Horizontal Circle

Question

A 2.7×10^3 kg satellite orbits the Earth at a distance of 1.8x10^7 m from the Earths center. The satellite experiences a force of 3500 N from the Earth. What is the period of the satellite?

Answer 1

Centripetal Acceleration (a_c)

a_c = (3500 N)/(2700 kg) = 35/27 m/s²

Angular Velocity (ω)

a_c = r ω² where ω is the angular velocity in rad/s

ω = √(a_c/r)

Period (T)

T = 2π/ω = 2π√(r/a_c) = 2π√[(1.8 × 10⁷ m)/(35/27 m/s²)] = 22,754 s = 6.32 hr

Answer (rounded to 2 significant figures)

The period of the satellite is 6.3 hr