Question

A satellite of mass 5530 kg orbits the Earth and has a period of 6680 s . Part A Determine the radius of its circular orbit. Part B Determine the magnitude of the Earth's gravitational force on the satellite.

Answer 1

Here,

part A)

let the radius of the circular orbit is r

as T^2/r^3 = 4pi^2/(G * M)

(6680)^2/r^3 = 4pi^2/(6.673 *10^-11 * 5.98 *10^24)

solving for r

r = 7.67 *10^6 m

the radius of the orbit is 7.67 *10^6 m

part B)

magnitude of earth's gravitational force = G * M * m/r^2

magnitude of earth's gravitational force = 6.673 *10^-11 * 5.98 *10^24 * 5530/(7.67 *10^6)^2

magnitude of earth's gravitational force = 37510 N

the magnitude of earth's gravitational force is 37510 N