A satellite in Earth orbit has a mass of 109 kg and is at an altitude of 1.98 106 m. (Assume that U = 0 as r → ∞.)?

Question

(a) What is the potential energy of the satellite–Earth system?

(b) What is the magnitude of the gravitational force exerted by the Earth on the satellite?

(c) What force, if any, does the satellite exert on the Earth? (Enter the magnitude of the force, if there is no force enter 0.)

Answer 1

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Re = earth's radius = 6378 km = 6.378 x 10^6 m and altitude h = 1.98 x 10^6 m

let a = Re + h = 8.358 x10^6 m

Gravitational potential energy U = GMm/r -->  set r = a, m = 109 kg and M = 5.972 x 10^24 kg

U = 5.195x10^9 J

Force = F = GMm/r^2 = U/r = 621.54 N

F = force exerted by earth on satellite and by Newton's laws, the force exerted by the satellite on earth