Question

A 37.4 kg satellite circles planet Cruton every 7.57 h. The magnitude of the gravitational force exerted on the satellite by Cruton is 94.3 N. (a) What is the radius of the orbit? (b) What is the kinetic energy of the satellite? (c) What is the mass of planet Cruton?

These are what I got, all of them the HW website said were wrong:
(a) 2.21e7 m
(b) 4.87e8 J
(c) 1.85e25 kg

Let me know how you get to your answer! Thanks.

Answer 1

Mass of satellite, m = 37.4 kg

Time period of revolution, T = 7.57 h

Angular frquency of revolution, ω = 2π/T = (2*3.142) / (7.57 * 60 * 60) rad/s = 2.3x10^-4 rad/s

a) Let the radius of circular orbit be r.

The gravitational force acting on satellite by planet Cruton equals the centrepetal force = mω²r = 94.3 N

(37.4 * (2.3x10^-4)² * r) = 94.3

r = 4.77x10⁷ m

b) Kinetic Energy of satellite = (1/2)mv² = (1/2)mω²r² = (1/2) * 37.4 * (2.3x10^-4)² * (4.77x10⁷)² J = 2.25x10⁹ J

c) Let the mass of planet Cruton be M.

Gravitational force acting between Cruton and satellite = GMm/r² = 94.3 N

(6.67x10^-11) * M * 37.4 / (4.77x10⁷)² = 94.3

M = 8.6x10²⁵ kg