
Name(Engli sh)
Sea of
Crisis
Sea ofSerenity
Sea of Tranquility
Sea ofVapors
Sea ofFertility
Sea ofN ectar
Sea ofCold
Border Sea
Smyth s Sea
Southern Sea
Sea of
Rains
Ocean of Storms
Sea ofMoisture
Sea ofClouds
Sea of
Isles
Known
Se a
Phase
F
F
F
B
F
F
B
F
F
F
L
L
L
L
L
L
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Exercise
O-4
Observations of a Total L un ar Eclipse
Introduction:
In this exercise youwillmake observations of one of the sky's m ore impress ive events, a
total
eclipse
of
the
moon.
Measurements and
Observations:
At
15
minute intervals sketch
the
boundary
of the
earth s shadow
on
your lunar
map
(page 17)
as
it
creeps
acrossthe moon. Note the
time
ofeach ofyour
observations.
Record your results inyour lab
book. During totality,
or the
total phase
of the
eclipse,
rate
with your unaided
eye the
luminosity
or
L-value
of the moon according to the so-called
Danjon
system inw hich the ratings are as follows:
L=0 Very dark ec lipse. Moon almost invisible, expecially
at
mid-totality.
L=l Dark eclipse with gray or brow nish coloration. D etails on moon dist inguishable only w ith difficulty.
L=2 Deep red or rust-colored eclipse. C entral regions of the m oon are dark and outer rim of moon relatively
bright.
L=3 Brick-red eclipse. Rim of moo n yellow ish and relatively brig ht.
L=4
Very
B right copper-red or orange eclipse w ith a bluish very bright luna r rim.
Record yourrating
in
your
lab
book.
Calculations:
Use th e
technique
in
appendix
A-3 to
determine
th e
diameter
dss of the
shadow edge. Measure
the diameterdu of the moonon the same scale. Calculate the diameter
DES
of the earth sshadow at
th e
lunar distance using
the
scaling equation
S
x 3500 km
Compare your value
o fDES
wi th
the
value
o f
12,700
km for the
linear diameter
of the
earth itself.
Choose
any tw o of
your shadow observations
an d
measure
the difference AX in the
shadow positions
on your lunar map and the diameter
XM
of the moon. Express the time
difference
A*
between your two
observations
in
hours
an d
then calculate
the
velocity V
of the
moon
as it
enters
the earth s
shadow
from
Enter your results inyour lab book.
AX
3500
VM A T
x
x km /h r
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If the moon
takes
27.3 days or 655 hours to complete oneorbit
about
the
earth, calculate
the
circumference CMof the
moon s orbit
and the
radius
RM of the
moon s orbit,
or the
mean
distance
between
the moon and the
earth
using:
VM x 655
R
Cu
RM
~
Record
all of
your results
in
your
lab
book.
Questions:
1.
Sketch the relative positions of the earth, moon and sun at the time the lunar eclipse occurred. On
the basis of your sketch, during what phase(s) of the moon would youexpect the next such eclipse to
occur?
2. Discuss
(a) why the
moon
is
visible when
it is
totally inside
of the earth s
shadow
and (b) why the
brightness and color of the total phase change from lunar eclipse to lunar eclipse.
3. Discuss the geometric relationship between the diameter of theearth s shadow at the moon s
distance
and the linear diameter of the
earth
itself. In particular, what do your results tell youabout the linear
diameter of the sun compared to
that
of the earth andmoon?
4.
Some individuals
believe
that
the phases of the
moon
are caused by the
moon
passing through the
earth s
shadow. Howwould you respond to such aclaim?
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Exercise 0-5
Observations of a Partial Lu nar Eclipse
Introduction:
As the
moon orbits
the
earth,
from
t ime
to
t ime
it
enters
th e
earth s shadow. Such
an
event
is
called a lunar eclipse or an eclipse of the mo on. If the m oon is com pletely immersed in earth s shadow ,
the
eclipse
i s
said
to be a
total eclipse.
On the
other hand,
if the
immersion
is not
complete, then
the
eclipse
is
said
to be
partial.
In
this exercise
yo u
will make observations
of a
partial lunar eclipse.
Measurements
and
Observations:
Center the moon in your telescope s field of view. At 15 minu te intervals sketch the bounda ry of
the earth s
shadow
on
your lunar
map
(page
17) as it
creeps across
the
moon. Note
t he
time
of
each
of
your observations. Also record your impressions of any and all color changes
that
youperceive across
the
lunar surface
as the
eclipse progresses.
Calculations:
From yourobservations, estimate the maximum percentage of the
lunar
surface which was
covered
during this partial eclipse
to
about
10
percent
or so.
Record this estimate
in
your
lab
book.
Measure the diameter dw of the lunar ma p and the largest radial distance d between the shadow
edge
and the
lunar edge
at the
maximum phase
of the
eclipse. Record your results
in
your
lab
book.
Calculate
the
anglea
by
which
the
moon missed being
totally
eclipsed using
the
scaling equation
ds
a 0.5
degrees
where 0.5 degrees is the angular diameter of the moon. Enter your result in your lab book.
Questions:
1. Sketch
the
alignment
of the
ear th, moon,
and sun at the
t ime
of
this eclipse. From your diagram,
at
wha t phase of the m oon does a lunar eclipse
occur?
How does this prediction agree with what you
actually observed?
2. Show by means of diagrams how a partial eclipse of the moon differs from a
total
eclipse of the moon.
3.
Which type
of
eclipse, total
or
partial,
do you
think occurs more frequently? Explain your answer.
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Exercise
O-6
Visual Observations of the Planet Mercury
Introduction:
Th e
planet Mercury
is a
most elusive objectowing
to the
size
of its
orbit ,
the
speedthat
it
moves
in its
orbit ,
and the
size
of
this planet.
In
this exercise
you
willtake advantage
of an
appartit ion
of
this
planet which is calledgreastest eastern elongation in order to make some telescopic observations.
