# Total mechanical energy of orbiting satellite

1. Nov 9, 2012

### aloman

1. The problem statement, all variables and given/known data
what would be the total mechanical energy of a 200 kg satellite in a geosynchronous orbit around the earth? The only known data is the radius of the earth and mass of the earth the mass of the satellite, m=200 kg, it would have a period of T=24h, but i do not know the radius of the orbit.

2. Relevant equations

WNC=E2-E1

Fc=mac

3. The attempt at a solution

I don't know how to get an answer with out knowing the radius of the orbit. I tried to make use of the period however i would still need the radius as the velocity is dependent on the radius of the orbit.

I would appreciate any help.

2. Nov 9, 2012

### grzz

If F=ma is used for the satellite and the value of G is given then the radius of the orbit can be found.

3. Nov 9, 2012

### aloman

how would the gravitational constant help?

F=ma
GMEm=mv2
r2 r

the only thing i can think of would be

v2=GME
r

but then i have two unknowns the v and r.

4. Nov 9, 2012

### grzz

Note that v = rω

and ω = 2π/T where the value of T is known.

5. Nov 9, 2012

### PeterO

You can look up the Radius of the moon's orbit, and the Period of the Moon, then apply R3/T2 to find the radius of the orbit with a period of 24 hours [1 day].