## Three body orbital motion

Discussions on classical and modern physics, quantum mechanics, particle physics, thermodynamics, general and special relativity, etc.

### Three body orbital motion

Hi all,

I have this thing in mind since a few years and it is sometimes begging to come out, so this time, I decided to open the door.

While orbiting the sun, the earth/moon gravity center follow a constant path around it, but each time the two bodies are not in line with that path, considering their own pro-grade orbital speed one around the other, they both travel at the wrong speed with regard to their individual orbital distances with the sun: the one that is closer to the sun is going too slow at that shorter orbital distance, so it should begin to get closer to it a bit while accelerating its orbital speed as if it was at the apogee of an orbital revolution, and the one that is farther is going too fast at that longer orbital distance, so it should begin to get away a bit while decelerating its orbital speed as if it was at the perigee of an orbital revolution.

Anybody wants to play with that curious thing so that it stops crying for a while? :^)

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### Re: Three body orbital motion

Remember that the motion of the Earth and Moon relative to the Sun just follows geodesics that is determined by the spacetime (s.t.) gradient at that their respective positions. When the Moon is the closer one, it moves in a s.t. gradient caused by the Earth and Sun working against each other, so the gradient is less. When the Moon is on the other side, the two s.t. gradients work together, so it is steeper, which is compatible with a higher orbital speed relative to the Sun.

It is interesting that when the Moon is closest to the Sun, the spacetime gradient is still towards the Sun, i.e. Moon's orbit never curves away from the Sun. It is the only moon in the solar system doing this, so in that sense the Moon is a planet and not a moon! We live in a double planet system...
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PS: For anyone interested, attached is a box on the Moon that I wrote in my eBook some 10 years ago.
Attachments
Moon-Earth.pdf
Is the Moon a Planet or what?
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### Re: Three body orbital motion

Hi Burt,

If the earth/moon rotation would be retrograde instead of prograde, as for Triton and Neptune, with the same curve of the space/time gradient, inversely, the orbital speed wrt the sun of the closer body to the sun would be increased, and the orbital speed of the farther one would be decreased. Would the two systems behave differently? Is the Triton/Neptune system behaving differently than the Earth/Moon one?

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### Re: Three body orbital motion

I think a retrograde orbit at the distance of our Moon would not have been stable or at least with widely varying orbital parameters. If the Moon was much closer so that its orbit curved away from the Sun at closest point, it could have been fairly stable. Triton is much closer to its primary in terms of gravity gradient. I have not calculated it, but I trust Asimov to have been right.

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### Re: Three body orbital motion

BurtJordan wrote:It is interesting that when the Moon is closest to the Sun, the spacetime gradient is still towards the Sun
I've been thinking, but forgive me it's an addiction. :)

Following your reasoning, if the moon would suddenly stop its orbital motion around the earth while it is on the sun's side, in such a way that it would stay on the line between the earth and the sun for a while, it would nevertheless fall on the sun. Then why doesn't it already fall on the sun when it crosses that line since it is already going too slow wrt the sun to stay at that orbital distance with it?

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### Re: Three body orbital motion

Was it an irrelevant question?

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### Re: Three body orbital motion

Inchworm » 31 Mar 2016, 18:34 wrote:Was it an irrelevant question?

No, sorry, i was out of town for the 1st two weeks of March, so I have missed it. Will answer as soon as I have time.
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### Re: Three body orbital motion

Inchworm » 02 Mar 2016, 20:14 wrote:
BurtJordan wrote:Then why doesn't it already fall on the sun when it crosses that line since it is already going too slow wrt the sun to stay at that orbital distance with it?

The reason it stays in orbit around Earth is that Earth is falling to the Sun faster at that point. Remember that at the point you specified, Earth's gravity subtracts from the Sun's on the Moon. For Earth, the Moon's gravity adds to the Sun's.

I have not made the sums for a 'stopped Moon', but gravitational intuition tells me that the same thing will be at work. However, the great disturbance to its orbit around Earth may cause the Moon to eventually leave its Earth orbit and follow its own around the Sun.

