Why does the total energy in a satellite's orbit change when it loses control?

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SUMMARY

The total energy of a satellite in orbit is defined by the equation -GMm/2r, where G is the gravitational constant, M is the mass of the Earth, m is the mass of the satellite, and r is the radius of the orbit. When a satellite loses control and descends towards Earth, its potential energy decreases as r decreases, converting into kinetic energy. While the total energy of the system remains constant in a closed system, the energy levels change according to the equation as the satellite transitions to a lower orbit, resulting in a more negative total energy value. This energy difference is a crucial aspect of orbital mechanics.

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Hi everyone. I know about the equations of gravitation but something is still bothering me.

The equation for total energy of a satellite in an orbit is -GMm/2r

However, when the satellite suddenly lose control and heads to the Earth, why does the total energy in the system change according to r? Excluding air resistance of course... I always thought in a closed system, total energy remains constant? I am quite blur and my teacher just asked us to memorize the eqns.

Thanks.
 
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I think the potential energy of the satellite is converted to its kinetic energy when it starts falling towards the Earth ... its potential gets lesser and lesser as r decreases i.e. as it falls towards the Earth ...

experts, please correct me if i am wrong, I am not very sure abt my answer :)
 
HMS said:
I think the potential energy of the satellite is converted to its kinetic energy when it starts falling towards the Earth ... its potential gets lesser and lesser as r decreases i.e. as it falls towards the Earth ...

experts, please correct me if i am wrong, I am not very sure abt my answer :)

We are talking about total energy here.

My best guess (another theory!haha) is that the Earth AND the Object is the system. But it still does not make sense as both objects are moving closer to each other (although distance moved by Earth is negligible), both are losing total energy... Why is there energy loss? I am still confused
 
qazxsw11111 said:
The equation for total energy of a satellite in an orbit is -GMm/2r
That's the total energy (kinetic plus potential) of a satellite in a circular orbit, where r is the radius of that orbit.

However, when the satellite suddenly lose control and heads to the Earth, why does the total energy in the system change according to r?
It doesn't.
Excluding air resistance of course... I always thought in a closed system, total energy remains constant?
Correct--the total energy remains constant.
 
So when it changes orbit, energy levels will follow the eqn -GMm/2r. When r is decreased (go to a lower orbit), -GMm/2r becomes more negative. So there is an energy difference. But where does the difference go?
 
Just another question (unrelated to this qn), when gravitational potential is 0 is gravitational field strength zero. I have a hunch that it isn't and cannot explain why or think up another example to support it. Anyone?
 
If you neglect friction why would the satellite change its orbit?

What do you mean by "lose control"?
If the orbit is changed on purpose then there is a force acting on the satellite (produced by the rocket engines).
Or the satellite may collide with something else - again external force.
 

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