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Thread: The Moon leaving Earth's orbit

  1. #1
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    Question The Moon leaving Earth's orbit

    The Moon is leaving Earth orbit at approx. 1cm/year (I think that number is correct). Does anybody know how many years from now it will actually leave orbit? How far away will it have to be for the Earth's gravity to no longer be able to hold it? Google turned up very little on this and I couldn't find anything by searching the forum.

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    38,250,000 years just to get twice the distance. And wouldn't the rate be continually decreasing since the tidal forces acting on the speed would diminish? And, wouldn't tidle locking happen before that. Therefore, would the moon leaving orbit even happen?
    Besides, the sun's going to blow up and engulf the moon before that happens anyway.

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    The Moon will never leave orbit-- to expel the Moon gradually would require giving it an infinite amount of angular momentum (in Kepler's law, angular momentum increases with distance like the square root of distance). The
    Earth's rotation does not have infinite angular momentum, so it never happens. What would happen first is that the Earth's rotation would essentially stop, or actually, would rotate so slowly that it would keep the Moon at a fixed point in the sky, and there would be no further angular momentum transport from the Earth to the Moon. So NEOWatcher has that right-- but nothing in particular will happen to the Moon when the Sun expands into a red giant.

  4. 2005-Oct-26, 05:26 PM
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    Quote Originally Posted by NEOWatcher
    Therefore, would the moon leaving orbit even happen?
    I don't know, but it seems possible.

    Quote Originally Posted by NEOWatcher
    Besides, the sun's going to blow up and engulf the moon before that happens anyway.
    When is that susposed to happen?

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    The Sun will not "blow up" in the usual sense, but it will expand into a red giant. Twice, actually. The second time should engulf Earth, I am told. But that won't be for another 5 billion years, and the Moon's orbit will not be terribly affected, I don't think anyway. The outskirts of the Sun will not be very dense by that point.

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    Once the moon reaches its farthest distance from Earth, when it is tidally locked (which it is not quite yet), then it will stop migrating away from Earth, and come back. The return trip is caused by friction with solar tides, and will take about 50,000,000,000 years. Of course the sun will do its red giant thing, and M31 will collide with the Milky Way, in about 5,000,000,000 years. So the migration process might not get a good chance to do much. The last measured recession rate I saw was 3.82±0.07 cm/year in 1994.

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    The Earth would lose its grip on the Moon at about 1.5 million kilometers, the edge of the Earth's Hill Sphere. But it will never get there for the reasons forementioned.

    Quote Originally Posted by Ken G
    The outskirts of the Sun will not be very dense by that point.
    So the Earth and Moon will continue to orbit the center of the Sun while IN the Sun! The Sun would encompass 360 degrees of sky. How weird would that look? I wonder if we could see other stars in the sky on the side of Earth facing away from the core.

    And even though the outskirts of the Sun encompassing Earth would be extremely hot, it would also be extremely tenuous, and not very efficient at conducting its heat to Earth. So the Earth might take thousands of years to heat up appreciably.

    And the Earth and Moon would probably leave trails in their paths much like a shooting star.

    But ultimately, Earth probably would spiral in towards the core. I wonder how long that would take?

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    The sun's red giant phases will probably just about engulf the Earth's current orbit, but not the Earth itself. By the time the Sun swells to this size, it will have lost enough mass that Earth & Moon will have shifted outwards and will escape being swallowed.

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    Quote Originally Posted by Joff
    The sun's red giant phases will probably just about engulf the Earth's current orbit, but not the Earth itself. By the time the Sun swells to this size, it will have lost enough mass that Earth & Moon will have shifted outwards and will escape being swallowed.
    Ah, that's interesting, I did not realize it was so close to the edge. I wonder if this is pushing the accuracy of the simulations? After all, anything with a convection zone is being modeled in a fairly heuristic way. So maybe we don't know for sure what the fate of Earth will be, though it does sound like Earth's orbit will be pretty far out by then, so I'll buy Joff's argument, at the right price.

