# Cosmic perpetual motion?

Ok, I'm almost certainly incorrect but I want to see where I'm going wrong.

Let's say the earth had only ocean, and a little jut of land somewhere amongst this ocean that had a turbine that collected energy as water ran through it.

Now consider the moon orbiting the earth, pulling the water up at the closest point between the earth and moon, which then disperses again as the moon continues orbiting. Wouldn't this cause water to run through the turbine. And if the earth+moon was a closed system and the moon was on a perfect trajectory so that it never fell to the earth, wouldn't this be infinite energy over infinite time?

What am I getting wrong?
Thanks.

Related Classical Physics News on Phys.org
The tidal motion of the water is effectively damping the system; the moon loses energy and will slowly move towards the Earth. I think you are describing a very intricate cosmic dam.

The tidal motion of the water is effectively damping the system
the moon loses energy and will slowly move towards the Earth.
Wow!!! Thanksyou. How does the moon lose momentum though? Wouldn't you need a force acting on the moon to dislodge it from its "golden" trajectory and have it collide with earth?

tiny-tim
Homework Helper
Welcome to PF!

Hi operationsres ! Welcome to PF!
… And if the earth+moon was a closed system and the moon was on a perfect trajectory so that it never fell to the earth, wouldn't this be infinite energy over infinite time?
No, because the Earth-Moon system will gradually lose energy, probably by the Earth rotating slightly more slowly …

eventually the Earth would only rotate once a month, keeping the same face to the Moon, and then of course the tide wouldn't move, and the turbine wouldn't work!

D H
Staff Emeritus
The tidal motion of the water is effectively damping the system; the moon loses energy and will slowly move towards the Earth.
You are correct that the tidal motion acts as dampening effect. However, the change in the orbit of the moon depends on the rotation rate of the planet versus the moon's orbital rate. The moon will slowly move away from the planet if the planet's axial rotation rate is faster than the moon's orbital rate. The converse holds only if the planet's axial rotation rate is slower than the moon's orbital rate (and at that point the moon is so far from the planet that tidal interactions are very small).

You are correct that the tidal motion acts as dampening effect. However, the change in the orbit of the moon depends on the rotation rate of the planet versus the moon's orbital rate. The moon will slowly move away from the planet if the planet's axial rotation rate is faster than the moon's orbital rate. The converse holds only if the planet's axial rotation rate is slower than the moon's orbital rate (and at that point the moon is so far from the planet that tidal interactions are very small).
What if the two values are at the exact correct values so that the moon stays in orbit forever?

What if the two values are at the exact correct values so that the moon stays in orbit forever?
I believe the answer to this is in tiny-tim's post:

"eventually the Earth would only rotate once a month, keeping the same face to the Moon, and then of course the tide wouldn't move, and the turbine wouldn't work!"

This is a very nice little problem.

Oh so the tide sloshing around everywhere will have the dampening effect you guys are talking about and cause the earth's spin to slow? Why would this occur?

Or do you mean to say that the spin will slow because the spin is actually going against the gravity of the moon?

Wait a minute... the Earth doesn't have to be spinning for the tides to move. The moon just has to be orbiting earth?

I think the dominant mechanism would be viscosity. At the seabed, we use a "non-slip" boundary condition which states the fluid velocity is equal to the solid velocity. There are shear stresses due to the flow of the water which are transferred to the sea floor through this non-slip condition which create a torque on the Earth opposite to its angular motion.

I think the dominant mechanism would be viscosity. At the seabed, we use a "non-slip" boundary condition which states the fluid velocity is equal to the solid velocity. There are shear stresses due to the flow of the water which are transferred to the sea floor through this non-slip condition which create a torque on the Earth opposite to its angular motion.
That makes so much sense thanks for clearing it up.

Damn, no free energy!

What about if we alter the model so that the earth isn't spinning at all. Then we introduce an orbiting moon at the "golden" angle/momentum. The earth shouldn't start spinning as it's not currently spinning, the pressure to spin one way is counterbalanced by the pressure to spin the other way, both of these pressures extending perpendicular to the cross section of the point on earth that's closest to the moon. Is this wrong?

D H
Staff Emeritus
What about if we alter the model so that the earth isn't spinning at all. Then we introduce an orbiting moon at the "golden" angle/momentum. The earth shouldn't start spinning as it's not currently spinning, ...
What is this "golden" angle?

