Astronomy HOMEWORK Chapter 2 9th ed 7. Which planets can never be seen at opposition? Which planets never pass through inferior conjunction? Inferior planets never acheive opposition, and superior planets never achieve inferior conjunction. Check figure 2-4 if this isn’t clear. Hence: neither Mercury nor Venus is ever seen at opposition; Mars, Jupiter, and Saturn never pass through inferior conjunction. 8. At what configuration (superior conjunction, greatest eastern elongation, etc.) would it be best to observe Mercury or Venus with an Earth-based telescope? At what configuration would it be best to observe Mars, Jupiter, or Saturn? Explain your answers. The best configuration to observe a planet is when it is at the greatest angular distance from the Sun. This is Greatest Elongation for the inferior planets and Opposition for the superior planets. 17. Convert: (a) 8.3 pc (parsec) into light-years; (b) 6.52 light-years into parsecs; (c) 8450 AU into kilometers; (d) 2.7 × 103 Mpc into kiloparsecs.

3.26 ly (a) 8.3pc=(8.3 pc) = 27.06 ly 1 pc 1 pc (b) 6.52 ly = (6.52 ly) =2.00 pc 3.26 ly 1.5 × 108 km (c) 8450 AU = (8450 AU) =1.27 × 1012 km 1 AU 1000 kpc (d) 2.7 × 103 Mpc = (2.7 × 103 Mpc) =2.7 × 106 kpc 1 Mpc

22. The orbit of a spacecraft around the Sun has a perihelion distance of 0.5 AU and an aphelion distance of 3.5 AU. What is the spacecraft’s orbital period? Refer to Figs 2-8a and 2-9 for the term major axis. The major axis is 3.5AU+0.5AU = 4.0 AU. Hence its semimajor axis is 2.0 AU. Use Kepler’s 3rd Law: P 2 = a3 = (2.0)3 =8.0. Take the square root to get the period P : P = p(8.0) = 2.8=2.8 yr. The period is in Earth-years if the semimajor axis is in AU for our solar system. 27. Which planet would you expect to show the greatest variation in apparent brightness as seen from Earth? Explain your answer. [Only consider situations when you can see the planet.] Mars. The factors to consider are: • How much percentage variation in illumination by the Sun is there for a given planet as it follows its orbit? • How much percentage variation is there in the distance to the planet from Earth? and • How much percentage variation is there in the fraction of the surface that we see illuminated? None of the planets makes a large percentage change in its distance from the Sun. Mercury only makes a moderate change in its distance from Earth, which tends to be canceled by its phases. Fact is, Mercury can hardly be seen except near Greatest Elongation, so it’s a never far from being a half-Mercury phase if visible. Venus makes a large fractional change (0.3 to 1.6 AU), but this is offset by the smaller fraction of illuminated surface we see due to the phases. See Fig 2-10. All the outer planets are seen in a near-full to gibbous phase, so there is little change in fraction of the surface we see illuminated. For Mars, the distance varies from 0.52 AU at opposition to 2.52 AU at conjunction (if this isn’t obvious, see table 2-3 and sketch the two orbits, marking opposition and conjunction). This is a factor of 5 in distance. Later we will see that this corresponds to a factor of 25 in apparent brightness. Jupiter’s distance varies from 4.20 to 6.20 AU, a factor of 1.5. The percentage variation in the distance to Saturn and the outer planets is even less. So: Mars shows the greatest variation in apparent brightness over a synodic period. If you found found “Mercury” on the internet (instead of thinking!), the author of that answer considers theoretical brightness when lined up with the Sun.