A satellite will travel indefinitely in a circular orbit around a planet of the

Question

A satellite will travel indefinitely in a circular orbit around a planet of the normal component of the acceleration of the satellite is equal to g(R/r)^2, where g is the acceleration of gravity at tje surface of the planet, R is the radius of the planet, and r is the distance from the center of the planet to the satellite. Determine the speed of a satellite relative to Earth (g=32.2 ft/s^2, R = 3960 mi) if the satelitte is to travel indefinitely in a circular orbit 100 mi above the surface of the Earth. A satellite will travel indefinitely in a circular orbit around a planet of the normal component of the acceleration of the satellite is equal to g(R/r)^2, where g is the acceleration of gravity at tje surface of the planet, R is the radius of the planet, and r is the distance from the center of the planet to the satellite. Determine the speed of a satellite relative to Earth (g=32.2 ft/s^2, R = 3960 mi) if the satelitte is to travel indefinitely in a circular orbit 100 mi above the surface of the Earth.

Explanation / Answer

Solution:-

Given

Height of satellite from earth surface = 100 miles = 100*1609.34 meter

= 1.60934 *105 meter

Radius of earth = 3960 miles = 6.38 * 106 meter

Mass of earth(Me) = 5.58 * 1024 kg

Gravitational constant (G) = 6.67 *10 -11 N m2/kg2

r = radius of earth + Height of satellite from earth surface

r = 6.38 *106 + 1.60934 * 105 =   6.540934 *106 meter

Speed of satellite(v) = (G Me/r)

                                     = ( 6.67 *10-11 * 5.58*1024/( 6.540934*106))

                                   = 7543 m/s

Speed of satellite(v) = 4.68 miles/s    Answer

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