Question

A satellite has a mass of 5966 kg and is in a circular orbit 4.12 × 10⁵ m above the surface of a planet. The period of the orbit is 1.9 hours. The radius of the planet is 4.58 × 10⁶ m. What would be the true weight of the satellite if it were at rest on the planet’s surface?

Answer 1

Orbital speed , v = 2pi*[4.58e6+4.12e5]/(1.9*60*60)

                    = 4586 m/s

v = sqrt(GM/r)

4586^2 = 6.67e-11*M/(4.58e6+4.12e5)

4586^2*(4.58e6+4.12e5)/[6.67e-11] = M

   M= 1.574e24 kg

weight on planet surface, F = GMm/r^2

         = 6.67e-11*1.574e24*5966/(4.58e6)^2

      = 29860 N answer