Moon's increasing altitude due to resonance.

[AbnormallyHonest]

When the Moon's rotatio and revolution became synched, doesn't it loose its angular momentum prematurely because the rotation is now maintained by tidal forces and not momentum? Wouldn't that momentum be transferred into linear momentum (perhaps a nudge). Also, due to resonance, won't the moon maintain its orbital period from a larger orbit that should have a longer orbital period? Wouldn't that create acceleration to maintain that period which would increase the altitude of the Moon? It seems more plausible than a tidal bulge leading it around. Even if the mass is unevenly distributed, doesn't the Earth still have a gravitational mean center?

If you were to spin two rubber balls on a table with the same angular momentum, what would happen if the surfaces of the two balls touch? The friction represents the tidal lock.

Edited March 18, 2017 by AbnormallyHonest

[Enthalpy]

The momentum corresponding to the Moon's spin is much lower than the one corresponding to its orbit. Logically enough: different distances over the same time for the same mass.

[AbnormallyHonest]

The momentum corresponding to the Moon's spin is much lower than the one corresponding to its orbit. Logically enough: different distances over the same time for the same mass.

 

This idea doesn't use angular momentum as an explanation for the Moon's rotation. I'm suggesting that the tidal lock was the friction needed to transfer the Moon's angular momentum to linear momentum, which would have been the "push" to start the acceleration of it. This is an attempt to show that the rotation of the Moon is actually maintained by the tidal force which would transfer other forces due to conservation Once set in an unstable orbit for it's period, resonance is actually what absorbs momentum from the Earth to maintain it's orbital period from and ever increasing altitude.

Edited April 13, 2017 by AbnormallyHonest

[frankglennjacobs@gmail.com]

At the risk of falling into Speculation again, the Earth was formed rotating as well as orbiting. At random.

 

Whenever the Moon was formed, it, too, was rotating and orbiting. At random.

 

Immediately the tidal thing kicked in and immediately the two bodies began influencing one another.

 

There is tremendous energy in a rotating, orbiting planet or moon. This comes from the tremendous energy in the rotating, orbiting protoplanetary disk.

 

(Not understanding this, some astronomic sketches from just a few hundred years ago depicted angels pushing the planets -- or maybe just push-starting them.)

 

Energy is transferred from Earth to Moon in a rather complex manner by the tides they raise in each other. (Don't ask me about that, because I'd just start speculating again.)

 

After millions of years of tidally influencing one another, a planet and its moon may become tide-locked, with the moon always facing the same side to the planet. Even more, the planet can do the same, in time.

Edited April 26, 2017 by frankglennjacobs@gmail.com

[AbnormallyHonest]

At the risk of falling into Speculation again, the Earth was formed rotating as well as orbiting. At random.

 

Whenever the Moon was formed, it, too, was rotating and orbiting. At random.

 

Immediately the tidal thing kicked in and immediately the two bodies began influencing one another.

 

There is tremendous energy in a rotating, orbiting planet or moon. This comes from the tremendous energy in the rotating, orbiting protoplanetary disk.

 

(Not understanding this, some astronomic sketches from just a few hundred years ago depicted angels pushing the planets -- or maybe just push-starting them.)

 

Energy is transferred from Earth to Moon in a rather complex manner by the tides they raise in each other. (Don't ask me about that, because I'd just start speculating again.)

 

After millions of years of tidally influencing one another, a planet and its moon may become tide-locked, with the moon always facing the same side to the planet. Even more, the planet can do the same, in time.

 

I would argue that their rotation and revolution are not at random. As you said they are a direct result of the rotation of the accretion disk prior to their formation. The rotation would be a direct conversion of the rotation of the disk into angular momentum with respect to the density of the object during the accretion process. Think of a figure skater tucking in her arms while doing a spin. Ironically enough, almost every moon in the solar system is effected by some tidal mechanism, it's just their way. Therefore, I would hypothesize a tidal lock is associated for a body revolving around a revolving body. e.g. the most dependent gravitational body, and hence the most vulnerable to a resonant oscillation. The tidal lock is probably due to the differing forces acting on the smaller body and effecting it's mean gravitational center. I'm not sure that the disparity in the gravitational force alone would be enough to transfer momentum so rapidly... at least not at an appreciable distance. Otherwise, we should assume all the planets should be tidally locked to the sun, which isn't true, even for the closest planets.

