1. Properties of Stars How do we measure stellar luminosities?
How do we measure stellar temperatures?
How do we measure stellar masses?

2. Brightness of a star depends on both distance and luminosity.
Its color tells us its temperature (recall blackbody radiation).

3. Luminosity:
Amount of power a star radiates
(energy per second = watts)
Apparent brightness:
Amount of starlight that reaches Earth
(energy per second per square meter)

4. Thought Question
These two stars have about the same luminosity— which one appears brighter (i.e. has a larger apparent brightness) ?
A. Alpha Centauri
B. The Sun

5. Luminosity passing through each sphere is the same.
Area of sphere:
4π (radius)2
Divide luminosity by area to get brightness.

6. The relationship between apparent brightness and luminosity depends on distance:
We can determine a star’s luminosity if we can measure its distance and apparent brightness:
Luminosity = 4π (distance)2  (Brightness)

7. Thought Question
How would the apparent brightness of Alpha Centauri change if it were three times farther away?
A. It would be only 1/3 as bright.
B. It would be only 1/6 as bright.
C. It would be only 1/9 as bright.
D. It would be three times as bright.

8. The parallax angle depends on distance.
Parallax Angle as a Function of Distance

10. Parallax Angle and Distance
One degree has 60 ‘arcminutes’ and one arc minute has 60 arcseconds.
So there are 3600 arcseconds in one degree.

11. Parallax and Distance
The inverse of the parallax angle in arcseconds equals the distance to an object in parsecs.
The nearest star is about 4 light years away, so p = 0.75 arcseconds.
This is the largest parallax angle, all other stars have small p values. 11

12. Most luminous stars:
106LSun
Least luminous stars:
10-4LSun
(LSun is luminosity of the Sun)

13. Hottest stars:
50,000 K
Coolest stars:
3000 K
(Sun’s surface is 5800 K)

14. Remembering Spectral Types
(Hottest) O B A F G K M (Coolest)
Oh, Be A Fine Girl/Guy, Kiss Me
Only Boys Accepting Feminism Get Kissed Meaningfully

15. Which of the stars below is hottest?
Thought Question
Which of the stars below is hottest?
A. M star
B. F star
C. A star
D. K star

16. Lines in a star’s spectrum correspond to a spectral type that reveals its temperature:
(Hottest) O B A F G K M (Coolest)

17. Spectral Type Spectral types form a temperature classification system.
It is based on the fact that different spectral lines occur at different temperatures.
The problem is that you need very long exposure times to measure faint spectral lines.
So can only do a few thousand stars this way.
To classify millions of stars we use the stars color to estimate the blackbody temperature (i.e. to estimate the spectral type).
The color of a star can be measured with only a very short exposure time.

18. To measure Stellar mass we use Binary Stars
Orbit of a binary star system depends on the strength of gravity.
So the orbits depend on the mass of the two stars.

19. Types of Binary Star Systems
Visual binary
Eclipsing binary
Spectroscopic binary
About half of all stars are in binary systems.

20. Visual Binary
We can directly observe the orbital motions of these stars.
We can only see visual binaries if they are very near Earth.

21. Eclipsing Binary We can measure periodic eclipses.
Download an eclipsing binary animation from
We can measure periodic eclipses.

22. Spectroscopic Binary
Download a spectroscopic binary animation from
R. Pogge, Ohio State University.
We determine the orbit by measuring Doppler shifts.

23. We measure mass using gravity.
Isaac Newton
We measure mass using gravity.
Direct mass measurements are possible only for stars in binary star systems.
4π2
G (M1 + M2)
p2 = a3
p = period
a = average separation
This should look familiar … it is Newton’s general expression for Kepler’s 3rd Law.

24. Need two out of three observables to measure mass:
Orbital period (p)
Orbital separation (a or r = radius)
Orbital velocity (v)
For circular orbits, v = 2πr / p v r M

25. (MSun is the mass of the Sun.)
Most massive stars:
100MSun
Least massive stars:
0.08MSun
(MSun is the mass of the Sun.)
(some very rare stars may have > 100 MSun)

26. Now do the lecture tutorial section on Binary Stars.
When you have finished do the tutorial section on Parallax and Distance.