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    Has the Moon's increasement from Earth been measured & verified? Reason I ask, is I have heard that "1cm per year" story since I was a little kid (from '50s).

    To be honest, I can not understand two objects held in gravity drifting apart.

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    Apparently the moon was supposed to have left six years ago

    All you need happen to make the moon leave and move at relativistic speeds so you can have a new adventure every week is a nuclear explosion at a disused nuclar dumpsite on the moon.

    Now where did they put that

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    Sticks, I have just watched Season 1 boxset of this fabulous old show! Amazing FX, psychedelic stories, great serious acting etc... Is funny how the Moon is blasted out of orbit, and in the next few episodes it is passing planets, black holes, etc he! But I forgive it for that, it is still quite brilliant.

    But my question remains however, Why is Moon leaving us when gravity holds it to Earth? Is rest of Universe pulling it away gravitationally??

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    Quote Originally Posted by SillyMidOff
    Has the Moon's increasement from Earth been measured & verified? Reason I ask, is I have heard that "1cm per year" story since I was a little kid (from '50s).
    Reflectors were left on the moon as part of the Apollo project (also some were left by Russian robot missions, but they aren't as well aligned). Lasers are bounced off these to measure the distance.

    To be honest, I can not understand two objects held in gravity drifting apart.
    It has something to do with tides and rotation. In a nutshell, some of earth's rotation energy is accelerating the moon. While earth's rotation is slowed, the moon moves to a higher orbit.

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    Quote Originally Posted by Andreas
    Reflectors were left on the moon as part of the Apollo project (also some were left by Russian robot missions, but they aren't as well aligned). Lasers are bounced off these to measure the distance.

    It has something to do with tides and rotation. In a nutshell, some of earth's rotation energy is accelerating the moon. While earth's rotation is slowed, the moon moves to a higher orbit.
    Hmm, but against "what" are we measuring these convenient "rotations"? Is not Einstein relativity valid?

    (NOTE: I don't know, I'm just very curious!)

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    Lightbulb 3.82±0.07 cm/year

    Quote Originally Posted by Ken G
    I wonder if this is pushing the accuracy of the simulations?
    Yes, the race is in fact too close to call from 5 billion years out. In any case, it is hard to believe that dynamic friction with the fierce stellar wind, as the sun evolves to a red giant, will not cause Earth to eventually be consumed by the sun.
    Quote Originally Posted by SillyMidOff
    Has the Moon's increasement from Earth been measured & verified?
    Yes. The value that I gave earlier (3.82±0.07 cm/year) comes from the ongoing effort at Lunar Laser Ranging (LLR), which uses corner mirrors left on the moon by Apollo astronauts, specifically to make those measurements, and was published in 1994 (Lunar laser Ranging: A Continuing Legacy of the Apollo Program, J.O. Dickey, et al., Science 265: 482-490, July 22, 1994). There is also quite a bit of data from geology & paleontology, from which one can derive lunar recession rates, over the history of the Earth-moon system. I review all of that in my webpage on the Talk.Origins Archive: The Recession of the Moon and the Age of the Earth-Moon System. That's the most recent published value that I am aware of, but I haven't looked too hard either (I'm too lazy to sift through the 140 references, a task left as "an exercise for the student"). The currently measured rate is anomalously high, because of resonance between the Earth-moon tides and the size of the ocean basins (which varies as the continents migrate due to plate tectonics).

    The precision & accuracy of the LLR measurements is such that we can now use them to probe questions in fundamental physics, such as the possible time variation of Newton's gravitational constant (G in the Newtonian gravity formula F = Gm1m2/r2), and the validity of general relativity.

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    Quote Originally Posted by Tim Thompson
    Once the moon reaches its farthest distance from Earth, when it is tidally locked (which it is not quite yet), then it will stop migrating away from Earth, and come back.
    The moon is tidally locked to the Earth. The moon is receding because the Earth is not tidally locked to the moon, nowhere near I would say. When the moon stops migrating away, the Earth's day will be as long as the moon's orbit period, which will be longer than our present month.