[KipIngram]

Does this line of reasoning hold any water?

 

A coalescing planetoid absorbs material from just outside its own orbit and just inside its own orbit. A particle orbiting further out than the planetoid has more angular momentum out there than an equal mass orbiting at the planetoid radius would, and a particle orbiting further in has less. So the material that tends to land on the inside face of the planetoid has to be "boosted," and the material landing on the outside face delivers a boost. Both of those effects conspire to excite planetoid rotation such that the inner face moves against the direction of orbit. That's the right direction, since that makes the solar day longer than the sidereal day.

 

So if that's a valid argument it provides a mechanism for converting orbital angular momentum of material into rotational angular momentum of the coalescing planet.

 

Said more tersely, "accretion tends to add angular momentum to the outer face of the planet and remove angular momentum from the inner face, leading to rotation."

 

I feel like that's something of a stretch for me, so please don't beat me up too badly if it's nuts. :-|

On a similar line of reasoning, if you start with multiple bodies in their own orbits (different radii), and then you combine them into one body, is rotation required to conserve both kinetic energy and angular momentum? I'll go see if I can put some math behind that - back in a bit.

Ok, so for circular orbits V = (u/R)^0.5, where u = GM. Let's consider a group of bodies all of mass m in circular orbits of different radii Ri. The angular momentum of one of them is m*Vi*ri, which is m*(uRi)^0.5 So total angular momentum is

 

L = (m*u^0.5)*Sum(Ri^0.5)

 

Similarly, V^2 is u/R, so the kinetic energy of one body is m*u*/2R. So total kinetic energy is

 

K = (m*u/2)*Sum(Ri^-1)

 

We need potential energy too. That's -um/R, so total potential energy is

 

U = -(m*u)*Sum(Ri^-1)

 

So looks like total energy is

 

E = K + U = -(m*u/2)*Sum(Ri^-1)

 

Ok, so that doesn't include the self interactions. I'm going to finish the line of reasoning anyway, and then we can talk about whether mutual gravitation of the bodies is enough to matter.

 

Neglecting the mutual interactions, we have to have energy balance, so Sum(Ri^-1) has to stay constant. If that stays constant, Sum(Ri^0.5) can't. So the only way to make up the difference for angular momentum would be for the combined body to rotate, right?

 

Since we're free to make m whatever we like as long as it m << M, I'm going to say that we could make the mutual gravitation potential energy contributions negligible?

By the way, I apologize for my plain text formulae - I haven't mastered any of the cool LaTex stuff yet.

Shoot - I totally forgot to consider rotational energy. :-| Doesn't necessarily foul the idea, but I'm going to have to tinker with the math some more now.

Ok, I did a simple test case with radii 2, 3, and 4. I got an angular momentum conserving radius of 2.94, and an energy conserving radius of 2.77. If some of the energy goes to rotation, that leaves less for orbital motion, which would reduce the 2.77. So considering rotational energy just means we have more angular momentum to make up. And since bigger orbits have more angular momentum, the analysis does say that rotational angular momentum has to be in the same direction as orbital angular momentum.

Edited May 26, 2017 by KipIngram

[Mordred]

If you want the kinetic energy term for your calcs you can apply the Jeans instability equations. ( though I would have to brush up on em. myself)

 

https://en.m.wikipedia.org/wiki/Jeans_instability

 

This intro applies to stars but there are calcs using Jeans for planetary formation.

https://www.google.ca/url?sa=t&source=web&rct=j&url=http://www.ast.cam.ac.uk/~pettini/STARS/Lecture11.pdf&ved=0ahUKEwjzmbyDu4zUAhWHwlQKHbJQC0sQFgghMAA&usg=AFQjCNFrLXQx4ECJTFxu04SQxOSiaYojwg&sig2=CNmMlSp6pL7JanBLLQv4BQ

 

section 13.2 next link.