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### Re: Three body orbital motion

If there would be no moon, there would still be tides on the earth, and the way I see it, it would not only be due to the presence of the sun, but also because both sides of the earth would not be traveling at the right speed at their own orbital distance from the sun. For instance, if the rotation of the earth was retrograde, in such a way that its surface facing the sun would travel at the right orbital speed for that distance, it would have no reason to move towards the sun to create a tide, would it? Now, if the tide effect on the earth surface would then depend partly on the transitional surface speed of the earth wrt the sun, shouldn't there also be a tide effect due to the transitional speed of the moon and the earth wrt the sun? In other words, shouldn't the trajectory of the earth towards the moon make two small bulges at their transit like the earth tides do?

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### Re: Three body orbital motion

Inchworm » 03 Apr 2016, 00:40 wrote:For instance, if the rotation of the earth was retrograde, in such a way that its surface facing the sun would travel at the right orbital speed for that distance, it would have no reason to move towards the sun to create a tide, would it?

This does not sound right. Firstly, it is Earth's center of mass that determines its orbital speed around the Sun. Secondly, the crust-tides are caused by fact that the Sun's gravity pulls stronger on the near side of Earth than on the far side, hence stretching Earth in the radial direction and compressing it in the tangential directions. The amplitude range (up minus down) does not depend on Earth's rotation or the orbital speed around the Sun, but the tidal rotation period does, of course.

As an aside and contrary to popular believe, the ocean tides are not formed like the crustal tides (stretching of Earth). It is the horizontal dragging of water by the tidal gravitational forces of the Sun and the Moon, causing currents that make the water "wash up" at certain points an retreating at others.

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### Re: Three body orbital motion

BJ wrote:This does not sound right.
As far as orbital motion is concerned, if it is contrary to observations, it is probably wrong, but it seems to me that it could apply to tides without contradicting the measures.

Firstly, it is Earth's center of mass that determines its orbital speed around the Sun.
Yes, and it is the same for orbital motion. This is precisely why I say that its surface is not traveling at the right orbital speed at that moment.

Secondly, the crust-tides are caused by fact that the Sun's gravity pulls stronger on the near side of Earth than on the far side, hence stretching Earth in the radial direction and compressing it in the tangential directions.
This is precisely why satellites have to be traveling faster when they are closer to the earth, and slower when the are farther.

As an aside and contrary to popular believe, the ocean tides are not formed like the crustal tides (stretching of Earth). It is the horizontal dragging of water by the tidal gravitational forces of the Sun and the Moon, causing currents that make the water "wash up" at certain points an retreating at others.
It is not really an aside to me, because the dynamic action I am proposing would also reduce or accelerate the earth surface speed on its orbital motion with the sun a bit as if it was at the apogee or at the perigee of an elliptic trajectory with the sun. On the sun's side, moving as if it was at an apogee, the surface would progressively be trying to move towards the sun while accelerating, thus working against friction to decelerate its pro-grade motion a bit, and on the far side, moving as if it was at a perigee, it would progressively be trying to move away from the sun while decelerating, thus also working against friction to decelerate its pro-grade motion a bit. This would move the water tides sideways a bit, and against the pro-grade motion of the earth, thus producing a kind of a tidal wave moving towards the east coasts of the seas.

But it should also affect the earth crust, pushing it slowly to the west with time where its two opposite parts are inline with the sun, thus pushing them towards the two other parts that are not affected by the tide effect at that moment, because they would then be following the same path around the sun that the center of gravity of the earth is following. If that principle doesn't contradict the observations as far as the tides are concerned, it seems to me that it might be used to explain some of the motions of the tectonic plates, but if it really affects tides on earth, shouldn't it also affect the earth/moon trajectories around the sun, thus affecting the earth/moon distance a bit? Could that motion be too small for our instruments to measure it, or could it be that we did not think of giving attention to that motion yet?

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### Re: Three body orbital motion

Inchworm » 03 Apr 2016, 17:24 wrote:This is precisely why satellites have to be traveling faster when they are closer to the earth, and slower when the are farther.

