# Problem Set ONE

• Due Friday, January 17, 2001, at beginning of class.

1. If the Earth is rotating, you, by standing on the Earth's surface, must be moving through space. [Ignore the Earth's orbital motion around the Sun in answering these questions.]
• Assume you live at the equator of the Earth. How fast are you moving through space if Earth rotates? (Your final answer should be in km/sec.)
• Assume you rent a room from Santa Claus at the Earth's North Pole. How fast are you moving through space if Earth rotates?
• Assume you live in Nashville, TN (latitude of Nashville is 36 degrees North). How fast are you moving through space if Earth rotates?

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• Assume for simplicity that Jupiter's orbit around the Sun is a perfect circle. Calculate the velocity with which Jupiter moves through space as it orbits the Sun? (Your final answer should be in km/sec; see links for Jan  14-18 for help; use appendix in text for needed numerical values.)

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• If the plane of the Moon's orbit stayed absolutely fixed in space (the lunar, orbital plane is tilted about 5 degrees to the ecliptic plane), about how often could a solar and/or lunar eclipse occur?  What would your answer be if the tilt of the lunar orbital plane were 0 degrees? 90 degrees?

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• Use Kepler's third law to calculate the orbital periods for objects orbiting the Sun at distances of a) 0.1 AU and b) 100 AU.

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• Calculate:

• the mass of Jupiter in units of the mass of the Earth ("how many Earth masses is Jupiter?")
the diameter of Saturn in units of the diameter of the Earth
the mass of the Moon in units of the mass of the Earth
the mass of Vesta in units of the mass of the Earth
the volume of Pluto in units of the volume of the Earth