# Homework Help: Energy of Satellites(Homework question)

1. Apr 27, 2015

### Vlad137

Hi,

1.
I have a question all based upon a 100kg satellite in orbit 620km above Earth's surface,
I need to find the total energy (at rest), kinetic energy (in orbit), and binding energy (in orbit) of said satellite.

2.
I have tried to get the answer for the kinetic energy in orbit using:
1/2mv^2 = Total Kinetic Energy

I believe this is correct, getting the velocity by using the satellite motion formula v = sqrt[(GM)/r], where r is the radius of the earth + the distance the satellite is from the earth's surface.

3.
1/2(100kg){sqrt[(2GM)/r]}^2 = Total Kinetic Energy
1/2(100kg)[(6.67 x 10^{-11} x 5.98 x 10^{24}kg) / (6.38 x 10^{6}m + 620'000m)]
Total Kinetic Energy = 2.85 x 10^{9} Joules
(is this correct???)

However, I'm having trouble grasping how to get total energy and binding energy.
Could someone explain binding energy to me in terms of a satellite in orbit?

I understand the total energy during orbit will involve kinetic energy, but it asks for energy at rest and I'm not sure which type of energy it has during this time? Is it grav. potential energy?

Any help would be appreciated, thank you.

2. Apr 27, 2015

### Staff: Mentor

Hi Vlad137,

In future, please keep and use the formatting template headings when you create a new thread in the homework sections of Physics Forums.

The two types of energy that are important to orbits are kinetic energy and gravitational potential energy. You have stated a formula for kinetic energy, can you state one for gravitational potential energy?

The total mechanical energy is the sum of the above two energies, and is a constant for a given orbit. Orbits with total energies less than zero are bound orbits. If the energy is greater than or equal to zero then the obit is not bound an the object will head off to infinity (unless it happens to impact the central body it's orbiting).

I'm not sure what your question means by the "total energy (at rest)". Perhaps they're looking for the gravitational potential energy alone.

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