Yes, but this seems to not hold for rigid or semi-rigid bodies. If you tether a small mass to a satellite, it will oscillate, wasting some orbital energy through stress heating of the materials, until it eventually settles in the lowest total energy state with the tether nominally hanging directly towards the Earth. This is also basically why the Moon is showing us approximately the same face forever.

I'm not sure what exactly you are after, but the tidal effects on dynamically orbiting systems is complex. For instance the crustal tides of Earth play a tiny role in volcanic actions, but I think its effect on tectonic plate movement is negligible. Remember, the horizontal component of the tidal force changes direction every six hours (sinusoidal). Water has time to react, but not the crust.

Due to the stretch and squeeze of the crustal tides, Earth's rotation rate is slowing a tiny bit on average (causing leap-seconds now and then). This loss in angular momentum is transferred to the Moon and it slowly moves away from Earth.

So yes, the orbital dynamics of permeable objects like the Sun/Earth/Moon system creates interesting effects, but to calculate them require massive computing resources.

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### Re: Three body orbital motion

BurtJordaan » April 4th, 2016, 3:28 am wrote:Remember, the horizontal component of the tidal force changes direction every six hours (sinusoidal). Water has time to react, but not the crust.
Water is sucked from the coasts when the motion towards the sun pulls the middle of the seas upwards, and when it pulls on the lands after, it might also kind of suck their coasts, but the sideways motion I am trying to figure out would push the lands towards west each time they would suffer a tide, what would push them against the lands that are not suffering the tides at that moment because they are traveling at the same height the center of gravity of the earth is traveling, thus creating their subduction, and slowing up the earth's rotation since that motion would always be westward.

Due to the stretch and squeeze of the crustal tides, Earth's rotation rate is slowing a tiny bit on average (causing leap-seconds now and then). This loss in angular momentum is transferred to the Moon and it slowly moves away from Earth.
There is no physical mechanism to explain that energy transfer, its only a mathematical calculation, whereas the motion that I am describing is totally physical: no need to use the energy conservation principle.

So yes, the orbital dynamics of permeable objects like the Sun/Earth/Moon system creates interesting effects, but to calculate them require massive computing resources.
If I knew how to do it, I would try to develop an equation that integrates all the tiny delta distances that the earth surface would suffer westward during the time it moves the known delta distances towards the sun, and compare them to the tectonic plates drift. Do you know what it would look like? I think that the tide numbers are more heuristic than calculated as far as the shores are concerned, but is the large deformation effect on a whole sea or on a whole continent calculable to a certain degree or do we need a simulation?

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### Re: Three body orbital motion

Inchworm » 04 Apr 2016, 16:23 wrote:Water is sucked from the coasts when the motion towards the sun pulls the middle of the seas upwards,...

Not quite, but i guess it is a matter of interpretation. According to NOAA chapter 3, section 4.:
4. The Tractive Force. It is significant that the influence of the moon's gravitational attraction superimposes its effect upon, but does not overcome, the effect's of the earth's own gravity. Earth-gravity, although always present, plays no direct part in the tide-producing action. The tide-raising force exerted at a point on the earth's surface by the moon at its average distance from the earth (238,855 miles) is only about one 9-millionth part of the force of earth-gravity exerted toward its center (3,963 miles from the surface). The tide raising force of the moon, is, therefore, entirely insufficient to "lift" the waters of the earth physically against this far greater pull of earth's gravity. Instead, the tides are produced by that component of the tide-raising force of the moon which acts to draw the waters of the earth horizontally over its surface toward the sublunar and antipodal points. Since the horizontal component is not opposed in any way to gravity and can, therefore, act to draw particles of water freely over the earth's surface, it becomes the effective force in generating tides.

I can't agree that there is no theory for a physical effect for the momentum transfer. As the 'bulge' in the Earth's crust circulates, it acts as a 'brake' on Earth's rotation. Some of the energy goes into tidal heating of Earth and some must go to the moon's orbit. The bulges does not have to be offset from the moon's vector in order for this to work. Tidal locking of satellite rotations works on the same principle.

