Question

A satellite orbiting the earth is directly over a point on the equator at 12:00 midnight every four days. It is not over that point at any time in between.Part AWhat is the radius of the satellite's orbit?

Answer 1

106417026.88435 m

Step-by-step explanation:

T = Time period of the satellite = 4 days

m = Mass of the Earth = 5.972 × 10²⁴ kg

G = Gravitational constant = 6.67 × 10⁻¹¹ m³/kgs²

Time period is given by

`T=2\pi\sqrt{(r^3)/(GM)}\\\Rightarrow r=\left((T^2GM)/(4\pi ^2)\right)^{(1)/(3)}\\\Rightarrow r=\left(((4* 24* 60* 60)^2* 6.67* 10^(-11)* 5.972* 10^(24))/(4\pi ^2)\right)^{(1)/(3)}\\\Rightarrow r=106417026.88435\ m`

The radius of the satellite's orbit is 106417026.88435 m