# Angular momentum in planetary/satellite orbital systems

If a planet had a large massive satellite, on a long elliptical orbit, would the planet's rotation slow and speed up depending on the distance of the moon from the planet?

I'm thinking of how a skater, the classical example of angular momentum, speeds up when bringing in her arms, and slows down when extending them. Would that happen to a rotating planet? different rates of rotations? even small ones?

thank you.

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Cool question. I don't think the moon's rotation would change in the way you're thinking.

To conserve the angular momentum of the moon around the planet, its speeds up when its closer to the planet (Kepler's law... etc). The ROTATION of the moon has no angular momentum with regard to the planet; it only has angular momentum relative to itself, and therefore needs to remain constant.

On a different level however, tidal forces will act on the moon's rotation... i'm not sure how the details of that work however.

Cool question. I don't think the moon's rotation would change in the way you're thinking.

To conserve the angular momentum of the moon around the planet, its speeds up when its closer to the planet (Kepler's law... etc). The ROTATION of the moon has no angular momentum with regard to the planet; it only has angular momentum relative to itself, and therefore needs to remain constant.

On a different level however, tidal forces will act on the moon's rotation... i'm not sure how the details of that work however.
well, i'm not interested in the moons rotation, though i guess that's moot since in te system, both bodes are essentially moons of one another.

The earth's rotation slows due to the moon's tidal force, and as a result the moon moves further away, conserving angular momentum. So the earths' rotation DOES affect the moon's distance. Slow the earth's day down, and the moon recedes from the earth. So the rotation of the individual bodies in the system does affect and is affected by the orbits of the other body. The question is, in what way precisely.

And would the inverse be true. If you pushed the moon closer to the earth, would the earths' day shorten?

because the moon deffinately recedes as a result of the day lengthening. Which it does gradually over time. Except for events like the tsunami of 2004, where the earth 's day decreased by a small amount.

I remember reading in some book by arthur C clarke in which the moon was destroyed, that hte immediate reaction was the earth's rotation slowing down. Clarke was a rigorously scrupulus sci fi writer and was a scientist himself, and this just came to me now.

i just can't find a clear explanation anywhere.

D H
Staff Emeritus
If a planet had a large massive satellite, on a long elliptical orbit, would the planet's rotation slow and speed up depending on the distance of the moon from the planet?
That doesn't happen, at least not in the sense you are thinking. But see the discussion at the end.

I'm thinking of how a skater, the classical example of angular momentum, speeds up when bringing in her arms, and slows down when extending them.
That's not a particularly good analogy. The skater's arms are attached to the skater. They rotate at the same rate as does the skater as a whole. A moon's orbit period and a planet's rotation period can be quite different. The Moon, for example, orbits the Earth every 27.3 days.

The earth's rotation slows due to the moon's tidal force, and as a result the moon moves further away, conserving angular momentum. So the earths' rotation DOES affect the moon's distance. Slow the earth's day down, and the moon recedes from the earth. So the rotation of the individual bodies in the system does affect and is affected by the orbits of the other body. The question is, in what way precisely.
This is a very, very slow process. One solar day was 21.9 hours long 620 million years ago. The mechanism by which this happens is called tidal locking; here's the http://en.wikipedia.org/wiki/Tidal_locking" [Broken] on the subject.

And would the inverse be true. If you pushed the moon closer to the earth, would the earths' day shorten?
No, at least not if you attach some big honking rockets to the Moon and use those rockets to bring the Moon closer to the Earth.

The Moon and Sun do have a short-term effect on the Earth's instantaneous rotation rate. Here is a plot of excess length of day (length of one solar day less 86,400 seconds):

http://www.iers.org/images/figc.png [Broken]

The bottom two subplots show that zonal tides do affect the Earth's rotation rate. The Moon and Sun raise tides in not just the oceans but in the Earth as a whole (http://en.wikipedia.org/wiki/Earth_tide" [Broken] on Earth tides).

Here your ice skater analogy is a very apt. The ice skater, by pulling her arms in / pushing her arms out, is changing her moment of inertia. These Earth tides (plus the ocean tides, to a lesser extent) caused by the Moon and Sun act to change the Earth's inertia tensor. The Earth's inertia tensor oscillates because of the tides, but oscillates with 288 or so different frequencies (tidal theory is a convoluted mess.) The largest oscillations are the semidurnal and diurnal tides. The Lunar fortnightly and monthly oscillations represent less than a tenth of the total, but it is not zero. The shape of the Moon's orbit does have an affect on the Earth's rotation rate, albeit a very small one.

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So then, if the shape of the moon's orbit DOES have an effect on the rotatoin rate, albeit a very small one, what would have to change for that effect to be a great one? THe mass of the moon to increase a zillion fold? The eccentricty of the orbit to change radically so that the effect would be more pronounced?

just curious