Measurements and
Observations:
Locate
the planet Merc ury in your telescope. Sketch the
view
of the planet in your lab book noting
the shape and color of the planet as
well
as any surface featuresthat you can see on the disk. Note
also the degree to which the planet appears to
twinkle
in the telescope. Record all of your results in
your lab book. Locate astar about the same alti tude above the horizonas Mercuryand note in your
lab
book
the
degree
to
which
the
starappears
to twinkle
compared
to the
planet Mercury.Repeat this
observation for astarthat is nearly overhead, and record this result in your lab book.
Questions:
1. On the basis of you r sketch of the shape of the planet
Mercury,
draw a diagram of the relative positions
of the Ea rth, M ercu ry, and the Su n at the time of your observation.
2. Explain
w hy
each
of the
factors listed
in the
introduction make Mercury
a
difficult object
to
observe
from the
Earth.
3. On the basis of your observations is the old saying that stars twinkle, planets don't true? Explain.
4. On the basis of your observations, can youprovidean explanation for the phenomenonof
twinkling?
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Exercise O-7
Visual
Observationsof the Planet Venus
Introduction:
Tonight
you will
observe
the
planet Venus.
Measurements and Observations:
Using your telescope,locatethe planet Venusand inyour labbook makea sketch of the planet's
diskas itappearsin the field ofv iew. Sketch any details on the diskthatyou can detect in moments of
clear seeing when
the
earth'satmosphere steadies
up for a few
tenths
of a
second. Note
the
colors
ofsuch details as well as the colorof theoverall disk. Check for any objects in the field of view which
might be satellites of Venus. Record all of your
data
in your lab book as well as the focal length of
the eyepiece
that
youused inmaking yourobservations. Also
obtain
from your
instructor
the
angular
separation between Venus
and the Sun at the
time
of
your observations
and
record this value
in
your
lab book.
Repeat the above observations using an eyepiece having a different focallength. Record all of these
results inyourlab book.
Questions:
1. Comment on the number offeatures
which
yo uobservedonVenus' image. Explain your resultin terms
of
the atmosphere, ifany, ofVenus.
2.
Prom your observed
shape
of Venus, sketch the relative positions of
Venus
the Earth, and the Sun at
the time you made your observation. Can your observations be accounted for by having Venus orbit the
Earth?
Explain.
3. If the mean distance between
Venus
and the Sun is about 0.7 astronomical units, determine by means
ofa scaled
diagram
(see
below),
the valueof the maximumpossible angularseparation between Venus
and the Sun as
seen from
the
Earth. Assumethat Venus moves
in a
circular orbit about
the Sun and
that thedistance between the
Earth
and the Sun is 1.0astronomical units.
Venus
ngleofMaximum
ngular Separation
Earth
NotToScale
Orbit
of
Venus
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Exercise
0-8
Visual Observations of the Planet Mars
Introduction:
Tonight youwill observethe planet Mars. Becauseit is the closest
outer planet
it often offers some
of
the
best viewing.
Measurements and Observations:
Using your telescope, locate the planet M ars and in your lab book mak e a sketch of the planet's
disk
as it
appears
in the field of
view. Sketch
anydetails on the
disk
that you can
detect
in moments of
clear
seeing when the earth s atmosp here steadies up for a few tenths of a second. N ote the colors
of
such details as
well
as the colorof the overall disk. Check for any objects in the field of
view
which
might be
satellites
of
Mars. Record
all of
your data
in
your
lab
book
as
well
as
the focal length
of the
eyepiecethat you used in making your observations.
Repeat
the above
observations using
an
eyepiece having
adifferent
focal length.
Recordall of
these
results
in your lab book.
Questions:
1. Discuss the problemsassociated with sketching Marsat the telescope.
2 . Compare
a nd
contrast
the
o bserved colors
of the
M artian disk
and
d etails perceived
at
high magnification
with tho se perceived at the lower mag nificatio n.
3. To
whatextent,
if
any,
did the
higher magnification permit
you to
better
seedetail on the
disk
of Mars?
4. If you
observed starlike objects
in the vicinity of
Mars
which
might
be
satellites
of
Mars, indicate what
additional
observations
yo u
would make
in
order
to
verify
or
disprove that such objects
are
indeed
Martian satellites.
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Exercise 0-9
Visual Observations
of the
Planet
Jupiter
Introduction:
Jupiter is the largest planet in our solar system. In fact it is larger than all the oth er planets
comb ined. Because of its size and b rightne ss it is one of the most interesting obje cts to observe throu gh
a small telescope.
Measurements and Observations:
Using your telescope
locate
th e
planet Jupiter ,
and in
your
lab
book make
a
sketch
of the
planet s
disk as it appears in the field of view. Sketch any details on the diskthat you can detect in moments of
clear seeing when th e
earth s
atmosph ere steadies up for a fewtenths of a second. Note th e colors
of
such details as well as the color of the overall disk. Check for any objects in the field of view which
might besatellitesof Jupiter. Record all of yourdata in your lab book as
well
as the focal length of the
eyepiece that
yo u
used
in
making your observations. Repeat
the
above observations using
an
eyepiece
having a
different focal
leng th. Record all of these results in your lab book.
No w
m ake a sketch in your lab boo k of Jupite r 's disk as
well
as any and all star-like objects in the
field ofview.
Determine the number of these objects whichlie along Jupiter s equatorial plane, or the line along
the largest dimension of Jupiter 's ob long disk. The n umber of such objects which are visible can range
from zero up to four, but usually at
least
two of these Galilean satellites are visible.
Having
identified the Galilean satellites
which
are visible in the telescope, note
the
order ofapparent
brightness
as
well
as any
colors
you are
able
to
detect
fo r
these objects.
Using the sky almanac chart provided to yo u by the instruc tor, identify which of the Galilean
satellites,
lo,
Callisto, Ganymede,an d Europa were visible at the t ime yo u made your observations.
Questions:
1.
What,
ifanyth ing ,i sunusual about th e overall shape of Jupiter 's disk?
