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Astro 1:HW 4 Solutions (Winter 08)

Astro 1:HW 4 Solutions (Winter 08) - UCSB Winter 2008 Astro...

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UCSB Winter 2008 Astro 1 - Homework #4 Solutions 2/1/08 4.2 In what directions do the planets move relative to the background stars (or if you like, the celestial sphere) when they are in direct motion? When in retrograde motion? How does the sun move relative to the background stars? The other planets move around the Sun in the same way that the Earth does, that is, counterclockwise looking down from the north celestial pole and in more or less the same plane. So normally (normal at least for the superior planets), when the planets are in direct motion, they appear to move from west to east relative to the background stars. When the (superior) planets are in retrograde motion, when the Earth is passing them by in it’s own faster orbit, the motion is from east to west. The inferior planets just move from one side of the Sun to the other. The Sun itself is stationary relative to our orbit, so it always moves west to east. 4.9 4.9 Is it ever possible to see Mercury at midnight? Mercury is one of the two inferior planets, so its orbit is smaller than our own. That means when Mercury is closest to us, it is between the Earth and the Sun. When Mercury is farthest away from us the Sun is between it and us. In both cases Mercury is in the same direction as the Sun, so we can only see it during the day. When Mercury is not in line with the Sun it will appear to one side of, but never far from the Sun. 4.14 What are the foci of an ellipse? If the Sun is at one focus of a planets orbit, what is at the other? Wikipedia says: ”In mathematics, an ellipse (from the Greek ???e????, literally absence) is a locus of points in a plane such that the sum of the distances to two fixed points is a constant. The two fixed points are called foci (plural of focus)”. In the book the condition that the sum of distances to two points is fixed is demonstrated by a loop of string of fixed length allowed to slide around two thumbtacks at the foci (p.75). In the solar system, the planets follow elliptical orbits with the Sun at one focus and nothing at the other. NOTHING. 4.19 A comet with a highly elliptical orbit (that means the foci are really far apart) has a period of 125 years. At the perihelion, the comet comes VERY close to the Sun. What is the comet’s average distance from the Sun? What is the farthest it can get from the Sun? The average distance from the Sun is just the semi-major axis (a) (see Box 4-2 or note 1
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that for one limiting case of the ellipse, the circle, the semi-major axis is just the radius, which is clearly the average distance from center). We can get (a) from Kepler’s third law.
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