Can someone tell what I'm doing wrong with this question?

Question

A satellite circles the earth in an orbit whose radius is six times the earth's radius. The earth's mass is 5.98  10²⁴ kg, and its radius is 6.38  10⁶ m. What is the period of the satellite?

I used the formulas v = Sqrt GM/ r and then t=2pi r /v and I got 5067.85

Answer 1

Hi Giselle V.,

You have the equations correct. With v = √(Gm_e/r) and T = 2πr/v you should get T = 2π√(r³/Gm_e).

T = 2π√{[6*6.38x10⁶]³/[(6.67x10^-11)(5.98x10²⁴)]} = 74511.66 seconds or 20.70 hours.

I hope this helps, Joe.