2. Compare and contrast the observed colors of the details on Jupi ter's disk perceived at hig h magnifica tion
with those perceived
at the
lower magnification.
3. Are
there
an y
signs
of any of the
following
on
Jupiter 's disk: eruptive features, atmospheric features,
geological features, impact features?
4.
Jupiter
rotates
once every9.8hours. Throu gh what angle has the
planet
rotated whileyou are in the
laboratory session this evening.
5. Suppose that a background star was located in the field of view of you r telescope. Describe how you
might distinguish such
a
star from Jupiter's Galilean satellites.
6.
Suppose that
yo u
observed Jupiter
and saw no
Galilean satellites. Describe
the
conf igurat ion
of the
satellites which would produce such a result.
7. On the basis of your observations,
which
of the Galilean
satellites
do you think might be the
largest?
Explain
th e
assumptions that
you
make
in
formu lating your answer.
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Exercise 0-10
Visual Observations of the Planet Saturn
Introduction:
Tonight you will observe the pla net Sa turn. Satu rn is famo us for its glorious system of rings, and
is
a
very exciting object
to
view
in a
telescope. Although
it is
very distant ,
its
size
and
brightness make
it relatively easy to v iew.
Measurements
and
Observations:
Locate the planet Saturn in your telescope and place the planet s image in the center of the field of
view. Sketch the image of Satu rn in your lab book. Note the shape of the pla ne t, any starlike objects
yo u
can see in the field of
view, par t icular ly
in the
vicinity
of the
p lanet ,
the
orientation
of the
ring
system, and the approximate ratio R of the diameter of the outer boundary of the rings to the diameter
of
the
disk
of the
planet itself,
an d
record
all of
these observations
in
your
lab
book.
Questions:
1.
If Saturn s diameter
DS T
is about 120,000 kilometers, estimate the diameter of the outer edge of
Satu rn s rin g system in kilometers using the scaling relationship
=
DS T
x
R
2.
Using
th e
charts provided
b y
your inst ructor , determine which,
if
any,
of the
star-l ike objects
in
your
field of
view
are actual satellites of Saturn.
Identify
each by name.
3.
Every
15
years
the
rings
of the
planet Saturn appear edge-on
as
seen
from the
Earth. Show
by
means
of
diagrams
w hy
such
an effect occurs.
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Exercise
0-11
Visual Observationsof a Comet
Introduction:
Inthis
exercise you
will have
an
opportunity
to
observe
a
relatively
rare
event
in the night
sky,
the
appearance
of a
bright comet.
Measurements
and
Observations:
Locate
the
head
o f the
comet
in
you r telescope
and
carefully sketch
the
position
of the
bright central
region
w ith respect to any backgrou nd stars visible in the field of view. O n a separate page, sketch the
comet
head, noting
the
size
an d
brightness
of the
nucleus,
if
any, relative
to the
size
an d
brightness
of
the
overall surrounding
fuzz of thecomet s coma.
Carefully examine
the
region
of the sky
around
the
comet
and
determine
the
extent
to which the
comet
has a
visible
tail.
Note
the
color
and
brightness
distribution exhibited by the various regionsof the comet. Record all of your observations in your lab
book.
Estimate the ratioof the sizeofeach of the following relative to the sizeof the telescope'sfield of
view:
nucleus,
head,
tail.
Record these estimated ratios as
R
nu
cieus
^head>
-^taii
your
lab book.
After at
least
30 minutes sketch for a second time the position of the nucleus of the comet
relative
to the
background
stars.
Compare
your tw o
position sketches
an d
estimate
th e
ratio
-Rmo tion of the
amount of the comet's motionto the
size
of the telescope'sfield ofview. N ote also the valueof the total
elapsed timet
t{
between your
tw o
position observations.
Questions:
1. Fromyour observations, in what direction relative to the sun is the comet's tail pointing?
2.
Using
the
size
foeid of the
telescope's
field ofview in
degrees provided
to you by
your instructor,
find the
linear
sizes
of the
nucleus, head,
an d
tail
of the
comet
from
your estimated
R
values
and the
equation
linear
size
=
f i e l
x R x distance
200,000
3.
Determine
the
angular velocity V
a
ng
of the
comet
across the sky
using
Hmotion field
ang
t
* 1
How does your result compare with the moon's motion across the sky at a
rate
of about 0.5 degrees/hour?
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Exercise 0-12
Observations
ofMessier Objects
Introduction:
In 1781the F rench astronome r C harles Messier published a catalogue of 103 fuzzy patches of light
or
diffuse
objects
whichmight
be
mistaken
forcomets by
Messier
and other
comet hunters
of the
day.
The resulting catalogue contains some of the most famed and photographed objects in all of astronomy,
an d inthisexercise you will make observations of at leasttwo of the objects from Messier s
catalogue.
Measurements and Observations:
Using the finder chart prov ided to you by your instructo r, locate the first of yo ur Messier ob jects
and center it in your telescope sfield of view. Have your instructor verify
that
you have indeed found
the given objec t. Sketch the object in you r lab book, noting the shape, co loration, if any, and details
in the object, ifany.Estimate the ratio r of the angular sizeof the object compared to the diameterof
your telescope's
field ofview.
Record
all of
your observations
in
your
lab
book. Repeat
the
observations
for
each of the Messier objects assigned to you by your instructor. Record all of your results in your lab
book.
Calculations:
Calculate the approximate angularsizeaof eachofyour M essier objects usingthe scaling
equation
where
aa
is the angular diameter of your telescope's field of view as determined by you or given to you
by
yur
instructor. Enter
all of
your results
in
your
lab
book.
Calculate th e linear sizeD ofeach ofy our M essier objects using the equat ion
D
d
206265
whered is the distance to the object given to y ou by your instructor, and enter y our results in your lab
book.