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    Quote Originally Posted by SillyMidOff
    Hmm, but against "what" are we measuring these convenient "rotations"? Is not Einstein relativity valid?
    It shouldn't matter. In the geocentric reference frame, the moon is revolving around the earth once every ~25 hrs. In this frame, due to the inelasticity of the earth, the tidal bulge lags behind the moon's revolution, leading to the effects described above.

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    Lightbulb Why the moon recedes & why it's coming back

    Quote Originally Posted by SillyMidOff
    But my question remains however, Why is Moon leaving us when gravity holds it to Earth? Is rest of Universe pulling it away gravitationally??
    The moon is receding from Earth because of tidal forces, which are a consequence of the fact that Earth & the moon are both extended objects (not point masses), and that they both spin. Imagine that Earth & the moon are just sitting still. The side of Earth nearest the moon is pulled towards the moon harder than the more distant side, so Earth bulges towards the moon. But they are not just sitting still, Earth spins around once every 24 hours, and that spin pulls the bulge out in front of the slower moving moon (which goes around Eath only about once every 29 days). Now the bulge acts like a sling, pulling the moon slightly from its forward direction. That pull transfers energy from Earth, to the moon. As a consequence, the spin of Earth is slowing down slightly, and the energy transferred to the moon moves it away slowly. The motion of the moon is measured at 3.82±0.07 cm/year. The slowing of Earth is measured as a change in the length of day, which increases now at about 0.0015 seconds per day per century.

    Eventually, the moon will reach a maximum distance from Earth, at which time both will be tidally locked to each other, the moon showing the same face always to Earth, and Earth always showing the same face to the moon. The moon is now almost, but not quite yet, tidally locked. Earth is a long way from it. The process will take about 50,000,000,000 (50 billion) years. Once that has happened, solar tides will continue to slow the moon down, and it will begin a return journey to Earth (Phobos has already begun its return journey to Mars). The return journey will take close to another 50,000,000,000 years. I had forgotten about the two parts of the trip when I posted earlier that the moon would be back in 50,000,000,000 years. Actually, it's closer to 100,000,000,000, just in case you were worried about it (seems like a long time, but a minimal red dwarf star will stay on the main sequence a thousand times longer, about 100,000,000,000,000 = 100 trillion years).

    My explanation of tides & the bulge is only a "first order" explanation, and is good enough for this purpose. But keep in mind that the real tidal interaction is more complicated. The ocean tides are more important than the Earth tides, for instance. The varying size of ocean basins will change the rate of recession quite a bit. And the interior of Earth is not solid, but is a viscous fluid mantle. That fluid motion also affects tides. But those are topics for a mre detailed discussion, not necessary here.

    Quote Originally Posted by hhEb09'1
    The moon is tidally locked to the Earth.
    I don't think it will be tidally locked until its libration goes away. We can see about 59% of the moon, but we should be able to see only 50% when it is locked.

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    Quote Originally Posted by Tim Thompson
    I don't think it will be tidally locked until its libration goes away. We can see about 59% of the moon, but we should be able to see only 50% when it is locked.
    But to get rid of libration, the orbit would need to be circular. Do you really need a circular orbit to be considered tidally locked?

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    Do you really need a circular orbit to be considered tidally locked?
    No! Mercury is tidally locked to the Sun in a 3:2 ratio.

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    Lightbulb Circular Orbits?

    Quote Originally Posted by pghnative
    But to get rid of libration, the orbit would need to be circular. Do you really need a circular orbit to be considered tidally locked?
    I think yes. See, for instance, Solar System Dynamics, C.D. Murray & S.F. Dermott, Cambridge University Press, 1999 (p. 167 in the 2001 paperback reprint that I have). Tidal friction always acts to reduce orbital ellipticity, and should circularize the orbit. In a 2-body system, that would certainly happen. But I really don't know if solar tides, or even planetary perturbations, would prevent a really circular orbit, in the real Earth-moon system.

