Question

A satellite has a mass of 5959 kg and is in a circular orbit 4.85 × 105 m above the surface of a planet. The period of the orbit is 2.4 hours. The radius of the planet is 4.52 × 106 m. What would be the true weight of the satellite if it were at rest on the planet’s surface?

Answer 1

generally for circular orbit R you can say \(\large m \omega^2 R = \frac{GMm}{R^2}\)

so \(\large GM = \omega^2 R^3 = \left( \dfrac{2\pi}{T} \right)^2 R^3\)


if the object were at rest on the planet's surface radius \(r_o\) its weight W would be \(W = \dfrac{GMm}{r_0^2}\large = \left( \dfrac{2\pi}{T} \right)^2 R^3 \dfrac{m}{r_o^2}\)

Answer 2

you have all the numbers you need but you need to be very careful how you use them...