Question

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

Answer 1

Answer: the radius of the satellite's orbit  is  r = 8.78×10⁷m

Explanation:

given the time period, T= 3days

converting the time in days to seconds is given as;

time, T=(3*24*60*60) sec

T=259200 sec

from the force relation;

mv²/r = Gm×M/r²

v²=G×M/r ---------------(1)

and

V=2pi×r/T

V²=4×pi²×r²/T²

====>

from equation  (1) , we have

4×pi²×r²/T²=G×M/r

this becomes;  4×pi²×r³/T² = G×M

r³ = G×M×T²/(4pi²)

r³ = 6.67×10⁻¹¹×(5.97×10²⁴)×(259200)²/(4pi²)

==> r=8.78×10⁷m

radius of the orbit, r=8.78×10⁷ m