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### Re: Three body orbital motion

This site uses three different positions of the moon/earth gravitational system to illustrate the two forces that produce tides, because this way, it shows why centrifugal force is present. But it omits to consider that centrifugal force is a dynamic force, and it subsequently omits to analyze tides as a dynamic motion. While the two respective CG of earth and moon (E and M) travel around a common CG at their own orbital speed, their surfaces don't, so to me, these should not follow the same trajectory, they should follow a trajectory that accounts for their own speed at that distance from the CG of the other body. As I already pointed out, it should not change the height of the tides, but it should affect punctually their orbital speed, thus shifting them westward a bit. The seas would not register that motion since they flow back in place after, but the crust would because subduction doesn't flow back: it would constantly move westward, thus constantly slowing the earth's period of rotation until it doesn't rotate anymore. It seems to me that this explanation is more concrete than the conservation of energy law. When we put satellites on orbit, we know that, to change their height, we also have to change their orbital speed. If we lower a satellite that is stable without accelerating it after, we know it will start accelerating its orbital speed all by itself while falling towards the earth a bit, and if we higher it without decelerating it after, we know it will start decelerating its orbital speed all by itself while getting away from earth a bit. Why would it be different for the earth surface?

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### Re: Three body orbital motion

Inchworm » 08 Apr 2016, 19:40 wrote:The seas would not register that motion since they flow back in place after but the crust would [not] because subduction doesn't flow back: it would constantly move westward, thus constantly slowing the earth's period of rotation until it doesn't rotate anymore. It seems to me that this explanation is more concrete than the conservation of energy law.

Yes, there are two bulges moving from east to west around Earth every 24 hours and they waste energy that slows Earth down. The conservation of angular momentum law only serves to (partially) explain why our moon is slowly receding from Earth, because it is the main agent causing the bulges.

A more direct explanation is that the crustal bulges lag the moon in its apparent east-west shift around Earth. This means it creates a small offset in the gravitational field to the east of the median of the Sun/moon tidal gravity vector. This offset causes orbital energy to be transferred to the moon. There are many interpretations, but I think these are the mainstream thoughts.
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### Re: Three body orbital motion

BurtJordaan » April 9th, 2016, 4:10 am wrote:
Inchworm » 08 Apr 2016, 19:40 wrote:The seas would not register that motion since they flow back in place after but the crust would [not] because subduction doesn't flow back: it would constantly move westward, thus constantly slowing the earth's period of rotation until it doesn't rotate anymore. It seems to me that this explanation is more concrete than the conservation of energy law.
Yes, there are two bulges moving from east to west around Earth every 24 hours and they waste energy that slows Earth down.
It seems to me that the frictions created by the motion of the tides would be the same on both sides of the bulges, and that they would thus nullify themselves, having no effect on the earth's rotation.

The conservation of angular momentum law only serves to (partially) explain why our moon is slowly receding from Earth, because it is the main agent causing the bulges.
Again, it seems to me that, with no friction differential to account for the tides, only the loss in heat due to the same friction would stand, which is what the conservation of energy law is about. As I said, the dynamic principle that I am talking about would not only add a bit to the bulges, but it would also shift them westward a bit, what it would also do in the case of the three orbiting body problem. It would thus slowly move the earth and the moon away from one another as the data show, and it would move them a bit westward in the same time, thus slowing down their orbital speed, which is absolutely necessary for them to stay at that orbital distance from one another. The energy conservation explanation doesn't tell us about the link between distance and speed, but that dynamic gravitational motion principle does.

A more direct explanation is that the crustal bulges lag the moon in its apparent east-west shift around Earth. This means it creates a small offset in the gravitational field to the east of the median of the Sun/moon tidal gravity vector. This offset causes orbital energy to be transferred to the moon. There are many interpretations, but I think these are the mainstream thoughts.
Here is wiki about that hypothesis:

"However, Earth's rotation drags the position of the tidal bulge ahead of the position directly under the Moon. As a consequence, there exists a substantial amount of mass in the bulge that is offset from the line through the centers of Earth and the Moon. Because of this offset, a portion of the gravitational pull between Earth's tidal bulges and the Moon is not perpendicular to the Earth–Moon line, i.e. there exists a torque between Earth and the Moon. This boosts the Moon in its orbit, and slows the rotation of Earth."

