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Determine the speed of a satellite relative to the indicated planet if the satellite is to travel indefinitely in a circular orbit 100 mi above the surface of the planet. (See the information given in Probs. 11.153 and 11.154.)

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Answer:

v = √[ GM / (R + 160934.4 meters) ]

Explanation:

The speed of an object in a circular orbit (in meters per second) is

v = √(GM/r)

where

G = 6.6743e-11 m³ kg⁻¹ sec⁻²

M = the sum of the masses of the planet and the satellite in kilograms

r = the radius of the circular orbit in meters

If the planet's radius, R, is 100 miles, then

v = √[ GM / (R + 160934.4 meters) ]

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