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What is Tide Lock?

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#1 Brian Albin

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Posted 23 February 2018 - 12:28 AM

Is it known how gravity works to cause our moon to constantly face us?

 

Wikipedia says this:
"Tidal locking occurs when the long-term interaction between a pair of co-orbiting astronomical bodies drives the rotation rates into an harmonic ratio with the orbital period. This effect arises from the gravitational gradient (tidal force) between the co-orbiting bodies, acting over a sufficiently long period of time. Once tidal locking is achieved for one of the bodies, there is no more net transfer of angular momentum between the two objects, although there can be some back and forth transfer over the course of an orbit. In the special case where the orbital eccentricity is nearly zero, tidal locking results in one hemisphere of the revolving object constantly facing its partner, an effect known as synchronous rotation."

 

I was not smart enough to understand that. For those of you who understand, do you know if that author was stating what is considered in the scientific community to be known fact, or is it a theory, or is it only speculative guessing?

 

Brian



#2 gavinm

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Posted 23 February 2018 - 12:33 AM

Definitely fact. The Moon is tidally locked to the Earth, which is why we only ever see one side.



#3 gavinm

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Posted 23 February 2018 - 12:43 AM

If your question was 'what is tidal locking?' then I can offer a simplistic explanation I tell my High School students.

The Moon's gravity creates the tides on Earth. This requires energy transfer and ultimately energy is lost to heat due to friction. On Earth, this energy can be dissipated due to friction from the motion of the Seas with the Earth's crust (and seabed). The Moon has no 'moving' parts so there is little way for the Moon to dissipate this energy loss itself. It does so by decreasing it's rotation (angular momentum). Due to the fact this has been happening for billions of years, now that the Moon is tidally locked, the rotation can't dissipate the energy so it is slowly losing linear speed instead. This results in the Moon slowly moving away from Earth, which is also measurable (about a centimetre a year).


Edited by gavinm, 23 February 2018 - 01:13 AM.

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#4 Codbear

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Posted 23 February 2018 - 01:54 AM

If your question was 'what is tidal locking?' then I can offer a simplistic explanation I tell my High School students.

The Moon's gravity creates the tides on Earth. This requires energy transfer and ultimately energy is lost to heat due to friction. On Earth, this energy can be dissipated due to friction from the motion of the Seas with the Earth's crust (and seabed). The Moon has no 'moving' parts so there is little way for the Moon to dissipate this energy loss itself. It does so by decreasing it's rotation (angular momentum). Due to the fact this has been happening for billions of years, now that the Moon is tidally locked, the rotation can't dissipate the energy so it is slowly losing linear speed instead. This results in the Moon slowly moving away from Earth, which is also measurable (about a centimetre a year).

Great explanation gavinm!

 

I use the earth-moon system example to teach my student the conservation of angular momentum. So much to learn from our nearest neighbor.



#5 MikeTahtib

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Posted 23 February 2018 - 02:23 AM

If the moon is losing energy to the Earth and slowing down, why isn't it moving closer?  I can see how angular momentum would be conserved if there was no energy loss, but it seems like the moon is doing real work on the earth.  If the moon were to stop completely, I would expect it to drop straight into the earth, not rocket out into space.  What am I missing?



#6 gavinm

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Posted 23 February 2018 - 03:25 AM

Its just a fact of Newtonian mechanics. As orbiting bodies slow down, their radius increases.

Think a whirlpool or tornado. As the air moves inwards, it speeds up. This is the same, but in reverse.



#7 MikeTahtib

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Posted 23 February 2018 - 06:22 AM

I understand there is a relationship that connects an orbital velocity to a radius, and that the lower something is, the faster it has to go to stay in orbit, and that if it goes higher at the same speed, it will escape.  Although as I type that, something seems off, because it implies a small increase in velocity would push the object to a higher orbit, where even lower speeds are required, yielding a fundamentally unstable system where a small increase in velocity would induce a progressively higher orbit until the satellite escaped the planet, which doesn't seem right.

What I'm struggling with is the energy balance.  It seems like for something to move away from the earth requires an expenditure of energy, since at a higher elevation, it will have higher potential energy. In order for the moon to do work on the earth, it must be giving up some energy in the form of its velocity.  In order to remain in orbit after that, it must go higher, but that requires energy also.  The only things I see working on it are a gravitational force vector pointing towards the earth, and its velocity perpendicular to that vector.  What pushes it upwards?  As you get further from the earth, the gravity vector gets smaller, and you have to go slower to stay in orbit, but what would push you up there to begin with? 

My understanding of orbit is that it is a compromise between falling and moving perpendicular to gravity.  When you move forward at the same rate that you accelerate to the side, you stay in orbit.  If you slow down, the sideward acceleration would bring you closer to the ground.

When they want to bring a space capsule out of orbit, don't they turn it around and fire rockets to slow it down, not speed it up?

There must be something more subtle going on than is readily apparent.



#8 Jim Davis

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Posted 23 February 2018 - 06:45 AM

If the moon is losing energy to the Earth and slowing down, why isn't it moving closer?  I can see how angular momentum would be conserved if there was no energy loss, but it seems like the moon is doing real work on the earth.  If the moon were to stop completely, I would expect it to drop straight into the earth, not rocket out into space.  What am I missing?

The Moon is not losing energy. It is actually gaining it. It is the Earth that is losing it. It's the reason they keep injecting leap seconds into atomic clocks, to compensate for the Earth slowly losing angular momentum.



