Question

The mass of a satellite in geostationary orbit is 1,847 kg. The mass of Earth is 5.97*1024 kg. Because of the force Earth exerts on the satellite, it accelerates. The magnitude of the acceleration is 0.223 m/s2, and it is directed towards Earth. What is the magnitude of the force in N the satellite exerts on Earth

Answer 1

411.88 N

Step-by-step explanation:

Given that:

mass of satellite m = 1847 kg

mass of the earth M = 5.97 × 10²⁴ kg

centripetal acceleration a = 0.223 m/s²

The magnitude of the force exerted by the earth on the satellite = the centripetal force that is being exerted by the satellite.

∴

`m (v^2)/(r) = G (mM)/(r^2)`

`ma = G (mM)/(r^2)`

`G (mM)/(r^2)= 1847 * 0.223`

`G (mM)/(r^2)= 411.88 \ N`