Chapter 17
By reading this chapter, you will learn
17-1 How we can measure the distances to the stars
17-9 How we can use binary stars to measure the masses of stars
172 How we measure a star’s brightness and luminosity
17-10 How we can learn about binary stars in very close orbits
17-3 The magnitude scale for brightness and luminosity
174 How a star’s color indicates its temperature
17-
5 How a star’s spectrum reveals its chemical composition
17-11 What eclipsing binaries are and what they tell us about the sizes of stars
17-6 How we can determine the sizes of stars
17-7 How H-R diagrams summarize our knowledge of the stars
17-
8 How we can deduce a star’s size from its spectrum

D = 1 / p
D = distance to a star in parsec
P = parallax angle
Parallax only works for the stars that we can measure the apparent change in position. 500lys is about the upper limit!
Hipparcos (89 – 93) contributed greatly for this purpose!

If too far for Parallax:
Apparent brightness of the stars and inverse square law!

Apparent magnitudes of the stars in Pleiades and
Orion’s surroundings

Now you are somewhat familiar with the method to measure distances, Please work on “Distant objects” worksheet (part of your homework for this week!)
Imagine that you have received pictures of children from near by planetary systems. Picture shows a child on his or her 12th birthday. The pictures were then send electronically to us on the day of the child’s birthday. (lys = light years)
• Yvone lives on a planet orbiting Garg, which is 9.5 lys away from the sun.
• RYAN lives on a planet orbiting NORDSTROM, which is 14 lys away from the sun.
• Julie lives on a planet orbiting Bray-Ali, which is 21.5 lys away from the sun.
• MALLEREY lives on a planet orbiting LEWIS, which is 6 lys away from the sun.
• RAQUEL lives on a planet orbiting VASQUEZ, which is 4.5 lys away from the sun.
• MICHELLE lives on a planet orbiting LA HUE, which is 8.2 lys away from the sun.

Proper / radial motions

Color -> Temp
(recall Wien’s law)

1. If a star has parallax angle of 1/5 arc-sec, what would be the distance to the star? A)1/5, b)1. c)5, d)25 pc
2. Star A and B have same luminosity. If star A is
4 times closer to Earth then star B, then
_____ to earthly viewer.: a=A is 4 x brighter, b=B is 4x brighter, c=A is 16 times brighter d=B is 16 times brighter, e=A is 64x brighter
3. Apparent magnitude is measure of: a=light output, b=light received by the observer, c=temperature of light source
4. Which color star is hotter? A=red. B=white, c=blue
Click “ enter to review the questions C, c, b, c

Color
O B-V
Temp (K)
30k
– 50k
B B-W 11k – 30k
A White 7500
– 11k
F Y-W 5900 – 7500
G Yellow 5200 – 5900
K Orange 3900 – 5200
M O-R 2500 – 3900
L Red
T Red
1300 – 2500
T<1300
L and T are brown dwarfs
Spectral types (O, B, A, F, G, K, and M), based on the major patterns of spectral lines
Williamina Fleming (standing): left,
Annie Jump Cannon: right

Stefan – Boltzmann law
L = 4 p
R 2 s
T 4
L = Luminosity
R = radius s
= constant
T = temp
Inverse square law
L = 4 p d 2 b
L = Luminosity b = brightness (W / m 2 ) d = distance

Inverse square law
L = 4 p d 2 b
L = Luminosity b = brightness (W/m 2 ) d = distance
Stefan – Boltzmann law
L = 4 p
R 2 s
T 4
L = Luminosity
R = radius s
= constant
T = temp
Use of these laws tell us distance, radius and luminosity.
How about mass?

1. Williamina Fleming and Annie Jump Cannon were involved in developing: a=luminosity class, b=spectral class, c=distance measurements
2. Which type of star is hotter? a=G2V, b=A1II, c=M4III, d=O1Ia e=K7IV
3.
The sun’s spectrum is perfect continuous spectrum. a=ture, b=false, c=we don’t know!
4. Which type of star is more stable? a=G2V, b=A1II, c=M4III, d=O1Ia e=K7IV
5. H-R diagram is a plot of: a=mass vs. temp., b=Hydrogen vs. radius, c=Luminosity vs. age, d=mass vs. luminosity, d=luminosity vs. temp.
Click “ enter to review the questions B,d,b,a,d

Visual binary : 2 stars can be observed as 2 with mutual gravity
Spectrum binary : appear to be one star with incongruous spectrum.
Spectroscopic binary : appear to be one but shows Doppler shifts
Optical Double : Appear to be close, but just close line of sight.

Kepler’s 3 rd law:
total
M = mass,
3
2 a = semimajor axis p = orbital period
Example:
Distance between two stars
= 1.8AU
Time to orbit each other =
0.7 years
M = (1.8) 3 / (0.7) 2 =

1. Binary system means: a=stars young, b=stars are very large, c=stars are old, d=2 stars
2. Binary system let the astronomers measure
____ for the first time: a=mass, b=temperature, c=age, d=Hydrogen content,
3. For the eclipsing binary, we can observe ____ to determine their motion. A=Doppler shift, b=Luminosity, c=apparent magnitude
(brightness), d=temperature change
Click “ enter to review the questions D, a, a&c