 

https://www.google.ca/url?sa=t&source=web&rct=j&url=http://web.mit.edu/12.004/TheLastHandout/PastHandouts/Chap13.Formation.pdf&ved=0ahUKEwjzmbyDu4zUAhWHwlQKHbJQC0sQFggsMAM&usg=AFQjCNH4gpQbkxF5dCKQQB9SKLHjif1Hfw&sig2=433mmPSGncTS_nfvO_e7Pg

Edited May 26, 2017 by Mordred

[KipIngram]

Oh, cool - that looks like it has to do with what circumstances cause a region of "stuff" to coalesce into a single object?

[Mordred]

correct but includes planets, stars, but also CMB. (part of baryon acoustic oscillations.) In essence it correlates rate of collapse via thereby providing a kinetic term. The sound waves is a mathematical descriptive for the hydrodynamics according to the thermodynamic laws as well as GR.

[KipIngram]

Mordred, this morning I was able to carry through a more careful version of what I did above. I included terms for potential energy both before and after collapse, and then noted that I could officially neglect them, because doing so took an equality over into an inequality which still implied that conserving energy resulted in a final radius too small to have the necessary angular momentum, thus requiring rotation. So it turned out to be unnecessary to have an actual value for the potential energy terms. I just relied on the fact that the collapsed potential energy would be "more negative" than the un-collapsed potential energy.

[AbnormallyHonest]

Mordred, this morning I was able to carry through a more careful version of what I did above. I included terms for potential energy both before and after collapse, and then noted that I could officially neglect them, because doing so took an equality over into an inequality which still implied that conserving energy resulted in a final radius too small to have the necessary angular momentum, thus requiring rotation. So it turned out to be unnecessary to have an actual value for the potential energy terms. I just relied on the fact that the collapsed potential energy would be "more negative" than the un-collapsed potential energy.

That would make sense. As an object moves away from us due to the transfer of momentum, once it moves far enough away from us that the asymmetrical center mass (the Moon's center mass being about 2 km from its actual center) becomes less influential than the angular momentum, the angular momentum would begin to absorb the linear acceleration so the period and the altitude would find equilibrium. Only that angular momentum would now be less than the orbital period giving the satellite an parent retrograde rotation. Perhaps not too different than the rotation vs revolution ratios we see of Mercury and Venus whom probably both were gravitationally locked at some point in their history.

[beecee]

. Perhaps not too different than the rotation vs revolution ratios we see of Mercury and Venus whom probably both were gravitationally locked at some point in their history.

A great rundown on tidal locking and synchronous rotation in WIKI.

https://en.wikipedia.org/wiki/Tidal_locking

extract:

"This state can result from the gravitational gradient (tidal force) between two co-orbiting bodies, acting over a sufficiently long period of time"

Edited July 2, 2017 by beecee

[AbnormallyHonest]

A great rundown on tidal locking and synchronous rotation in WIKI.

https://en.wikipedia.org/wiki/Tidal_locking

extract:

"This state can result from the gravitational gradient (tidal force) between two co-orbiting bodies, acting over a sufficiently long period of time"

 

Yes it does make sense, except the tidal bulge of the Earth's Ocean's pulling the Moon. I believe it causes traction which reduces the angular momentum, but I believe the mechanism to transfer that energy to the Moon has to do with the Moon's mean gravitational center being altered by oscillating between the Sun and Earth, creating torque that causes the Moon to "wobble" and that wobble is how it maintains it's resonant period. As it increases in altitude, the wobble will reduce and the angular momentum will take back over once it stops, but in a 1:1 or less than 1:1 ratio. (It would appear retrograde) I also believe that Moons are more prone to tidal locking because of their constant shifting of the mean gravitational center by oscillating between the Sun and parent planet to the outside of both, which creates torque that effects the angular momentum. It is the idea of mean gravitational center that causes me to reject the notion of the tidal bulge leading the moon and accelerating it. The only gravitational friction/traction would be from the Moon's unevenly distributed mass, otherwise the liquid water is exactly the thing that prevented the Earth from becoming tidally locked because the semi-diurnal and diurnal tides balance the gravitational center of the Earth preventing it from being gravitationally lopsided.

Edited July 10, 2017 by AbnormallyHonest