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

Answer:

106417026.88435 m

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

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

The radius of the satellite's orbit is 106417026.88435 m