Question

While in a geosynchronous orbit around Earth, a 560 kg communications satellite has a weight of 125 N. The distance of the satellite from the Earth's surface is?

Answer 1

Answer on Question #43411, Physics, Mechanics — Kinematics — Dynamics

While in a geosynchronous orbit around Earth, a 560 kg communications satellite has a weight of 125 N. The distance of the satellite from the Earth’s surface is?

Solution

Weight is equal to gravity force.

$F=\frac{GM_{Earth}m_{sat}}{(R_{Earth}+R_{orbit})^{2}}$

Hence, distance to surface is

$R_{orbit}=\sqrt{\frac{GM_{Earth}m_{sat}}{F}}-R_{Earth}=\sqrt{\frac{6.67\cdot 10^{-11}\cdot 5.97\cdot 10^{24}\cdot 560}{125N}}\approx 42.2\cdot 10^{6}-6,4\cdot 10^{6}=$

$=35.8\cdot 10^{6}\,m=35800km$

http://www.AssignmentExpert.com/