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Problem 1 a. The apogee and perigee altitude (distance from the surface of Earth) of the...

Problem 1

a. The apogee and perigee altitude (distance from the surface of Earth) of the Chandra X-rays Observatory are 139,200 km and 9,620 km (final orbit after 4th burn, Aug 7, 1999). Estimate its orbital period (in hours). Hint: the mass of Chandra is much smaller than the mass of Earth.

b. Communications and weather satellites are often placed in geosynchronous “parking” orbits above Earth. These are the orbits where satellites can remain fixed above a specific point on the surface of Earth, i.e. their revolution period is equal to 1 sidereal day (8.6164 × 104 sec). At what altitude must these satellites be located? Note: the concept of geosynchronous satellite was invented by the Sci-fi author Arthur C. Clarke, and a geosynchronous orbit is also called “Clarke orbit”.

c. Is it possible for a satellite in geosynchronous orbit to remain “parked” right overhead any arbitrary location on the surface of Earth? Why yes or why not?

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