# Homework Help: Velocity needed to maintain orbit

1. Jan 27, 2010

### BoldKnight399

An Earth satellite remains in orbit at a distance of 6104 km from the center of the Earth. What speed would it have to maintain? The universal gravitational constant is 6.67X10^-11 N m^2/kg^2. The mass of the earth it 5.88X10^24 kg. Answer in units of m/s.

So again, missed the class. I'm crying. Most of my classmates are crying. (the few exceptions finding everything else to do in the world BUT help....) I tried this:
I knew that it had to go into the equation:
Vt=2piR/T
since I didn't have T i used the equation:
R= [(G x m x T^2)/(4pi)^2]^(1/3)
sooo that became:

6104000m=[(6.67X10^-11)(5.98X10^24kg)(T^2)/(4pi)^2]^(1/3)
(2.274X10^20)= (3.98866X10^14)(T^2)/(4pi)^2
T=9488.369sec
so then plugging back in I got:

Vt=(2pi)(6104000m)/9488.369sec
thus the answer was 4042.06066 m/s

guess what? That was wrong.

If anyone has any ideas where I messed up or if I just had a "100% FAIL" moment, I would love to hear it.

2. Jan 27, 2010

### rl.bhat

Centripetal force on the satellite is
G*M*m/(R+h)^2 = m*v^2/(R+h)
S0 v=sqrt[GM/(R+h)]
Now solve.

3. Jan 27, 2010

Thank You!!