# If earths rotation stoped, the moon would be released.

by cvjacques
Tags: rotation and gravity
P: 219
 Quote by EMFsmith ........ and in one interesting consequence of this is that the Moon is gradually drifting further and further away from the Earth at a rate of just under 4 centimeters per year.
Though I knew this was happening, it only just now occurred to me that the drift must be accelerating, even if only at the tiniest rate.
Thanks
PF Gold
P: 12,161
 Quote by narrator Though I knew this was happening, it only just now occurred to me that the drift must be accelerating, even if only at the tiniest rate.
What would be the reasoning behind that assertion? Are you referring to the 1/r potential?
P: 219
 Quote by sophiecentaur What would be the reasoning behind that assertion? Are you referring to the 1/r potential?
Excuse my ignorance, I may know it as something else, but what is the 1/r potential?

As for my reasoning: At some point, perhaps when the moon breaks free, it will depart from us at a much faster rate. Unless the drift remains at a constant speed until it does break free, then it must be accelerating away from us even now, if only at a tiny rate of acceleration.
 Sci Advisor Thanks PF Gold P: 12,161 Gravitational potential follows a 1/r law(?). Why do you suggest that the Moon can "break free"? That is not what is happening at all.
P: 277
 Quote by DaveC426913 What? The Earth is slowing its rotation and will eventually be tidally locked with the Moon.
I believe Sophie was refering back to the OP which implied a sudden, abrupt cessation of rotation.
P: 32
 Quote by narrator Though I knew this was happening, it only just now occurred to me that the drift must be accelerating, even if only at the tiniest rate.
Even though the Moon is drifting away, Gravity has an infinite range, the Moon will not just drift off into space and loose its orbit with Earth.
P: 219
 Quote by sophiecentaur Gravitational potential follows a 1/r law(?). Why do you suggest that the Moon can "break free"? That is not what is happening at all.
I read the following from a Wiki article

In classical mechanics, the gravitational potential at a location is equal to the work (energy transferred) per unit mass that is done by the force of gravity as an object moves to that location from a reference location. It is analogous to the electric potential with mass playing the role of charge. By convention, the gravitational potential is defined as zero infinitely far away from any mass. As a result it is negative elsewhere.

I think I understand it, but I could be wrong. I'm not sure I understand the "as an object moves" part. Is there a better way of wording it?

Why do I suggest the Moon can break free? If it's moving away from us at 4cm/year then at some point won't its own inertia will be stronger than the gravity which keeps it in orbit? Or will it remain in orbit, regardless of distance (at least until some other body pulls it from us)?
 P: 217 "...though even at that, the Earth-Moon system is not expending any energy." IIRC, the system is losing some energy to tidal friction / turbulence. The Moon's 'retreat' rate seems to have altered when the passage between South America and Antarctica opened, so tides could flow over the sill. Previously, 'retreat' rates seem to have depended on continental grouping, always changing due plate tectonics... Uh, IMHO, the Moon should reach an equilibrium at one of Earth's 'trojan' points -- L4 / L5...
P: 219
 Quote by Nik_2213 Uh, IMHO, the Moon should reach an equilibrium at one of Earth's 'trojan' points -- L4 / L5...
I gather you mean one of the Sun-Earth trojan points...?
Thanks
PF Gold
P: 12,161
 Quote by narrator Why do I suggest the Moon can break free? If it's moving away from us at 4cm/year then at some point won't its own inertia will be stronger than the gravity which keeps it in orbit? Or will it remain in orbit, regardless of distance (at least until some other body pulls it from us)?
It may be moving away at that rate at the moment but, as it gets further away, its Kinetic energy is getting less because the total Energy (PE plus KE plus rotational energy of the two bodies) of the system is constant (in fact, it's reducing because of energy lost as heat through friction). It is, basically, slowing down in its recession for the same reason that a ball slows down when thrown upwards. Its orbit is getting a small amount of energy from the Earth's rotation but this is only whilst it lags behind the Earth. When they become totally locked there is no more energy available to ' throw the Moon off any further.
As with many situations, you need to consider the availability of Energy if you want to determine what will happen. In this case, there would never be enough energy available for tho Moon actually to escape.
P: 219
 Quote by sophiecentaur As with many situations, you need to consider the availability of Energy if you want to determine what will happen. In this case, there would never be enough energy available for tho Moon actually to escape.
Thanks for the explanation. That makes sense. I suppose I sometimes compare the gravity of celestial objects with the attraction between magnets, while forgetting the overriding force of earth's gravity on the two magnets (amongst other differences).
P: 15,319
 Quote by Nik_2213 "...though even at that, the Earth-Moon system is not expending any energy." IIRC, the system is losing some energy to tidal friction / turbulenceb.
No. They are trading energy back and forth, changing rotations and orbital altitudes, but the the system is not losing any energy to some external recipient.
Mentor
P: 15,166
 Quote by narrator Though I knew this was happening, it only just now occurred to me that the drift must be accelerating, even if only at the tiniest rate.
In the long term, the rate is decreasing, not increasing. Tidal force is roughly a 1/r3 force. As the Moon recedes from the Earth the tidal forces on the Earth decrease (and decrease quickly thanks to that 1/r3 form). It is these tidal forces that drive the transfer of angular momentum from the Earth's rotation to the Moon's orbit.