#9 llanitedave

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Posted 23 February 2018 - 10:25 AM

Its just a fact of Newtonian mechanics. As orbiting bodies slow down, their radius increases.

Think a whirlpool or tornado. As the air moves inwards, it speeds up. This is the same, but in reverse.

It doesn't quite work that way.  The as the radius increases, the orbital speed slows down.  It's a subtle, but very significant difference.  The Moon is actually gaining orbital energy at the expense of the Earth's rotation, which its tidal effect is gradually slowing.  The gain in energy sends it into a more distant orbit, which slows it down.


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#10 gavinm

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Posted 23 February 2018 - 03:31 PM

I agree, that's why I said it was simplistic explanation. I only ever refer to the Moons kinetic energy when I discuss this. For some reason, students can't get a grasp of the potential energy involved. The idea of potential energy increasing to zero is something they don't seem to be happy with.



#11 GlennLeDrew

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Posted 23 February 2018 - 07:47 PM

To understand how the energy transfer from Earth to Moon results in the Moon's orbit increasing...

 

The Moon raises a tidal bulge on Earth. The Earth's rotation drags this bulge out of line, so that it peaks *ahead* of the line connecting the two bodies' centers. This assymetric shape of the Earth results in the effective center of mass, as 'seen' by the Moon, to lie slightly ahead of the Earth-Moon line, in the same direction of the Moon's orbital motion, which pulls the Moon forward. Which adds energy to the Moon, hauling it into a larger orbit. This subtracts energy from Earth, slowing its rotation velocity.

 

This is not too unlike twirling a ball on the end of a string. When your hand describes a circle about a point, your off-center hand is acting like the 'dragged-forward' tidal bulge on Earth. Compared to a stationary hand, the twirling hand is adding energy, which results in a stronger centrifugal force pulling more strongly on the string.


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#12 GlennLeDrew

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Posted 23 February 2018 - 08:04 PM

As to tidal locking.

 

Earth raises a tidal bulge on the Moon, too. And the Moon is not perfectly spherically symmetric. Which over time has slowed its rotation velocity to today's ~1 month-long day.

 

As the Moon continues to have its orbit enlarged, the already tidally locked rotation will slow down in step. That is, its length of lunar day cannot now decrease more slowly than its orbit period, for this is braked whichever direction the Moon would rotate w.r.t. the Earth-Moon line. And so once established, synchronous rotation is maintained.

 

Eventually, as the Earth's spin slows and the Moon's orbit grows, both bodies will be in synchronous rotation, with each having the same side facing the other. At such time tidal forces are effectively nil, and absent other forces the configuration is fixed. But of course such things as the Sun and other planets, and any orbital eccentricity of Earth (about the Sun) continue to play a role.



#13 Brian Albin

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Posted 23 February 2018 - 10:33 PM

I thank everybody for the replies.

 

gavinm said:
"The Moon has no 'moving' parts so there is little way for the Moon to dissipate this energy loss itself. It does so by decreasing it's rotation (angular momentum)."

 

How does the moon decide to do that? By what mechanism does the moon sense a need to dissipate energy?  Why does it not heat up until it melts?  Or dissipate it's heat into space.

 

Brian



#14 llanitedave

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Posted 23 February 2018 - 11:05 PM

The Moon does dissipate it's tidal heat into space.  The amount that's generated is pretty small, and I believe it's in equilibrium between that gained and that dissipated.



#15 GlennLeDrew

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Posted 24 February 2018 - 12:49 AM

Tidal stress-induced heating of any import requires that the body lie sufficiently deep inside a gravitational potential that a significant gravitational gradient exists across its diameter. Such as for Jupiter's moon Io, where internal heating leads to volcanic activity. Earth's tides induced in Luna are miniscule by comparison.

 

Note that inside a certain distance from a gravitational well, known as the Roche limit, a body will succumb to tidal stress because its surface lies outside the body's own tidal limit; it gets torn apart. This is why I cringe when I see in sci-fi films sizeable moons or smaller planets lying ridiculously close to giant planets; in the real Universe they'd be converted into a ring system PDQ.



#16 Brian Albin

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Posted 24 February 2018 - 10:22 PM

Gavin's answer that the moon now faces us because it has lost the energy necessary to rotate seems false to me. Are not the Librations efforts of the moon to resume rotating?



#17 Jim Davis

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Posted 25 February 2018 - 07:55 AM

Gavin's answer that the moon now faces us because it has lost the energy necessary to rotate seems false to me. Are not the Librations efforts of the moon to resume rotating?

No. The Moon is rotating, once per month. But, its orbit is not circular. When it is closer, it is orbiting faster than it is rotating, so you see a bit more to one side. When far away it is rotating faster than it is orbiting, so you see the other bit. On average, it is rotating once per orbit. Check out this gif.

 

https://upload.wikim...se_Oct_2007.gif


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#18 GlennLeDrew

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Posted 25 February 2018 - 01:35 PM

Lunar libration is a manifestation of an eccentric (and tilted) lunar orbit, just as the solar analemma is a manifestation of Earth's eccentric orbit (and axial tilt.) Momentum ensures that the rotation velocity for both Earth and Moon are (for our purposes here) essentially absolutely constant over the period of an orbit--or many orbits.


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#19 Brian Albin

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Posted 25 February 2018 - 05:36 PM

I thank everybody for the helpful responses.

Brian




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