Total mechanical energy of orbiting satellite

[aloman]

Homework Statement

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.

Homework Equations

W_NC=E₂-E₁

F_c=ma_c

The Attempt at a Solution

I don't know how to get an answer without 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.

 

[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.

 

[aloman]

how would the gravitational constant help?

F=ma
GM_Em=mv²
r² r

the only thing i can think of would be

v²=GM_E
r

but then i have two unknowns the v and r.

 

[grzz]

Note that v = rω

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

 

[PeterO]

Homework Statement

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.

Homework Equations

W_NC=E₂-E₁

F_c=ma_c

The Attempt at a Solution

I don't know how to get an answer without 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.

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].