Lab Astro Mannual (Outdoor and Indoor Labs)

7/26/2019 Lab Astro Mannual (Outdoor and Indoor Labs)

1/82

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


2/82

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


3/82

Outdoor xcercises


4/82

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?


5/82

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


6/82

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


7/82

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.


8/82

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


9/82

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


10/82


11/82


12/82

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

13


13/82

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?

14


14/82

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.

15


15/82


16/82

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?

19


17/82

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

21


18/82

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.


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.

23


19/82

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.


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.

25


20/82

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.

27


21/82

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?

29


22/82

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.


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.

31


23/82

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?

32


24/82

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.


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


25/82

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


26/82

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


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


27/82

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?


28/82

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.


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.


29/82

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.


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.

39


30/82

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.

41


31/82

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?


32/82

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.


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?

45


33/82

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.


34/82

Indoor xcercises


35/82

Excercise 1-1

Math

Review and Scaling

Introduction:

In this lab we will review some tools necessary to do basic astronomy.


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

51


36/82

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 =

52


37/82

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

53


38/82

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)?


39/82

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.


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

55


40/82

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.


41/82

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

Documents

Lab Astro Mannual (Outdoor and Indoor Labs)