Total mechanical energy of orbiting satellite

AI Thread Summary
To calculate the total mechanical energy of a 200 kg satellite in a geosynchronous orbit, the radius of the orbit is essential but initially unknown. The satellite's period is 24 hours, which can be used to derive the radius using Kepler's third law, R^3/T^2. The gravitational constant (G) is crucial for determining the gravitational force acting on the satellite, which relates to its orbital velocity and radius. By substituting known values into the equations of motion and gravitational force, the radius can be found, allowing for the calculation of total mechanical energy. Understanding these relationships is key to solving the problem effectively.
aloman
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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



WNC=E2-E1

Fc=mac

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

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

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



WNC=E2-E1

Fc=mac

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].
 

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