Each of the following classes of objects can be found in the Messier Catalogue:
galaxies
open
star
clusters
supernova
remnants
globular clusters
gas/dustclouds
planetary nebulae
On
the basis of
yourobservations
and
previous calculations, identify
thecategory to
which
you
feel
each
of your Messier objects belongs. If you
feel
that a given object m ight belong in mo re than onecategory,
so
state. Enter
all ofyour conclusions in yourlab book.
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Questions:
1.
There
are
many other d iffuse
objects
which
can be
seen
in
small telescopes
but
which
do not appear in
the Messier Catalogue. If youwerea comet hunter howwouldyoudistinguish such an object f rom a
genuine
comet having
a
d iffuse appearance
and no
tail?
2
For those objects
which
could be assigned to more than one category discuss what additional observa-
tions and/or instrumentation
you
might make
or use in
order
to
resolve
the
ambiguity.
3
Why do you
suppose that there
are so
many fundamentally different kinds
of
celestial objects
in the
Messier Catalogue?
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Exercise 0-13
The Field of V iew of the Telescope
Introduction:
The angular diameter of a telescope tells us how large of a portion of the sky a telescope can see
at one
time.
For
example,
if 2stars are 1
apart
and
just
fit in the
telescopes
field of
view
the
angular
diameter of the telescope/eyepiece system is 1.
This
is
useful when
w e
view extended objects
like
nebulae,
an d
want
to
know
the
extent
to
which
a telescope with a given eyepiece
will
be able to see all of the nebula.
Measurements and Observations:
Align as accurately as possible the polar axis of your telecope mounting. Set your telescope on the
object assigned to you by your instruc tor. Tu rn off the telescope drive and m easure the total time T
that
it
takes
the
object
to drift
from
the
center
of the field of
view
to the
edge. R.ecord your
result in
your lab book.
Set the telescope on one of the aste risms in Table 0-13-1 on page 34, and on the basis of how much
or how
little
of the field of view th e
asterism occu pies, estimate
th e
angular size
of the
asterism
in
terms
of a fraction of the angular diameter of the telescope. If the asterism is larger than one field of
view
the
fraction will be larger than one. Record your results in your lab book.
Calculations:
Assumingthat it takes 240seconds for the field to drift atotal of one degree, calculate the angular
diameter
Da of
y our telescope s
field of
view using
Da
(degrees)
=
2 x T(sec)
240
degree
Calculate also the a ngular diame ter of the asterism you viewed.
Questions:
1. Explainwhy
your object appears
to drift acrossthe telescope sfield of
view.
2 . D erive the equation for D
a
Show explicitly why the 240 is present.
3.
How would th e values of T and
D
a be affected, if at all, if you employed a higher magnification eyepiece?
Explain.
4. If you were t o place Polaris (the Pole Star) in the field of
view,
describe ho w this object
would
drift
across the field of view, if at all. Explain
your
answer
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Table0 13 1
Possible Asterisms
to be
observed
The Belt of Orion
The
Milk Dipper
ow lin
Sagittarius
Corona Borealis
Th e
Head
of
Draco
The
Pleiades
Corvus
The Head of Hydra
The Circlet in Pisces
Th e
Keystone
in
Hercules
Th e ow l of the ig
Dipper
TheAquariusWater Jar
Delphinus
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Exercise O-14
Aligninga
telescope with
the
polar axis
Introduction:
In to nigh t s exercise you will align yo ur telescope with the polar axis of the
Earth
This is necessary
for
the telescopes clock drive to rotate the telescope in the proper direction. It is also necessary for the
setting circles
to be
accurate
Measurements and Observations:
First the wedge must be adjusted in altitude in correspondance with the lattitude of the Earth
Fort Collins is located at 40 N latt i tude so adjust the wedge so
that
the latt i tude scale points at 40.
Move
the entire telescope so
that
th e fork mount points north and
level
the telescope by adjusting
the tripods legs. You will find a bubble level on the telescopes mount.
Oncethe telescope is leveled make sur e the finder scope is
properly
aligned with the main telescope
Do this by locating an object on the g rou nd thro ug h the main telescope. Using the screws on the finder
scope adjust the finder scope until the object visible in the main telescope is right in the center of the
finder scopes cross hairs. Check the main telescope again to en sure the ob ject is still in the center of the
field
of
view of the telescope since you may have ac cidental y moved the telescope slightly when adjusting
the finder. Once the object is in the center of the field of
view
of both telescopes you can begin the final
stage of polar alignment.
Locate
the star Polarisin the sky. Thestar polaris is within a degree of the north celestial pole
and so
stays virtually stationary
at all
times. Move
the
telescope tube
so that it is
parallel
to the
polar
axis
of the
telescope
as
shown below
an d
lock
the DEC
lock.
Rotate the telescope or adjust the latitude scale until polarisis in the finder scopes field ofview.
Make min or adjustm ents u ntil polaris is near the center of the cross hairs of the the finder scope. Once
polaris is near the center of the finder scope check that polaris is near the center of the main telescopes
field
of
view. Make small adjustm ents to the telescope un til Polaris is near the cen ter. Have your
instructor
verify
yo u
have properly aligned your telescope.
Declination
drift
So far we have the telescope roughly polar aligned. This is usually good enou gh for most purposes.
However
if you want to use the telescope to do astrophotography the polar alignment must be very
precise. To mor e accurately alig n the telescope we use a technique called declination drift. This technique
is very time consuming so we will not actually align the telescope further. We will howev er use this
technique
to figure out in w hat d irection the alignm ent is off. In this m eth od we look at a couple of
guide
stars
and note how they
drift
out of the field of view. (Note: To actually use this method to
align
the telescope it is recommended
that
you have a piece of equipment called an illuminated reticle
ocular) .
Locate
a star
near
the
celestial equator
and
near
the
meridian (your instructor
can
help
you
wi th
this). Point y our telescope at this star using the highest magn ification eyepiece available. U se the D EC
fineadjustment knobs to determine which direction in the field ofview isnorth and which issouth Put
the
star
in the center of the field of
view
and turn the telescopes drive on. Time how long it takes for
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th e
star
to
d r i f t
out of the field of view if the
star
is
dr i f t ing
slowly you can time how long i t
takes
to
g o from th e
center
of the f ield of
view
to a
point half
w ay
between
t he
center
and the
edge
an d
multiply
by 2). Record how long th e star took to leave the f ield of view and in which direction the star moved .
