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Example G.8: Time Periods and Orbital Velocities of Satellites

Example:

A satellite is revolving at a height of 100 km above the surface of the Earth. Find its time period and orbital velocity.

Given: mass of the Earth = 6 x 1024 kg and radius of the Earth = 6.4 x 106 m.

Solution:

The height at which the satellite orbits the earth is 100 km or 0.1 x 106 m.

Therefore, the distance of the satellite from the center of the earth is (6.4 + 0.1) x 106 m = 6.5 x 106 m.

Substituting r = 6.5 x 106 and M = 6 x 1024, the time period of the satellite is T = 10381.08 s from equation (G.20) and its orbital velocity is v = 3.08 x 103 m/s = 3.08 km/s according to equation (G.21).

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