2. Homework #8
1) Suppose a comet of mass 2000 kg smashed into the Sun. It was measured to be traveling at 10 km/s. How much momentum was transferred to the Sun?
2) How much kinetic energy was transferred?
3) compare that to the amount of energy the sun gives off every second…

3. f a 1 / d2 Luminosity of Stars
Luminosity – the total amount of power radiated by a star into space.
Apparent brightness refers to the amount of a star’s light which reaches us per unit area.
the farther away a star is, the fainter it appears to us
how much fainter it gets obeys an inverse square law
its apparent brightness decreases as the (distance)2
f a 1 / d2

4. The apparent brightness (flux of radiant energy (f )) of a star depends on two things:
How much light is it emitting: luminosity (L) [Watts = Joules/sec]
How far away is it: distance (d) [meters]
f a L / d2 = L / area

5. f = L / 4pr2 4pr2 Luminosity of the Sun, L = 3.9x1026 Watts
Flux of radiant energy from the Sun = luminosity / area = f
f = L / 4pr2 r
4pr2
(Units are W/m2)

6. Colors of Stars Stars come in many different colors.
The color tells us the star’s temperature according to Wien’s Law.
Bluer means hotter!

7. lmax = 2.9x10-3 T
f = 5.67x10-8 T4

8. Masses of Stars
Mass is the single most important property of any star.
at each stage of a star’s life, mass determines…
what its luminosity will be
what its spectral type will be
The mass of a star can only be measured directly by …
observing the effect which gravity from another object has on the star
This is most easily done for two stars which orbit one another…a binary star!

9. The orbit of a binary star system depends on strength of gravity
I’m not sure where this came from, if it’s not on the CD, let me know.
The orbit of a binary star system depends on strength of gravity

10. Binary Stars (two stars which orbit one another)
Optical doubles
two unrelated stars which are in the same area of the sky
Visual binaries
a binary which is spatially resolved, i.e. two stars are seen (e.g. Sirius)

11. Binary Stars Spectroscopic binaries
a binary which is spatially unresolved, i.e only one star is seen; the existence of the second star is inferred from the Doppler shift of lines.

12. Binary Stars Eclipsing binaries
a binary whose orbital plane lies along our line of sight, thus causing “dips” in the light curve.

13. P2 = 42 a3 / G (m1 + m2) Binary Stars
The stars orbit each other via gravity.
So the laws of Kepler & Newton apply!
Remember Newton’s version of Kepler’s Third Law:
P2 = 42 a3 / G (m1 + m2)
If you can measure the orbital period of the binary (P) and the distance between the stars (a), then you can calculate the sum of the masses of both stars (m1 + m2).

14. SO...

15. For a few thousand stars we can now find:
the distance
the total luminosity
the temperature (color or spectral type)
the radius
CAN WE FIND ANY
RHYME, REASON, OR RELATIONSHIPS?

16. Looking for correlations:
Height vs. IQ ?
Height vs. Weight ?

17. L
B – V (Temperature
or spectral type)

18. The Hertzsprung-Russell Diagram
A very useful diagram for understanding stars
We plot two major properties of stars:
Temperature (x) vs. Luminosity (y)
Spectral Type (x) vs. Absolute Magnitude (y)
Stars tend to group into certain areas
BRIGHT
COOL
HOT
FAINT

19. burning stars reside on the main sequence of the H-R diagram
High-Mass Stars
Normal hydrogen-
burning stars reside on the main sequence of the H-R diagram
Low-Mass Stars

20. The Main Sequence (MS)
90% of all stars lie on the main sequence!

21. Stars with low temperature and high luminosity must have large radius
SUPERGIANTS
Stars with low temperature and high luminosity must have large radius
GIANTS

22. H-R diagram depicts:
Temperature
Color
Spectral Type
Luminosity
Radius
*Mass
*Lifespan
*Age
Luminosity
Temperature

23. Which star is the hottest?B
Which star is the hottest? D
Luminosity A
Temperature

24. Which star is the hottest?B
Which star is the hottest? D A
Luminosity A
Temperature

25. Which star is the most luminous?B
Which star is the most luminous? D
Luminosity A
Temperature

26. Which star is the most luminous?B
Which star is the most luminous? D
Luminosity C A
Temperature

27. C B
Which star is a main-sequence star? D
Luminosity A
Temperature

28. C B
Which star is a main-sequence star? D D
Luminosity A
Temperature

29. C B
Which star has the largest radius? D
Luminosity A
Temperature

30. C B
Which star has the largest radius? C D
Luminosity A
Temperature

31. Which star is most like our Sun?D
Luminosity B C
Temperature

32. Which star is most like our Sun?D B
Luminosity B C
Temperature

33. A
Which of these stars will have changed the least 10 billion years from now? D
Luminosity B C
Temperature

34. A
Which of these stars will have changed the least 10 billion years from now? D
Luminosity B C C
Temperature

35. A
Which of these stars can be no more than 10 million years old? D
Luminosity B C
Temperature

36. A
Which of these stars can be no more than 10 million years old? D A
Luminosity B C
Temperature

37. Regions of the H-R Diagram

38. How can two stars have the same temperature, but vastly different luminosities?
The stars have different sizes!!
The measured brightness of a star depends on 2 things:
surface temperature
surface area (radius)
The largest stars are in the upper right corner of the H-R Diagram.
f =  T4
f = L / 4  R2
so:
L =  T4 4  R2

39. L =  T4 4  R2
T R
Luminosity
L = constant
Temperature