Answer to Question #4584 in Mechanics | Relativity for Lala

Question

Find the speed of a satellite moving around the earth in a circular orbit that has a radius equal to three times the earth's radius of 6.38 106 m.

Answer 1

R- Earth radius, R= 6 378 100 m
The speed of satellite moving around the earth at a distance of r from the center of the earth is:
v = √[G*m(earth)/r].

Since G = 6.67 x 10^-11 N*m^2/kg^2, m = 6.0 x 10^24 kg, and r = 1.28 x 10^7 m:
v(satellite) = √[G*m(earth)/r]
= √[(6.67 x 10^-11 N*m^2/kg^2)(6.0 x 10^24 kg)/(3R+R)]
= 3960 m/s.