I understand that the bulges would not be inline with the two CGs, but I don't see how the force would work to slow down the moon's orbital speed or to exert less force on it so that it recedes a bit since the earth's CG, from whom all forces that act on the moon originate, would not change places. Do you? By the way, there is no maths to support this hypothesis: is it because it is only qualitative?

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### Re: Three body orbital motion

I tend to agree that the ocean tides (which are basically large scale tidal currents) do not contribute significantly to the Earth's rotation speed change. However, the tides do 'waste' some rotational energy through friction and this comes from the moon, so there must be a tiny effect. Same for the tidal heating of the interior 'wasting' energy.

However, the crustal bulges transfer more significant angular momentum to the moon. It increases the moon's orbital radius and that results in a slower orbital speed, but a larger orbital momentum relative to Earth. As you know, the same thing happens to a pro-grade satellite if you give it a small push in the pro-grade direction. Conservation of angular momentum and orbital energy in 2-body motion requires that Earth loses some angular momentum in the transfer process.

The direct mechanism is that the nearer bulge causes a gravitational vector (as seen by the moon) that points slightly to the east of the gravitational center of the Earth-moon system (hence it is a pro-grade 'push'). This is a standard astronomy calculation for when rotating primary bodies are not spherically symmetrical. It actually causes a Newtonian periapsis shift in the case of elliptical orbits (not the relativistic one that Mercury is famous for).

-J

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### Re: Three body orbital motion

I'm thinking.... Let's imagine two identical massive bodies that follow a circular orbit, and let's increase the orbital speed on one of them. Normally, increasing the orbital speed of a small satellite already on a circular orbit would produce an elliptic orbit whose perigee would be at the place and time where the original acceleration occurred. It would be the only observable effect because the smaller body does not affect the trajectory of the big one significantly. But since the two bodies of my example carry the same mass, accelerating one would affect the other one's trajectory, what would still produce the same kind of trajectory for both bodies since they are identical. Accelerating the fist body would thus put the other one in the same situation after a delay of c: it would accelerate its orbital speed, putting it also at the peri-apsis of its elliptic orbital trajectory wrt the other body.

With tides, there is no external force to change the orbital speed of either of the two bodies wrt one another, and moreover, there is no change in the orbital speed of the bulges wrt the other body either. On the contrary, adding a third body in the equation automatically gives us a periodic change in the orbital speed of both bodies and bulges, and with gravitation, smaller systems are always part of lager systems so it is always a many body equation. If that idea is right, while the earth/moon system would widen and slow down while orbiting the sun, the sun's system should do the same while orbiting the larger galaxy system. That phenomenon would thus not only be an energy issue as the mainstream theories all add to their explanations, it would also serve to keep a necessary synchronism between periodic motions of different scales. Of course periodic motions can be considered as waves, and waves carry energy, so the effect I am talking about could nevertheless be considered as a conservation of energy issue, but it is quite different from the mainstream one.

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### Re: Three body orbital motion

BJ wrote:The direct mechanism is that the nearer bulge causes a gravitational vector (as seen by the moon) that points slightly to the east of the gravitational center of the Earth-moon system (hence it is a pro-grade 'push'). This is a standard astronomy calculation for when rotating primary bodies are not spherically symmetrical. It actually causes a Newtonian periapsis shift in the case of elliptical orbits (not the relativistic one that Mercury is famous for).
Since that effect would produce a pro-grade motion, then I cannot see how it could account for the slowing down of the pro-grade orbital speed of the moon since it is a retrograde motion. Did I miss something?

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### Re: Three body orbital motion

A prograde orbital 'push' slows satellites down because orbital radius increases. Standard orbital mechanics - angular momentum and total orbital energy are both increased by such a push. On the other hand, 'braking' increases orbital speed, since orbital radius gets smaller and the conserved values decrease.