If
th e
star
dr if ted south the
polar
axis of the telescope is too fareast. If the
star d r i f ted
north the
polar
axis is too far
west.
N ow f i n d a
star near
th e
celestial equator
an d
about
20
degrees above
th e
eastern horizon again
your instructor can helpyou with
this .
Repeattheprocedure above and time howlong thestartakes
to
d r i f t
out of the f ield of view. This time if the
star
d r i f t s
south the polar
axis
is too low, if the
star
drif ts
north
the polar
axis
is too high.
Calculations:
Using your f indings from the declination d r i f t method estimate where the
polar
axis is off with
respect to Polaris an d m ake a sketch showing where the polar axis is pointing . For example if we
f ound
that thepolaraxis was too fareast and was
high
andthat the the star near the
horizon
tookabout
twice as
long
to d r i f t out of the field of view I would
sketch
th e fol lowing.
Polar axis
Polaris
Questions:
1. Explain how astar near the meridian
d r i f t i ng
north means the polar axis is too far west.
2.
Explain
h o w astar
near
th e
hor izon d r i f t ing nor th means
th e
polar axis
is too
h igh .
3. What
would polar is
do in the f ield of
view
of a
telescope
that w as
slightly m isaligned
an d
whose d r ive
was on?
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Exercise 0-15
A Planetary Position
Introduction:
The
right ascension (RA)
and
declination (DEC)
of a
planet
are
constantly changing, while
the RA
and DEC of astarare relatively fixed.
Using
the setting
circles
on thetelescopeand the
known position
of several nearby stars yo u
will
determineth e
R A , D E C )
position o f a planet.
Measurements and Observations:
A s
accurately
as
possible, align
the
polar axis
of
your telescope
so
that
it
points toward
the
North
Star, Polaris. Plug
the
telescope
in to start it
tracking.
Set the
image
of the
calibration star given
to
yo u by
your instructor
in the
center
of the field of
v iew.
Set the setting
circles
so
that they read
the
correct
R A and
DEC.
Set the
image
of the first reference star
given
to you by
your instructor
exactly
at the centerof the telescope s field ofv iew. Record the angular readings
f r o m
botho f the axes o fyour
telescope mounting
in you lab
book. Repeat this procedure alternately
fo r the
planet being observed
and the
second
and
third reference
stars
given
to you by
your
lab
instructor.
Record
all of
these readings
in y ou r
la bbook.
Calculations:
Calculate
th e
corrections
A to
your telescope position readings
fo r the
three reference
stars
employed
us ing th e
fo l lowing
equations:
RA=JM reading)- -RA true)
ADEC=DC reading)-DEC true)
where the positionso f the reference
stars
ar e those suppliedto you byyour instructor.
Find the average values o f A R A a n d ADEC fo r your reference stars an d record these values as
RA
an d
DEC
in
your
l ab
book.
Using
th e
average values
o f the
readings recorded
f o r
your planet,
RA andDEC find the RA and DEC foryour
planet
usingthe followingequations:
7L4 planet)
=
J?l4 planet
reading)
-
AJL4
DEC planet)=DEC(planet reading) - ADEC
Record yourresults inyour lab book.
Quest ions:
1. Describe the effect o f apoorly aligned polar axis o nyour RA-DEC measurements.
2. Discusst he effect o nyour measurementso f no t havingthe telescope tracking drive turned o n whi le th e
measu rements ar e
being made.
3. Under what circumstances
wi l l
th e valueso f
A.RA
an d ADECb eequal to zero? Explain.
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Exercise O-16
The
Magnitude Limit
Introduction:
On e
of the
most important things
a
telescope allows
you to do is to see
objects
too
faint
to be
seen
withthe naked eye. Inthislab youwill determine the
brightness
of the faintest starswhichcan beseen
with your telescope.
Measurements and Observations:
Usingthe finder chart p rovided by yo ur instruc tor locate the assigned starcluster in your telescope.
Have your
lab
instructor verify that
yo u
have indeed located this object
in
your
field of
view.
As accurately
as
possible, count
the
numberN0
ofstars
that
are
visible
in
yourstar cluster through
your telescope. Record yourresult inyourlab book.
Calculations:
Plot
in your lab book the apparent magnitude m versus N, the number ofstars brighter than
magnitude
m
using
the
data provided
by
your instructor. Draw
a
best
fit
straight line through
the
resulting set of
points. Prom your graph
an d
using
the
value
yo u
obtained
fo rN0
read
off the
value
m L which correspondsto your value ofN0. Record your value of
m
in your lab book. This
value
of
m
represents
an
approximate value
of
your telescope's limiting magnitude.
Questions:
1. Estim ate the uncertainty in your value ofN 0 and the corresponding uncertainty in yourm^ value.
2. Howmany
stars
inyourclusterdo youestimatewouldbe
brighter
than magnitude +13? Explain.
3. As the value of m continues to increase, discuss what happe ns to the plot of N versus m? Explain.
4. Measure the diameter DT of you r telelscope's aperature. Calculate the ratio of the brigh tness between
the naked eye limit and the telescope limit using
Compare
this
value withthe theoretical valueof Rwhichisgivenby
whereD
eye
isequalto the diameterof the humaneye and isequaltoabout0.5 cm or 0.2 inches. Discuss
any significantdifferences between the R values.
5.
Will
the magnitude
limit
be the
save every night?
Explain why or why
not.
6. In terms of the m agnitude limit and your answ ers to the two questions above discuss the adv antage the
Hubble Space
Telescope
has over similar sized ground
based
telescopes.
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Exercise 0-17
The Seeing Angle
Introduction:
The seeing angle is a way ofmeasuring the resolving power of a telescope on a given
night.