The Earth will start spinning in this scenario. What makes you think it won't?

Consider where high tide would be on such a flat, underwater Earth- always at a point whose radial vector points towards the moon (or, allowing a delay, somewhere the moon has recently been), because that is where the moon pulls the water.

As the moon orbits the Earth, it continually drags this high tide point around in circles, and through viscous action this moving body of water starts to exert a torque on the Earth in the direction of the angular momentum of the moon. So it will speed up.

What makes you think it won't?
Ignorance. MikeyW cleared it all up in his last post. Thanks a lot guys.

Could you have some multi-body system that acts as gravitational slingshots of each other that could endear continuous orbit without the planets eventually colliding or going off into space (with the cause preceding this being the changing rotational rate)? Hmm I'll have to think about it. Perhaps a computer simulation with an ever increasing number of bodies on each iteration can be carried out to determine if such a feat is possible. I guess it will turn out negative, no matter how many new bodies you add in different configurations, as a positive solution will yield free energy.

I know free energy is impossible, but I like thinking about loopholes as brain teasers.

Last edited:
D H
Staff Emeritus
Could you have some multi-body system that acts as gravitational slingshots of each other that could endear continuous orbit without the planets eventually colliding or going off into space (with the cause preceding this being the changing rotational rate)? Hmm I'll have to think about it. Perhaps a computer simulation with an ever increasing number of bodies on each iteration can be carried out to determine if such a feat is possible. I guess it will turn out negative, no matter how many new bodies you add in different configurations, as a positive solution will yield free energy.

I know free energy is impossible, but I like thinking about loopholes as brain teasers.
Torques will only arise if you have planets with movable parts. If the planet is rigid (eg. no water) then the gravitational force cannot distort it, and has nothing to "grab on to" to get it spinning. The water in this example is the stepping stone. It is distorted by the moon in the creation of tides, and this distortion holds energy like a spring when it is stretched. It then transfers this energy to the angular kinetic energy of the Earth.

If your planet is bare and has no water, you have nothing to distort, and there is no transfer of energy, just moving, but non-rotating, celestial bodies!

There are plenty of possible systems where the motion is eternally ongoing. One website has a series of the most interesting ones, and a little section on perpetual motion as well. I did a dissertation based on these algorithms so if you have some spare time there is a lot to be learnt from this website!

http://burtleburtle.net/bob/physics/eight.html

Torques will only arise if you have planets with movable parts. If the planet is rigid (eg. no water) then the gravitational force cannot distort it, and has nothing to "grab on to" to get it spinning. The water in this example is the stepping stone. It is distorted by the moon in the creation of tides, and this distortion holds energy like a spring when it is stretched. It then transfers this energy to the angular kinetic energy of the Earth.

If your planet is bare and has no water, you have nothing to distort, and there is no transfer of energy, just moving, but non-rotating, celestial bodies!
There should be SOME, a certain geophysical theory (wikipedia, tectonic plates :p) purports that the pressures on earth's crust caused by the moon orbiting causes tectonic plate movements.

It makes sense. If the earth has no spin and you plonk an orbiting moon, the constant forces on the earth should cause some dislodging of tectonic plates, which should cause spin of the earth, which should cause the eventual end of the system at some future time

There are plenty of possible systems where the motion is eternally ongoing. One website has a series of the most interesting ones, and a little section on perpetual motion as well. I did a dissertation based on these algorithms so if you have some spare time there is a lot to be learnt from this website!

http://burtleburtle.net/bob/physics/eight.html
Interesting, I'll have a look, thx.

Do you suspect it'd be possible to have an n-body system of which one body is covered with water?

Generally I think this will work. The main issue is finding stationary solutions of the n-body system, then the extra requirement is that the water body rotates in such a way that the high tide always points towards the centre of mass.

There are probably even stable systems which do this (three body system in an equilateral triangle configuration).

Generally I think this will work.
Yeah it makes sense that it would work... But doesn't that leave the door open for a free energy generator!?

No, because with the extra water condition I gave, the water on the planet is still with respect to the planet's surface, so any turbine you fix on the sea bed will not turn.

Oh so it would be impossible to have an n-body system, where one body has water and has fluctuating high-low tides? Its high tide would have to be in the same spot? If no to the latter, then how wouldn't the turbine move?

My guess would be yes, it would be impossible to have a stationary such system- it would decay.