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5 November, 11:37

Suppose you are at the earth's equator and observe a satellite passing directly overhead and moving from west to east in the sky. exactly 11.0 hours later, you again observe this satellite to be directly overhead. assume a circular orbit. how far above the earth's surface is the satellite's orbit?

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  1. 5 November, 13:27
    If we are assuming a circular orbit and if it moves from west to east directly overhead you are on the equator. A satellite can move overhead west to east only above the equator. Now in 11 hours the Earth has rotated 11/24 of a revolution so the satellite has made 1 11/24 rev (which equals 35/24 rev) in that 11 hours. For a period of

    T=11 (24/35) * 3600 = 27154.29 sec.

    r^3 = T^2 (GM) / 4 (pi) ^2

    Earths mass (M) = 5.98 e24 kg

    G (a constant) = 6.673 e-11

    Earths surface radius (R) = 6.371 e6 meters

    r = satellite orbital radius in meters

    replacing and clearing r:

    r = 19533487.08 m (this is the distance from the center of the Earth)

    h = r - R = 19533487.08 - 6.371 e6 = 13162487.08 m above the Earth's Surface
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