HOMEWORK SET #3
DUE: 17 OCTOBER

• show all steps in the simple required calculations. That way, if you make an arithmetic error on a question, it still may be possible for us to assign partial credit.

• write complete sentences. Be legible! We can't give a grade to something we can't read.

• cleanly labeled diagrams are almost always helpful and sometimes are required for a complete explanation.

• come to the help sessions if you are not absolutely clear on how to do any of the questions.

1. The orbits of the planets are not perfect circles (especially the orbits of Mercury and Pluto) and so they obviously receive higher solar fluxes when they are closer to the Sun than when they are farther away. Compare the apparent luminosity of the Sun seen at the surface of the Earth when the Earth is at its maximum and minimum distances from the Sun. Repeat the calculation for Mercury. Comment!

2. Star A has absolute magnitude m_A = +8, star B has m_B = +14, and star C has m_C = -2. Calculate how much more luminous star B is than star A. How much more luminous is star C than A? How much more luminous is star C than B?

3. What will the apparent magnitude of the Sun be, as viewed from a distance of 10 parsecs? (That is, compute its absolute magnitude.) The Sun's apparent magnitude is about -26.5. Comment!

4. Using all the data in Table A-7 (Appendix), make a plot that represents the HR diagram for the "Nearest Stars." You can use the HR diagrams of Chapter 8 to give you a guide as to how this should be constructed. Comment on the relationship of these stars' average properties (L,T) to that of the Sun.

5. Repeat this graphical exercise for "The Brightest Stars" (Table A-9). So, you should have gotten a very different-looking plot. Why?

6. Suppose you are an astronomer on a planet orbiting the brightest star in our skies (Sirius, or Alpha Canis Majoris A; see Table A-9), and suppose you look out toward our solar system. Without worrying about the relative brightnesses of the Sun and Jupiter in this question (you will see only the Sun, right?), what is the maximum back-and-forth angular wobble that you could see from your vantage point near Sirius for a) Jupiter, and b) the Sun, as they go around each other? Hint: see figure 8-11 of your text. A picture will help here a lot! I now grant to you all the typical, standard astronomical equipment, and ask you to observe the Sun-Jupiter system. If typical positional accuracies achievable with direct images are about 0.01 arc seconds, could you detect the wobbles of either of these objects?

7. Continuing with the Sun-Jupiter system: what are the orbital velocities of the Sun and of Jupiter around their common center of mass (consult your picture for the preceding question, and remember that distance equals velocity multiplied by time)? If the maximum accuracy attainable with present-day Doppler shift techniques is about 3 meters per second, could you detect the solar motion via the Doppler shifts of its spectral lines?

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