Astronomy 1 / Section 3 (S. Myers)

Problem Set #2 (due Wed 14 Feb 1996 5pm)

Chapters and Problems refer to the Seeds textbook. Remember that in the end-of-chapter problems in Seeds, ``Problems'' and ``Questions'' refer to different sets of exercises.

1. Suppose Eratosthenes had found that at Alexandria at noon on the first day of summer the line to the Sun had made an angle of 30 degrees to the vertical. At the same time in Syrene, 5000 stadia south of Alexandria, the noon Sun fell straight down a vertical well. Assuming that the unit of length, a stadium, is 1/6 km, what would he have found for the circumference of the Earth?
2. Chapter 4, Problem 5 (p.79). Use Kepler's Laws to find the orbital period of the space probe.
3. Chapter 4, Problem 7 (p.79).
4. If a star rises at 8:30 pm tonight, at approximately what time will it rise two months from now?
5. The mean distance from the Earth to the Moon is 384,404 km and light travels at 299,793 km/sec. How long do radar waves take to make a round trip to the Moon?
6. If a satellite has a nearly circular orbit at a certain distance from the Earth's center, it will have a period of revolution equal to one day, and can thus appear stationary in the sky above a particular place on the Earth on the equator. This is called a geosynchronous orbit and is used for communications and TV satellites. Using the fact that a circular satellite velocity at the Earth's surface is approximately 8.0 km/s, calculate the radius of the geosynchronous orbit.
7. The Hubble Space Telescope has a resolution of 0.1 arcsec in the visible waveband. What is the equivalent linear resolution on Mars, Jupiter, and Saturn at their closest approach to Earth?

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