Question

Calculate the speed of a satellite moving in a stable circular orbit about the Earth at a height of 5200 km

Answer 1

Gravitational constant = G = 6.674 x 10^-11 m³kg^-1s^-2

Mass of the Earth = M = 5.972 x 10²⁴ kg

Mass of the satellite = m

Radius of Earth = R_e = 6.378 x 10⁶ m

Height of the satellite from the Earth's surface = H = 5200 km = 5.2 x 10⁶ m

Radius of the orbit = R

R = R_e + H

R = 6.378x10⁶ + 5.2x10⁶

R = 11.578 x 10⁶ m

Speed of the satellite = V

The centripetal force needed for the circular motion of the satellite is provided by the gravitational force between the Earth and the satellite.

$\frac{mV^{2}}{R} = \frac{GMm}{R^{2}}$

$V = \sqrt{\frac{GM}{R}}$

$V = \sqrt{\frac{(6.674\ast 10^{-11})(5.972\ast 10^{24})}{11.578\ast 10^{6}}}$

V = 5867.27 m/s

Speed of the satellite in circular orbit about the Earth at a height of 5200 km = 5867.27 m/s