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The moons' spiraling oribts

  1. Jun 19, 2003 #1
    Some questions, based on things I've heard, but don't know to be true:
    The rotation of the moon has slowed down to the point that one revolution and one rotation have the same period. A number of the moons of Jupiter and Saturn also have this property. Mercury does something similar to this - something like 3 rotations for every 2 revolutions. Will this phenomenon ever occur to the other planets? Is the Earth day becoming longer? How does this occur?
    Also, I have heard of something called a "Roche" limit. When a moon's orbit comes within this limit, the planet's gravitational forces will cause the moon to break apart and the moon will become rings. Whether or not a moon will ever become a part of a ring system depends on whether the moon orbits the planet clockwise or counterclockwise as viewed from "above" the solar system. In other words, a moon either spirals in towards the planet or out from a planet (at an exceedingly slow rate) depending on the way it orbits the planet. Is this true for all orbits? Are the planets spiraling in towards the Sun? Could Mercury become a ring system of the Sun? When a moon becomes a ring system, is the new oribt stable or do the particles eventually become incorporated into the planet? Why does this spiraling occur?
  2. jcsd
  3. Jun 19, 2003 #2


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    This phenomenon, called gravitational or tidal locking, would eventually happen to all of the planets, given enough time. I don't believe that any of the planets experience a tidal force from the Sun large enough to cause tidal locking before the Sun dies, however. I don't have any calculations on hand to demonstrate this. If you're really interested, I will work the numbers out.
    The earth's rotation is slowing down, due mostly to the Moon's influence. Eventually, the Earth-Moon system will reach an equilibrium in which each body shows the other one face at all times. Tidal locking is a result of the tidal strains that one body exerts on another in a gravitationally bound system. In the case of two tidally locked bodies, the two bodies stretch each other out along the line connecting them, so they're rather egg-shaped. When the bodies are rotating, however, he bulges are carried by the bodies' rotation such that they are not exactly aligned with the line connecting the bodies. This misalignment generates a torque which slows the bodies down. The rotational kinetic nergy is dissipated by heating in the bodies.
    This is correct -- there is a minimal distance at which a moon must stay to avoid being pulled apart by tidal forces. You can calculate the distance, the Roche radius, fairly easily -- just equate the tidal forces on either side of the moon with the moon's self-gravity. When the tidal forces exceed the gravitational forces, the moon falls apart. For a planet and moon of equal density, the easiest case, the Roche radius is 2.4 times the planet's radius.
    I don't believe this has any consequence. What's special about being "above" the solar system? You can't really define an orbit as clockwise or counterclockwise without reference to some arbitrary convention.
    Once again, no, the orbit is of no consequence. What does matter is the difference in the rotational directions of the two bodies; when they rotate in the same direction, or in opposite directions, the results of tidal locking on the orbit are different. The planet-moon system always conserves angular momentum. The Earth and Moon both rotate the same way, counter-clockwise as viewed from above the Earth's north pole. As a result, as they slow down to reach tidal locking, the Moon's orbital radius increases. For a planet-moon system with opposite rotations, the orbit would decrease in radius.
    If it could, it already would be. Mercury is too dense to become a ring of the Sun. The Roche radius depends upon the density of the two bodies.
    It is most likely that the resulting particulates in the ring are individually too dense to be torn apart any further by tidal forces. As such, they are stable. However, they have so little mass that other moons, etc. end up perturbing them and throwing them out of the system. The rings slowly dissipate over time.

    - Warren
    Last edited: Jun 19, 2003
  4. Jun 19, 2003 #3


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    I'll take a shot at some of these. The condition in which we currently find our moon is a situation astronomers refer to as being "tidally locked". It is a result of the tidal forces the earth exerts on the moon (of course, it could just be a huge coincidence, but what are the odds?). And yes, these same forces are slowing the rotation of the earth, but our planet's rotation is slowing down to synchronize with the moon, not the sun, because the moon has a much stronger tidal effect on the earth than the sun does.

    AFAIK, the direction in which the moon orbits a planet is not a factor in whether or not that moon will break up. The only true deciding factor here is whether the moon is in a decaying orbit (one that brings it closer and closer to the planet). It just happens that the best example we have in our solar system of a moon with a decaying orbit is also the only moon that orbits in retrograde (the opposite direction from all the other orbits in the solar system). But these two properties of Neptune's moon Triton are probably effects of a common cause; Triton is probably not a moon that formed around Neptune, but rather a Kuiper Belt object that get trapped by the planet's gravitation.
    Last edited: Jun 19, 2003
  5. Jun 19, 2003 #4


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    Cause of all of this is tides.

    Let's look first at why the Moon always presents one side to the Earth.

    The Earth exerts a tidal force on the moon which tends to strecth it out along the line joining the Moon and Earth. This create "tidal" bulges. When the moon was rotating faster, different parts of the moon would pass through these tidal bulges, this created a friction which caused the moon to slow its rotation until it reached the state it is now in. This is known as being in tidal lock.

    The Earth undergoes the same with the Sun, But for the Earth, this is only part of the picture. The Moon also creates tidal bulges on the Earth, and because of the proximity of the Moon these are larger than those of the Sun,

    This causes two things to happen; One, the Earth slows in its rotation, and two, the Earth tends to drag the tidal bulges along with its rotation.

    The draging of the tidal bulges pulls them slightly out of alignment with the moon, Causing a "forward" pull on the Moon, The Earth transfers some of its rotational energy to the moon. Adding Energy to the Moon causes it to move into a higher orbit. This will continue until the Earth rotates at the same rate as the moon orbits.

    If the moon orbited the Earth in the opposite direction than the Earth rotated, this mis-alignment would pull counter to its orbital direction, the Moon would fall into a lower and lower orbit.

    So it really depends on whether the moon and planet rotate in the same direction as to which direction(in or Out) the Moon will spiral.

    If in, the Moon will get closer and closer. As it does so, the tidal forces on it get stronger. If the moon is large enough that it is primarily holds its shape due to gravity, it will eventually reach a point where the tidal forces exeed those holding it together and it will break apart. This distance is the Roche Limit.

    Once a ring sytem is formed, there will be no more tendancy for the components to continue spiraling. It was the fact that the intact moon pulled all in one direction that caused the tidal bulge which lead to the spiral, with a ring system, all the components are pulling in different directions, canceling each other out.

    As far as the planets go, they all revolve around the Sun in the same direction as the Sun rotates, so there is no tendancy for them to spiral inwards toward the sun.
  6. Jun 19, 2003 #5


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    Wow, can you tell we're all interested in tidal locking, or what?

    - Warren
  7. Jun 19, 2003 #6
    Actually the two are linked. The tidal effect transfers angular momentum from the planet to the moon in every case, so that if the moon is in a contrarotational orbit it will slow down and lose altitude, while those in a corotational orbit will gain altitude.
  8. Jun 20, 2003 #7


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    Yeah ! Great thread ! Thanks ! :smile:
  9. Jun 20, 2003 #8
    The moon is actually moving away from the earth, this is one of the key pieces of evedince used to explain the imact creation of the moon.
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