If an answer is numerical you must show the equation for credit.

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Question 1: About what fraction of stars have planets?
D) 90%

Question 2: Which star is the coolest?
B) Red


Question 3: What is the temperature of a star with a peak in its spectrum at 475 nm?
2.9x10⁶/475 = 6,105 K

4) What does the size and color of the dots represent?
Brightness and temperatures.

5) Assuming that stars A and B have the same size dot, what is their difference (other than temperature)?
A must be larger than B

6) Assuming that stars B and D have the same color, what is their difference?
D must be larger than A

7) Which of the lettered stars in the image will likely be around the longest?
A, it is the most red and the dimmest. So most likely to be on the main sequence (as compared to C which must be a giant to be brighter) and the lowest mass.

A cloud collapses to form 4 stars. Star A is 12 solar masses, Star B is 3 solar masses, Star C is 0.8 solar masses and star D is 0.4 solar masses. These stars all begin the main sequence at the same time and would be roughly the same distance from us.

8: What is the total luminosity of these 4 stars (in solar units) on the main sequence?
This is L_MS=M^3.5 for each star and then added together.
12^3.5=5986, 3^3.5=47, 0.8^3.5=0.46, .04^3.5=0.04
Totals to 6034L_Sun

9: After 15 billion years, how many stars are still on the main sequence?
This is t_MS=1x10¹⁰/M^2.5 and if we work clever, we can work less. Massive stars evolve very fast, so begin with Star B.
t_MS=1x10¹⁰/3^2.5=6.4x10⁸=640 Million years, so already less than 15 billion. This means Star A would also be gone. Since Star C is less massive than our Sun and we know our Sun will last 10 billion years on the MS, we really need to check if Stars C and D will be around after 15 billion years. Start with Star C
t_MS=1x10¹⁰/0.8^2.5=1.75x10¹⁰=17.5 Billion years, so it will be around.
Since Star C will be around, Star D also will. So the answer is 2 stars will be left.

10: What provides the energy against collapse for a horizontal branch star?
Fusion of He into C/O

Question 11: What is the main sequence luminosity and lifetime for a 2.5 solar mass star?
L_MS=M^3.5=2.5^3.5=24.7L_Sun
t_MS=1x10¹⁰/2.5^2.5=1.0x10⁹=1 billion years,

Question 12: How will our Sun end?
As a white dwarf.