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    Lightbulb Spin Orbit Resonance

    Quote Originally Posted by Kaptain K
    Mercury is tidally locked to the Sun in a 3:2 ratio.
    Mercury is not tidally locked, at least not in the same sense. Rather, it is trapped in a 3:2 spin-orbit resonance; its orbital period of 87.97 days is exactly 1.5 times its spin period of 58.65 days. The same Murray & Dermott book has a long discussion of this, in section 5.4 on "Spin-Orbit Resonance".

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    Quote Originally Posted by Tim Thompson
    Quote Originally Posted by Kaptain K
    Mercury is tidally locked to the Sun in a 3:2 ratio.
    Mercury is not tidally locked, at least not in the same sense. Rather, it is trapped in a 3:2 spin-orbit resonance; its orbital period of 87.97 days is exactly 1.5 times its spin period of 58.65 days.
    Does that mean it's in an energetic minimum and can't break through to full (1:1) tidal lock?

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    As I understand it, Mercury is in an energy minimum given its highly eccentric orbit. But any elliptical orbit always has excess energy, relative to its angular momentum. So if it had a mechanism, it would certainly "like" to have its orbit circularized, and I would suppose that this is what is happening even now. If so, it will eventually be locked to the Sun in the fashion Tim Thompson is talking about. But I don't know if this will happen, because it certainly has had a long time and it hasn't done so yet.

    But I don't understand something more basic about Mercury-- why does having a rotational resonance matter at all? Why doesn't the rock relax to the tidal forces in less than the 88 day (?) orbit? How does it remember the location of the bulge from orbit to orbit?

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    Mercury is a special case.

    PDF: Mercury: the planet and its orbit (André Balogh and Giacomo Giampieri)

    Colombo (1965) and Colombo and Shapiro (1966) demonstrated how the rotation rate can be exactly 1.5 times the mean orbital angular frequency, as a result of a non-zero eccentricity and a small permanent asymmetry in the equatorial plane of the planet ...

    ... the 3:2 resonance is due to permanent deformations on the equatorial plane, and to the non-zero eccentricity ....
    The asymmetry in the planet's equatorial plane is thought to have been caused by the Caloris Event, a massive asteroidal impact that produced Mercury's Caloris Basin.

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    Quote Originally Posted by pghnative
    But to get rid of libration, the orbit would need to be circular. Do you really need a circular orbit to be considered tidally locked?
    Maybe we need a new terminology to distinguish between "tidally locked with librations" (which is probably what most people mean when they use the term) and Tim's "tidally locked without librations", which is a stricter use of the term.

    Of course, even in Tim's case there will still be other librations (diurnal, for instance), which will allow us to see more than 50% of the Moon's surface.

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    Quote Originally Posted by Eroica
    Maybe we need a new terminology to distinguish between "tidally locked with librations" (which is probably what most people mean when they use the term) and Tim's "tidally locked without librations", which is a stricter use of the term.
    The first is more common. As Tim mentioned, in real life there are no perfect systems. Even the moons of Jupiter, which everyone agrees are tidally locked, are not locked in the second meaning. If they were, there would not be any tidal stress--which is blamed for an apparently frictional heat that manifests at their surfaces.

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    Quote Originally Posted by Eroica
    The asymmetry in the planet's equatorial plane is thought to have been caused by the Caloris Event, a massive asteroidal impact that produced Mercury's Caloris Basin.
    Ah, thanks, that's quite interesting. I'm surprised such a large planet can maintain such a deviation from its Roche potential, but then again, Mercury isn't all that big, and perhaps its metal content is quite rigid...

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    Quote Originally Posted by Ken G
    Ah, thanks, that's quite interesting. I'm surprised such a large planet can maintain such a deviation from its Roche potential, but then again, Mercury isn't all that big, and perhaps its metal content is quite rigid...
    The sustained bulges in the Earth's equator are a couple orders of magnitude larger than the tidal bulges. They may be more dynamically maintained, but the strength should be similar. They don't affect the tidal slowing in the Earth case because the effect is symmetrical, whereas the tidal bulge effect isn't. That would make a difference on Mercury though, because of the asymmetry of its orbit.

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