The
resolving
power tells
yo u
about
th e
telescope s ability
to
resolve
tw o
nearby objects into
tw o
distinct
images.
Measurements
and
Observations:
Using your telescope, locate each of the pairs of
stars
indicated to you by your instruc tor. Have
your instructor verifythatyou have found each object onyour
list.
Determine which of
these
starpairs
appear
to you to be a) two
separate stars,
b) a
single
but
elongated image,
and c) a
single image with
no hint of elongation. Record your results in your lab book.
Calculations:
Determine th e value of the seeing angle for this night in the following fashion: If one of the images
is
elongated, note
the
angle
of
separation. This angle
is
equal
to the
seeing angle
for the
night.
If all
ofthe images areeithercleanly
separated
or appear single,
note
the largestangle ofseparation Lfor
which the image remains single in appearanc e. Record this value in your lab book. Note the smallest
angle S for wh ich the image is cleanly separa ted into two
stars.
Record this result in your lab book.
Estimate
the
angle
ofseeingA for the
night using
the
following
equation:
Enter your results into your lab book.
Questions:
1. W hat is the significance of the seeing angle of an observer?
2.
Give
a
couple
of
reasons
why the
seeing angle changes
from
night
to
night.
3. The
theoretical
resolving
power
of a
telescope indicates
the
existence
o f a
min imu m possible seeing angle
for a telescope. Explain why this m inim um seeing angle can never be realized.
4.
In
t e rms
of teh
seeing angle
an d
your answers
to the
above
tw o
questions, explain
the
benefits
of the
Hubble
Space Telescope over similar sized grou nd based telescopes.
5. Is it possible for the seeing angle to be improved (made smaller) on a given night? Explain.
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Exercise O-18
The
Visual Magnitude
of a
Variable
Star
Introduction:
Variable stars
ar e
stars whose brightness varies periodically
in
time.
Th e
period
of the
star's
brightness is related to the mean absolute magnitude of the star. Thus if we measure the
apparent
magni tude
of the star
over time
w e can
determine
a lot
about
th e star,
especially distance.
In
this
lab
we
will
measure the apparent magnitude at one instant.
Measurements
and
Observations:
Locate the variable star assigned to you by your instructor in your telescope. Also identify tw o
comparison
starsin the field of
view w hose brightnesses bracket
the
apparentbrightness
of
your
variable
star. Have the instructor verify that you have indeed located the variablestar in your telescope.
Assign
a
grade
or
rating
to the
brightness
of the
variable star
as it
appears
to you in the
telescope according to the following scale:
Description Actual Magni tude
As
bright as the brighter comparisonstar MBR
Brighter than
halfway but not as
bright
as the
brighter comparison
star
MBR
Halfway in brightnessbetween the twocomparison stars MBR
Fainter than halfway but not as
faint
as the fainter comparison star MBR
As
faint
as the
fainter comparisonstar MBR
AM =
MFT
Calculations:
Calculate the actual magnitude for the variablestar by first determiningth e valueA M = MFT
MBR, whereMF T is the magnitudeof thefainterofyourtw ocomparison
stars
an d MBRis the magnitude
of th e brighter ofyour tw o comparison stars. Using this value for AM, calculate th e visual magnitude
of your variable star according to the values listed in the
table
above for a given rating. Record all of
your results in your lab book.
Questions:
1. Whatcolor does your variablestar appear to be when viewed through your telescope?
2.
Estimate
th e
uncertainty
in
your value
of M.
3. How does your measured value of m com pare with the ma ximum brightness listed for your variable
star?
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Exercise
O-19
The
Distance
to a
Globular Cluster
Introduction:
In
this exercise
you will
obtain
th e
distance
t o a
globular cluster using
a
technique often employed
by astronomers in dealing with remote objects in the universe.
Measurements and Observations:
Locate the
globular
cluster assigned to you by
yourinstructor
and center the object in
your
tele
scope s field of view. Estimate the ratio r of the ap parent size of the g lobular cluster relative to the
size of the entire field of view of the telescope. En ter your measurement in your lab book. Repeat this
measurement for at
least
one other eye piece and e nter those results in your lab boo k s well.
Calculations:
Calculate th e angular diameter
of the globular cluster fo r each eyepiece measurement using the
relation
a=ra
a
where
a
is the angular diameter of the telescope s field of view as measured by you or provided yo u
by
your instruc tor. Conve rt your results into arcseconds (one degree
=
3600 arcseconds.)
an d
enter your
results in your lab book. A ssumingthat the ty pical globular cluster has a linear diam eter of about 325 light
years,f ind the distance d to the globular cluster using the relationship
d(light years)=
325 x 2.06 x 105
Calculate
the
distance
to the
cluster measured
fo r
each eyepiece used. Find
th e
average value
of the
distance
an d
enter your result
in
your
la b book.
Questions:
1. Estimate the unc ertain ty in the value of the clu ster distance from the variation in values obtained with
different eyepieces.
2. As you employ different eyepieces, w hat quantities will remain the sam e in this exercise? What quantities
will
change w ith a change of eyepiece?
3. In
what year
did the
light from
the
globular cluster
yo u
observed leave
that
cluster?
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Exercise 0-20
Observations
of the Sun
Int roduct ion:
Because
our sun is the
star closest
to us, it has
been
studied
more than
any other star. It is the
only
star
close enough
to
show considerable details
on the
surface. Because
the sun is so
bright
on e
must be extremely careful not to look directly at the sun.
Measurements
and
Observations:
Place
the solar filter on your telescope. Have your instructo r
verify that
your telescope is indeed
safe fo r
observing
th e
sun.
Sketch the sun s disk in your lab book, recording the numb er and
pattern
of sunspots that ar e
visible,
any
structure
that you are able to see in the
individual sunspots,
and any
variation
in the
light
intensity over
t he
s un s disk. R ecord
all of
your results
in
your
lab
book
as well as the
time
an d
date
of
your
observation.
