orbiting planets and work

[MackandBlues]

So I've read that the Earth does no work on the moon when the moon orbits around the earth because the centripetal force is perpendicular and thus no work done. Yet Kepler's laws say that kinetic energy changes in an orbit and thus since kinetic energy changes there is work being done. I'm confused! Physics is my weakness.

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[milski]

If the Moon had a perfect circular orbit around the Earth what you say about the work done on it by the Earth would be true. For a lot of purposes the circular estimation is good enough and there is not anything else to discuss.

According to Kepler's law, the orbit is actually an ellipse. In that case the kinetic energy does change and the Earth does a certain amount of of work. Depending on the position along the ellipse, this works can be either negative or positive. It can be proven that within 28 days, by the time the Moon makes a full orbit around the Earth and is at the same position where it was 28 days ago, the total work done on it by the Earth is 0 and it has the same kinetic energy as before.

 

[neurodoc]

If the Moon had a perfect circular orbit around the Earth what you say about the work done on it by the Earth would be true. For a lot of purposes the circular estimation is good enough and there is not anything else to discuss.

According to Kepler's law, the orbit is actually an ellipse. In that case the kinetic energy does change and the Earth does a certain amount of of work. Depending on the position along the ellipse, this works can be either negative or positive. It can be proven that within 28 days, by the time the Moon makes a full orbit around the Earth and is at the same position where it was 28 days ago, the total work done on it by the Earth is 0 and it has the same kinetic energy as before.

I get your argument about the work done by the earth on the moon (and vice versa), but wouldn't the system you describe be a "perpetual motion machine?" Since PMM's are thermodynamically impossible, there must be more to the reality... Unless there is some way that energy is being "injected" into the earth-moon system, some energy is being dissipated (either by work being done or by frictional/heat losses).

 

[milski]

I get your argument about the work done by the earth on the moon (and vice versa), but wouldn't the system you describe be a "perpetual motion machine?" Since PMM's are thermodynamically impossible, there must be more to the reality... Unless there is some way that energy is being "injected" into the earth-moon system, some energy is being dissipated (either by work being done or by frictional/heat losses).

It is not completely perpetual but fairly long running machine.

The loss of energy comes from tides, friction, collisions with other bodies... None of these is very significant, so it takes a few million years.

The argument for 0 total work is easily done for any conservative force and works for solid bodies, excluding friction and similar losses of energy, just like you noticed.

 

[neurodoc]

It is not completely perpetual but fairly long running machine.

The loss of energy comes from tides, friction, collisions with other bodies... None of these is very significant, so it takes a few million years.

The argument for 0 total work is easily done for any conservative force and works for solid bodies, excluding friction and similar losses of energy, just like you noticed.

It takes a few million years for what? I guess for the orbital radius (earth-moon) to decrease by a certain quantity, along with some changes in the rotational velocities both the earth and the moon about their own axes. It's interesting that the moon's rotation is currently such that it completes a rotation about the earth in exactly one rotation about the lunar axis...which is why only one hemisphere of the moon is always visible from earth.