LAB 08

Astronomy 105 Laboratory

STELLAR PARALLAX

Lab 08 – Part 1

Heliocentric Parallax300 ly

1 AU Radar1 A.U.

Main-Sequence Fitting30,000 ly

Variable Stars300 Mly

billions of ly WD Supernovae

Cosmic

Distance

Ladder

Stellar Parallax

Sky - Angular Measurements

Locate “Star A” above the reference stars and “Star B” below

X

Distant

background

starsX

X X

Angular shifts

Telescope Field of View and Scale

Image of star Field

?

28”

A B

Known separation of stars A & B is 28 arc seconds

What is the angular separation of Stars C & D?

Find a unit conversion ( cm to arc seconds).

Measure the distance between A and B.

28 arc seconds is equivalent to 0.8 cm.

28 arc sec = 0.8 cm

0.8 cm

0.8 cm28 arc sec=

0.8 cm

cm1

arc sec=35

Plate Scale

Angular separation of Stars C & D

2.5 cm X 35 cm

arc sec = 88 arc sec

CD

MAIN-SEQUENCE FITTING

Lab 08 – Part 2

Open or Galactic Cluster

M13 - Globular Cluster

Distance-23,000 ly Size-150 ly

Finding a Star’s Distance

Stellar Parallax

Main-Sequence Fitting

1 2 3 4 5 6Brighter Dimmer

Magnitude Scale

Brightest stars in the night sky Faintest stars visible to

naked-eye

Measuring a Star’s Brightness

2.512

Magnitude Difference

Brightness Ratio (Brightness Difference)

1 (2.512)1 2.5 2 (2.512)2 6.3 3 (2.512)3 15.9 4 (2.512)4 40 5 (2.512)5 100 6 (2.512)6 251

Magnitude

Stellar Brightness

Apparent Magnitude (mv) - Brightness from Earth

Absolute Magnitude (Mv) - Brightness from 10 pc

Photometer

(measures

brightness)

10 meters1/4

Apparent Brightness and the Inverse-Square Law of Light

Apparent Brightness 1/d2

If this 100 Watt light bulb were observed to be 100 times fainter compared to the 10 meter distance; how far away is it?

√100 = 10

10 times farther away or 10 x (10 meters) = 100 m

100 W

100 W

100 W

100 W

20 meters

30 meters

40 meters

1/9

1/16

1370 watts/m2 343 watts/m2 55 watts/m2

Apparent Brightness 1/d2

Apparent Brightness and the Inverse-Square Law of Light

1 AU

= 4____1370

343

4 = 2

2 AU

= 25____1370

55

25 = 5

5 AU

Mv = 5

mv = 10

10 pc

Is the star closer than 10 pc

or farther away than 10 pc?

?

How much farther?

Distance Modulus = m - M

Distance Modulus = 10 – 5

If m-M > 0 then star’s distance > 10 pc.

If m-M = 0 then star’s distance = 10 pc.

If m-M < 0 then star’s distance < 10 pc.

Brightness Difference = 2.5125 = 100

= +5

Inverse-Square Law - Apparent Brightness ~ 1/d2

Star is 10x farther away than 10 pc or 10 X 10 pc = 100 pc

G2 V

√100 = 10

Finding a Star’s Distance

1. Brightness at standard distance (10 pc)

• Absolute magnitude

2. Measure apparent brightness

• Apparent magnitude

3. Use inverse-square law of light to find distance

Hyades Star Cluster

Pleiades Star Cluster

Taurus

Main-Sequence Fitting

Stars in a Cluster•Common Properties

•Distance

•Age

•Different Properties

•Spectral Types (temperature)

•Luminosity Class (size)

Main-Sequence Fitting

Pleiades stars have the same luminosities as the Hyades stars.

The Pleiades is 2.73 times farther away!

√7.5 = 2.73

They are farther away!

How much farther?

Why are the Pleiades stars 7.5 times dimmer?

Interstellar Dust

Reddens Light (stars appear cooler)

Dims Light (stars appear further away)

-4

-3

-2

-1

0

1

2

3

4

5

6

7

8

9

10

11

12

-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Ab

so

lute

Ma

gn

itu

de

(M

v)

Color Index(mb-mv)

Standard Main-Sequence

Pleiades Color-Magnitude Diagram

3.0

4.0

5.0

6.0

7.0

8.0

9.0

10.0

11.0

12.0

-0.30 -0.20 -0.10 0.00 0.10 0.20 0.30 0.40 0.50 0.60

Color Index

(mb-mv)

Ap

pa

ren

t M

ag

nit

ud

e (

mv)

9

1820

31

27

22

Color Index = 0.415

mv = 9.8temperature

Standard Main-Sequence

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

5.0

6.0

-0.30 -0.20 -0.10 0.00 0.10 0.20 0.30 0.40 0.50 0.60

Color Index

(mb-mv)

Ab

so

lute

Ma

gn

itu

de

(M

v)

Color Index = 0.415

Mv = 3.6

mv = 9.8

mv – Mv = 9.8 - 3.6 = +6.2

1. Using the average distance modulus

from several stars, calculate the

distance to the Pleiades star cluster.

2. Use the main-sequence fitting

technique to find the distance modulus

and calculate the distance to the

Pleiades again.

-4

-3

-2

-1

0

1

2

3

4

5

6

7

8

9

10

11

12

-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Ab

so

lute

Ma

gn

itu

de

(M

v)

Color Index(mb-mv)

Standard Main-Sequence

-4

-3

-2

-1

0

1

2

3

4

5

6

7

8

9

10

11

12

-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

Ap

pa

ren

t M

ag

nit

ud

e (

mv)

Color Index(mb-mv)

Pleiades Color-Magnitude DiagramAbsolute

Zero

Magnitude

THE END