Total mechanical energy of orbiting satellite

In summary, to find the total mechanical energy of a 200 kg satellite in a geosynchronous orbit around the earth, you will need to know the radius of the orbit. Without this information, you can use the formula F=ma and the value of G to find the radius, or you can look up the radius and period of the Moon and apply R3/T2 to find the radius of the orbit with a period of 24 hours.
  • #1
aloman
8
0

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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  • #2
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
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
Note that v = rω

and ω = 2π/T where the value of T is known.
 
  • #5
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].
 

What is the total mechanical energy of an orbiting satellite?

The total mechanical energy of an orbiting satellite is the sum of its kinetic energy and potential energy. In other words, it is the energy required to keep the satellite in orbit.

How is the total mechanical energy of an orbiting satellite determined?

The total mechanical energy of an orbiting satellite is determined by the satellite's mass, its speed, and its distance from the center of the object it is orbiting.

Why is the total mechanical energy of an orbiting satellite important?

The total mechanical energy of an orbiting satellite is important because it determines the stability of the satellite's orbit. If the energy is too high, the satellite may escape its orbit. If it is too low, the satellite may crash into the object it is orbiting.

How does the total mechanical energy of an orbiting satellite change over time?

The total mechanical energy of an orbiting satellite remains constant as long as there are no external forces acting on the satellite. However, if the satellite experiences drag from the Earth's atmosphere or gravitational pulls from other objects, its energy may change over time.

Can the total mechanical energy of an orbiting satellite be increased or decreased?

Yes, the total mechanical energy of an orbiting satellite can be increased or decreased by changing its speed or distance from the object it is orbiting. This can be achieved through the use of thrusters or gravitational assists from other objects.

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