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Orbits - total energy?

Hi guys,

I was just looking through an old Gravitational Fields assessment we did in class a few months back and came across a question about a satellite in orbit around Uranus.

It's a multiple choice question, and whilst 2 of the options are fairly clearly wrong there are 2 that are a little harder to choose between. The question is:

Here are 4 statements A, B, C and D about the satellite in its circular orbit.

Which one of the statements is correct?

A: It's orbital path is on an equipotential surface.

B: It's total energy must be greater than zero for a stable orbit.

C:

D:

Now, I understand why A is correct but can't work out why B would be correct. Surely, in any orbit it would have some GPE and some KE? Or is it because you take GPE as negative and KE as positive so in some orbits the total energy would cancel to give a 0 'net' energy?

Any help is greatly appreciated.
Reply 1
Original post by Saxandthecity
Hi guys,

I was just looking through an old Gravitational Fields assessment we did in class a few months back and came across a question about a satellite in orbit around Uranus.

It's a multiple choice question, and whilst 2 of the options are fairly clearly wrong there are 2 that are a little harder to choose between. The question is:

Here are 4 statements A, B, C and D about the satellite in its circular orbit.

Which one of the statements is correct?

A: It's orbital path is on an equipotential surface.

B: It's total energy must be greater than zero for a stable orbit.

C:

D:

Now, I understand why A is correct but can't work out why B would be correct. Surely, in any orbit it would have some GPE and some KE? Or is it because you take GPE as negative and KE as positive so in some orbits the total energy would cancel to give a 0 'net' energy?

Any help is greatly appreciated.



Potential energy for orbits is usually defined to be the work done in bringing the mass from infinity to a distance r away. Given that gravity is an attractive force, this means GPE<0. If something is bound (stuck) in an orbit, can you relate the KE and the PE in terms of magnitude?
(Consider what happens as the speed of the satellite increases)
I'm not sure I follow - is the sum of the GPE and KE not constant for a circular orbit?
Original post by Saxandthecity
Hi guys,

I was just looking through an old Gravitational Fields assessment we did in class a few months back and came across a question about a satellite in orbit around Uranus.

It's a multiple choice question, and whilst 2 of the options are fairly clearly wrong there are 2 that are a little harder to choose between. The question is:

Here are 4 statements A, B, C and D about the satellite in its circular orbit.

Which one of the statements is correct?

A: It's orbital path is on an equipotential surface.

B: It's total energy must be greater than zero for a stable orbit.

C:

D:

Now, I understand why A is correct but can't work out why B would be correct. Surely, in any orbit it would have some GPE and some KE? Or is it because you take GPE as negative and KE as positive so in some orbits the total energy would cancel to give a 0 'net' energy?

Any help is greatly appreciated.


this... the short answer is that closed, i.e. circular or elliptical orbits have -ve energy
zero energy is the escape energy (i.e. parabolic trajectory) and +ve energy gives you a hyperbolic trajectory.

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