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### Re: Three body orbital motion

Theoretically, if we want a satellite to keep a circular trajectory while moving it, we cannot increase the orbital distance without slowing down the orbital speed, or increase the orbital speed without diminishing the orbital distance: speed and distance are linked. A simple prograde push would induce an elliptical trajectory where the place and the moment of the push would represent the perigee, which means that, after the push, the satellite would begin to slow down and get away from earth until it would reach its apogee. This is precisely the effect that I am pointing to: when the sun/earth/moon system is aligned, and the moon is on the far side of the sun, it is going too fast at that height from the sun to stay on that orbit, so that it must begin an elliptical trajectory, it must begin to slow down a bit and to get away from the sun a bit, which is precisely what we observe with time. As you can see, this explanation doesn't need the conservation of energy principle as a mechanism, only as a confirmation. It seems to me that it could thus be more useful: for instance, as I pointed out, it might help to explain part of the tectonic plates' motions.

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### Re: Three body orbital motion

Inchworm » 15 Apr 2016, 17:31 wrote:This is precisely the effect that I am pointing to: when the sun/earth/moon system is aligned, and the moon is on the far side of the sun, it is going too fast at that height from the sun to stay on that orbit, so that it must begin an elliptical trajectory, it must begin to slow down a bit and to get away from the sun a bit, which is precisely what we observe with time.

I'm afraid I can't buy this argument. When the alignment that you refer to (opposition) occurs, the combined spacetime curvature of Earth+Sun is more on the Moon and hence it must go faster relative to the Sun to stay in the same orbit. The opposite happens when conjunction occurs.

If you do the sums with a tidally locked Moon and Earth, there is no further orbital energy transfer to the Moon from Earth tides and it would not spiral away. Your point says that it would, I think...

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### Re: Three body orbital motion

BurtJordaan » April 15th, 2016, 1:17 pm wrote:
Inchworm » 15 Apr 2016, 17:31 wrote:This is precisely the effect that I am pointing to: when the sun/earth/moon system is aligned, and the moon is on the far side of the sun, it is going too fast at that height from the sun to stay on that orbit, so that it must begin an elliptical trajectory, it must begin to slow down a bit and to get away from the sun a bit, which is precisely what we observe with time.

I'm afraid I can't buy this argument. When the alignment that you refer to (opposition) occurs, the combined spacetime curvature of Earth+Sun is more on the Moon and hence it must go faster relative to the Sun to stay in the same orbit. The opposite happens when conjunction occurs.
I apologize Burt, you gave this argument earlier and I didn't get it. It's crazy how mind only understands what it is awaiting to understand. Now, does it mean that, if we would run a simulation, the moon would always be traveling at the exact speed wrt the sun/earth system? In other words, could there be a sufficient motion surplus left for my hypothesis to hold? You said that when the GC of the Moon was closest to the Sun, the spacetime gradient was still towards the Sun, so I guess it is the inverse for the GC of the earth at that moment, otherwise the system would fall on the sun each time it is inline with it. This way the earth/moon system is always balanced wrt its GC, but it is not always balanced wrt the sun, in such a way that we could still imagine that the moon and the earth might be forced to accelerate away from one another a bit during their transit, but how would they manage to slow down their common orbital speed? Would that be enough to consider that, while moving away from one another, they would respectively find themselves at the aphelia and at the perihelia of an elliptical trajectory wrt the sun?

To be better understood, I think I have to be more accurate on the different ways the orbital speeds would get slowed in each situation: while the outside body would begin to decelerate wrt the sun, the inside one would begin to accelerate, but since the outside one would decelerate a prograde motion wrt the sun, it would slow down its orbital speed wrt the other body, and since the inside one would accelerate a retrograde motion wrt the sun, it would still slow down its orbital speed wrt the other body. It works even if it is complicated to imagine. The first time I had this idea, I did not know if it would work, and I was very impressed to see that it did. It could be a coincidence, but what a coincidence!!!

