Chapter 4: Problem 10
Which planets can never be seen at opposition? Which planets can never be seen at inferior conjunction? Explain your answers.
Chapter 4: Problem 10
Which planets can never be seen at opposition? Which planets can never be seen at inferior conjunction? Explain your answers.
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Get started for freeIt is quite probable that within a few weeks of your reading this chapter one of the planets will be near opposition or greatest eastern elongation, making it readily visible in the evening sky. Select a planet that is at or near such a configuration by searching the World Wide Web or by consulting a reference book, such as the current issue of the Astronomical Almanac or the pamphlet entitled Astronomical Phenomena (both published by the U.S. government). At that configuration, would you expect the planet to be moving rapidly or slowly from night to night against the background stars? Verify your expectations by observing the planet once a week for a month, recording your observations on a star chart.
Imagine a planet like the Earth orbiting a star with 4 times the mass of the Sun. If the semimajor axis of the planet's orbit is \(1 \mathrm{AU}\), what would be the planet's sidereal period? (Hint: Use Newton's form of Kepler's third law. Compared with the case of the Earth orbiting the Sun, by what factor has the quantity \(m_{1}+m_{2}\) changed? Has \(a\) changed? By what factor must \(P^{2}\) change?)
How did the ancient Greeks explain why the Sun and Moon slowly change their positions relative to the background stars?
What is the difference between the synodic period and the sidereal period of a planet?
Use two thumbtacks, a loop of string, and a pencil to draw several ellipses. Describe how the shape of an ellipse varies as the distance between the thumbtacks changes.
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