The growing consensus is that the Moon formed at about 4 to 6 Earth radii from the center of the Earth from the remnants of a collision between the proto-Earth and a Mars-sized body. That early Moon receded rather quickly from that initial orbit thanks to the huge tidal forces at such short distances.
 P: 217 According to Wiki (YMMV)... http://en.wikipedia.org/wiki/Tidal_acceleration "The rotational angular momentum of the Earth decreases and consequently the length of the day increases. The net tide raised on Earth by the Moon is dragged ahead of the Moon by Earth's much faster rotation. Tidal friction is required to drag and maintain the bulge ahead of the Moon, and it dissipates the excess energy of the exchange of rotational and orbital energy between the Earth and Moon as heat. If the friction and heat dissipation were not present, the Moon's gravitational force on the tidal bulge would rapidly (within two days) bring the tide back into synchronization with the Moon, and the Moon would no longer recede. Most of the dissipation occurs in a turbulent bottom boundary layer in shallow seas such as the European shelf around the British Isles, the Patagonian shelf off Argentina, and the Bering Sea.[10] "The dissipation of energy by tidal friction averages about 3.75 terawatts, of which 2.5 terawatts are from the principal M2 lunar component and the remainder from other components, both lunar and solar.[11]" And... http://bowie.gsfc.nasa.gov/ggfc/tides/intro.html "The tidal braking in the earth's rotation is actually caused primarily by friction in the oceans, where friction'' may refer to any number of physical mechanisms which have yet to be determined definitively. For example, bottom friction, induced by tidal currents flowing across the seabed, various kinds of wave breaking, and scattering of tidal waves into oceanic internal waves are all thought to play a role. For a recent overview of this subject, look up Walter Munk's paper Once again: once again--tidal friction,'' published in Progress in Oceanography, vol. 40, pp. 7-36, 1997." Unfortunately, the link to that paper is broken, but Google found... http://champs.cecs.ucf.edu/Library/J...20friction.pdf
Mentor
P: 15,166
 Quote by DaveC426913 No. They are trading energy back and forth, changing rotations and orbital altitudes, but the the system is not losing any energy to some external recipient.
Sure it is.

While angular momentum is conserved here, mechanical energy is not. As mentioned in the previous post, it is the lossiness of the system that ultimately is the cause of the recession of the Moon and the slowing of the Earth's rotation rate.
P: 15,319
 Quote by D H Sure it is. While angular momentum is conserved here, mechanical energy is not. As mentioned in the previous post, it is the lossiness of the system that ultimately is the cause of the recession of the Moon and the slowing of the Earth's rotation rate.
All the energy of which is conserved in the Earth-Moon system.
Mentor
P: 15,166
 Quote by DaveC426913 All the energy of which is conserved in the Earth-Moon system.
No, it is not.

Write the equations for angular momentum and mechanical energy. One is conserved, the other is not. The lost mechanical energy is transformed to heat, and that heat radiates away.
P: 15,319
 Quote by D H No, it is not. Write the equations for angular momentum and mechanical energy. One is conserved, the other is not. The lost mechanical energy is transformed to heat, and that heat radiates away.
Ah. OK. I was about to ask you how the energy escapes the system.

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