In order for a satellite to move in a stable circular orbit of radius 6588km at a constant speed, its centripetal acceleration must be inversely proportional to the square of the radius r of the orbit. what is the speed of the satellite and the time required to complete one orbit? the universal gravitational constant is 6.67259e-11 nm^2/kg^2 and the mass of the earth is 5.98e24kg.

Explanation:

Given that,

Radius in which the satellite orbits, r = 6588 km

Solution,

The centripetal force acting on the satellite is balanced by the gravitational force acting between earth and the satellite. Its expression can be written by :

, M is the mass of earth

v = 7782.53 m/s

Let t is the time required to complete one orbit. It can be calculated as :

t = 5318.78 seconds

or

t = 1.47 hour

Therefore, this is the required solution.

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