Determine
the number g of overall sunspot groups
that
you observed and the value of s, the
total
number of
indiv idual
spots.
Record your results
in
your
la b
book.
Calculations:
Calculate the observed sunspot nu mber N using the
defining
equation
=
W g
s
and record this result in your lab book.
Questions:
1.
Discuss
th e
factors which could
affect th e
observed value
of N for (a) a
given telescope
and (b) different
observers using
different
telescopes.
2. How
would
y ou
show that
th e
sunspots
you
observed
were no t
specks
of
dust
or
dirt
on the telescope s
lens or
mir ror?
3.
When Galileo
reported the
discovery
of
sunspots,
many
of his contemporaries
took
the
view
that these
objects were in fact planets passing between the
Earth
and the sun. Describe the observation(s) you
would make to prove Galileo correct.
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Indoor xcercises
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Excercise 1-1
Math
Review and Scaling
Introduction:
In this lab we will review some tools necessary to do basic astronomy.
Measurements and Observations:
Section
1 -
Math review
D ur ing
th e
semester
w e will
have
to do a
small amount
of
basic algebra.
The
main thing
to
r emember is whatever I do to one side of an equation I m ust do to the other. To solve an equation I
systematically isolate the variable I am lookingfor by mu ltiplying the correct factors to both sides of the
equation, so that the variable I want to solve for is alone on one side of the e quation in the num erato r.
A s
an example wewill solve the equation Z =
~
for X.First I must get X out of the denom inator of
th e
right hand side,
to do
this
I
m ult ip ly both s ides
b y
X,
which
leaves
m e
with
th e
equationX Z =Y.
N ow
I need to get
X
alone so I divide both sides by Z or equivalently mu ltiply both sides by
4).
(X)Z=-(X) = > XZ = Y = >
XZ
= Y
The following are the
ru les
f ors implifying
expressions with exponents.
X
n
X
Y
n
n
=
(XY}
n
(X
n
)
m =
Xn'm X
n
Y
m
cannot
e
simplified
Com pound fractions are fractions wher e either the numera tor or the den om inator also have
frac-
tions.
To simplify a
compound fract ion , bring
th e
bottom
fraction up to the top and flip it
over
as
shown below.
x
Y)
x l
)
Section
2 -
M ath wi th uni t s
When
you do
mathematics
on
num bers with uni ts
th e
result
m ay or may not
have
a
u n i t .
The
rules
to
determine
if it has a
uni t ,
and if it
does have
a
uni t , what
that
u n i t
is, are
simple. S imply
stated
whatever you do mathematically to a num ber you must do to the units. So if you divide a num ber with
uni ts
of
meters
by a
number with uni ts
of
seconds
th e
result
will
have units
of
meters
per
second
) .
A s an
example lets
say I m
using
the
equationX
=
L
^
wherea
= 2
m,b =
3
Kg,
and
c
= 4
s then:
X
C2mf-(3Kg) 4m
2
-3Kg
4-3m2-Kg
4s)
The
u n i t
fo r
X
here
i s
meters squared times Kilograms
per
second
or
equivalently Kilogram meter
squared per second).
It is
possible
for all of the
uni ts
to
cancel out,
th e
result
in
this case simply
has no
uni ts .
A
pure
number such asthisgives a
comparison
between two
objects.
For
example
to
compare
the diameter of
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earth (12756
Km)
to the diameter ofMars (6787
Km)
I would find the ratio of their diameters.
D
earth
12756Km
6787
Km
=
1.879
This tells meearth is 1.879 times larger than Mars. Note this is true regardless of what units the
diameter ofearth and Mars are measured in as long as they were measured in the same units.
This
is seen
often
in
astronomy
-
giving sizes
and
masses
in
te rms
o f known
celestial objects (normally
the
earth
or the
Sun) .
Ratiosof like quantities can be used to find scales, and to do un it transform ations. We will see how
this works in the next section and in a fu ture lab.
Section
3 -
Scaling
If I
look
at a
picture
of twotrees that are of
equal distance from
the
camera
and the
picture shows
on e of the trees being twice as tall as the other, then the tree actually is twice as tall as the
other.
If
I
know
th e
actual height
of one of the
trees then
I
know
the
scale
of the
picture.
In
order
to find the
height of theother
tree
I simply measure the height ofboth
trees
on the pictures and set up the
ratio
of
the size of the unknow n object on the picture to the size of the k nown object on the picture. I
also
set
up the
ratio
of the
actual size
of the un kn own
object
to the
actual size
of the
kno w n object. Since
th e
ratio
of the picture sizes is equal to the ratio of the actual size w e can now set up the
following
equality.
Measurement of unknow n object on picture _ Actual size of unk now n object
Measurement
o f
know n object
on
picture Actual size
o f
known object
I then solve for the number that I don t know (Actual size ofunknow n o bject).
Sometimes the scale for a picture is already known. The scale may be given as how the size of an
objecton the
p ictu re relates
to
it s real height, i.e.
1cm
=
Smiles.
Calculations:
Section
1 Math
review
Solve the following equations for
X
a =b
=Z
Simplify
the
fo l lowing
expressions.
c) X
2
-X
3 d) X3f e)
Section
2 - Math with units
Usingo =
2
m, b =3Kg, c= 4s,andg=10*J find the units ofK, V, M, P, W, andD.
a)
K =j6 (f ) b)V= *^p- c)M =
d)
P =
g-b-a e)
W =
f )
D =
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Section 3 Scaling
a
Figure
1 is a
p ic ture
of 3
bui ld ings .
W e
know bui ld ing
A is 400
feet tall.
Use
th is informat ion
to find
the heights of buildings B C .
i g u r e
1
b Use Figure 2wi thascaleof 3 cm = 4 Astronomical units to determine th e distance to go
from
A
B
-> C A in
Astronomical units.