If you do the sums with a tidally locked Moon and Earth, there is no further orbital energy transfer to the Moon from Earth tides and it would not spiral away. Your point says that it would, I think...
You're right, that's what it would mean: do you have any contradictory observation on hand? Afaik, many moons are tidally locked with their planets, but never the inverse.
Last edited by Inchworm on April 16th, 2016, 5:55 pm, edited 1 time in total.

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### Re: Three body orbital motion

Doublon

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### Re: Three body orbital motion

Inchworm » 16 Apr 2016, 23:46 wrote:
Burt wrote:If you do the sums with a tidally locked Moon and Earth, there is no further orbital energy transfer to the Moon from Earth tides and it would not spiral away. Your point says that it would, I think...

You're right, that's what it would mean: do you have any contradictory observation on hand? Afaik, many moons are tidally locked with their planets, but never the inverse.

The size of planets makes this unlikely, but it can be done on paper. Our Moon is the only one in the solar system big enough to cause a measurable slowing down of the planet's rotation rate, but the Moon will drift away too far before it's effect can tidally lock Earth to it.

I cannot say for sure that your proposition is implausible, because a mathematical solution would be overwhelming complex. But my gravitational intuition says that it is extremely unlikely to be the cause of the Moon's slow recession from Earth. On the other hand, the mechanism of the crustal bulges makes perfect physical sense.

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### Re: Three body orbital motion

I know I got good chances to be wrong, but thank's not to disillusion me completely. :^)

However, as with the link I can make between my theory on mass and our intellectual resistance to change, it seems to me that a theory that explains different kinds of things has more potential, and contrary to the bulges one, the one I suggest would have the potential to explain tectonic motions or any similar motion due to a three body problem, as with three galaxies for instance. In this case, it may have the potential to explain why they rotate too fast, or why their rotation curve is flat.

my gravitational intuition says that it is extremely unlikely to be the cause of the Moon's slow recession from Earth
One more question: if the moon is recessing from the earth/moon GC, then it seems to me that the earth must do the same for that GC to stay at the same distance from the earth surface all the time, otherwise it would have changed. Is there a way to know if it has?

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### Re: Three body orbital motion

Inchworm » 18 Apr 2016, 19:18 wrote:... contrary to the bulges one, the one I suggest would have the potential to explain tectonic motions or any similar motion due to a three body problem, as with three galaxies for instance. In this case, it may have the potential to explain why they rotate too fast, or why their rotation curve is flat.

Both of these would be very hard to buy into. I don't have the capacity to mine into the intricacies of either.

One more question: if the moon is recessing from the earth/moon GC, then it seems to me that the earth must do the same for that GC to stay at the same distance from the earth surface, otherwise it would have changed with time. Is there a way to know if it has changed?

Yes sure, since the distance between Earth and Moon is om the increase, both must go father from the common center of mass, proportional to their relative masses of course. It is the common center of mass that follows a near-ellipse around the Sun. No change in that orbit has been detected, other than what can be accounted for by the influence of the gas-giant planets and the tiny perihelion shift predicted by general relativity.

BurtJordaan
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### Re: Three body orbital motion

BJ wrote:Yes sure, since the distance between Earth and Moon is om the increase, both must go father from the common center of mass, proportional to their relative masses of course. It is the common center of mass that follows a near-ellipse around the Sun. No change in that orbit has been detected, other than what can be accounted for by the influence of the gas-giant planets and the tiny perihelion shift predicted by general relativity.
OK, then if the tide bulges on earth are actually producing the recession of the moon, at the same time and in the same proportion, a similar motion happening on the moon must be producing the recession of the earth, right? Is that mechanism taken into consideration separately or is the earth's motion only considered to be self adjusting to the moon's one?

Inchworm
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### Re: Three body orbital motion

The Moon's rotation is already tidally locked to Earth, so its 'bulges' always sit directly facing Earth and directly away from Earth.* Hence not further effect. But before it got tidally locked, it obviously must have contributed a little bit.

* Ignoring the small libration effect, because it pushes as much as it pulls...

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