Geosynchronous satellites orbit the Earth at a distance of 42000km from the Earth's center. Their angular velocity at this height is the same as the rotation of the Earth, so they appear stationary at certain locations in the sky. What is the force acting on a 1500kg satellite at this height?

Question

Geosynchronous satellites orbit the Earth at a distance of 42000km from the Earth's center. Their angular velocity at this height is the same as the rotation of the Earth, so they appear stationary at certain locations in the sky. What is the force acting on a 1500kg satellite at this height?
Hint: recall that force is related to centripetal acceleration.

Angeline · Accepted Answer

thank you so much

drwls · Answer

The velocity is V
= 2 pi*42*10^6 m/(24 h*3600 s/hr)

The distance from the earth's center is R = 42*10^6 m

The centripetal force acting is
F = m a = M V^2/R

and equals the gravitational attraction force.