Figure2
A
O
B
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Questions:
1. Th e
harmonic
law
relates
the
orbital period
of a
satellite
to the
radius
of the orbit. We can
write
the
hamonic law as:
a
_ G M
p 4^ 2
Where a is the
radius
of the
orbit,
p is the
orbital period
and M is the
mass
of the
object being orbited,
andG is a constant. Solvethe harmoniclaw for the orbital period.
The
orbital
period
is
related
to the
velocity
of the
satellite
by
27T
V
Use
this relationship
to find the
velocity
of the
satellite
i n
terms
of the
radius
of the
satellite
and the
Mass
of the
object beingorbited.
If
G has
units
of . 2 s isseconds),a has
units
of
m meters)
and
mass
has
units
of Kg Kilograms),
what
are the
units
of the
orbital period?
Whatare the unitsof the velocity?
2. The
largecrater
in thefollowing pictureis the
crater
Tycho.
Tycho
has a
diameter
of 85 Km. Use the
technique
in
Appendix
A-3 to
determine
the
diameter
of
Tycho on the picture and then determine the actual diameter of the small crater just to the right of Tycho
indicated by the
arrow)?
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Excercise
1-2
Unit transformations, and Calculators
Introduction:
In
this
lab we
will
continue
to review
some tools necessary
to do
basic astronomy
that we
begin
in
Math Reviewand Scaling.
Measurements and Observations:
Section 1 -Unit transformations
W e
can use
ratios
to do
unit transformations
if we
know
the
conversion factor.
The
conversion
factor
is just the ratio of one unit to ano ther. For example if I wish to find how many seconds are in
2.4 minutes
I set up the
ratio
of
seconds
to
minutes which
is
equal
to the
conversion factor
Jfseconds
60
seconds
2.4 minutes 1minute
I no w just solve for the unkn own X).
Section
2 -
More
on
unit transformations
When
I
solve
forX in the
above equation
I get
/
60
seconds\ in
seconds)
= 2.4
minutes
x
1
minute
Soto
change units
I
simply
multiply
the
number
by the
conversion factor
to get to the new
unit.
I
just have
to
make sure
I
write
my
conversion factor
so
that
the old
units
totally
cancel leaving
me
just
with
the new units.
Section 3 - Scientific notation
Scientific
notation allows
us to
write very large
or
very small numbers
in a
convienient fashion.
A
number written
in
scientific
notation
is in the
following
format
Y
x
10 where
Y
is a
decimal number
and
n isan
integer.
The
integer
n
tells
us how far to
move
the decimal
point the sign
tells you what
direction to move it) in order to write the
number
ou t
long
hand. For positive
n
you move the decimal
n
spaces
to the right (these are largenumbers) fornegativenyoumovethe decimaln
places
to the left
these
are
small numbers).
For
example:
4.2 x
106=4200000
and 5.2 x10~
5= .000052
If a
number
is
written
ou t
long hand
and you
wish
to
wri te
it in
scientific notation
yo u
determine
ho w many places yo u must move the decimal point so that there is one digit in
front
of the decimal
point.
If you had to
move
the
decimal point
n
places
to the left the
exponent
is n. If you had to
move
the
decimal point n places
to the
right
the
exponent
is
n.
For
example:
89000
= 8.9 x
UP
and
.0000034
- 3.4 x 10
6
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Section
4 -
Significant Figures
Whenever we
measure something
we
cannot measure
it to an
infinite level
of
accuracy. W hen
we
report a measuremen t we mus t
relay
the level of accuracy of the measurem ent. W e do this by rep orting
the number
wi th
the proper number of
significant
f igures. For example when I use a metric ruler (one
with centimeters)
to
measure
th e
length
of
something
I can only
measure
to an
accuracy
of
^
of a
centimeter, therefore
it
doe sn t m ake sense
to
report
a
measurement
of
1 52
cm
with this ruler since
w e
cannot be sure of the 2.
To determine the number of significant figures a number has we simply
follow
a cou ple of rules.
1) D igits other than zero are always significant.
2) Final zeros are always significant.
3) Zeros between two other significant digits are always significant.
4) Zeros between a decimal point and the first non-zero digit are never significant.
The
following
table gives several numb ers and the n um ber of significant figures it has.
Number Significant f igures
1.2 2
1.30 3
1.002
4
.00003 1
Often
t imes
we
mus t
do
calculations
of
numbers
we get
from
making measurements.
It is
possible
that the various measurements can be measured to
different
accuracy. For example I may be able to
measure
the
length
of an
object
to
j^
of a
centimeter,
but can
measure
the
mass
to
j^j
of a
ki logram.
A ny calculations
we do
wi th thesenumbers m ust correctly handle
th e differing
level
of
accuracy between
th e
two measurem ents. This is done with a simple rule
which states
that the result should have the
same number
of
significant
figures as the
number wi th
the
least number
of
significant
figures
used
in
the calculations. For example if I add 3.2 and 3.47 your calculator will give you 6.67, but you should
report
6.7 in
order
to
keep
t he
correct number
o f
significant
figures. The
moral
of the
story
is
that
yo u
ca n
roun your numbers,
and you can use
this rule
t o
determine
how
many digits
to
round them
to .
Section
5 -
Using
a
scientific calculator
Y ou will be using your calculator throughout the semester. There are a coup le of special keys
you must
be
aware
of in
order
to use it
properly. These
are the
square root key,
th e
exponentiate
key, scientific notation key, and the trigonom etric function (sin, cos, tan) keys. Th ere are many, m any
kinds of calculators out there and many ways to enter data into them, so it is not possible to cover all
possibilities here. Instead you
will
either have to play
with
your calculator until you figure out how to
use
it, or you
will
have to consult your calculators owners ma nual, or consult your instructor.
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Calculations:
Section 1 - U nit transformations
Knowing
that there
axe
2.54cm
in 1
inch
use the first
method
fo r
doing unit t ransformations
to
determine how long in inches a stick isthat is 7
cm
long .
Section 2 - More on unit transformations
Use
the second method for doing unit transformations to perform the
following