Orbital mechanics

[Tallahassee Bob]

After 75 years, this question has just now occurred to me......why are moon orbits stable for millions or even billions of years? Doesn't this require that the orbital velocity be exactly correct forever? Or does the diameter of the orbit somehow adjust automatically to the velocity of the object? It would seem intuitively that this can't be true, and that any orbiting object is in a metastable orbit that is actually slowly spiraling either inward or outward. So what's the answer?

[neufer]

After 75 years, this question has just now occurred to me......why are moon orbits stable for millions or even billions of years? Doesn't this require that the orbital velocity be exactly correct forever? Or does the diameter of the orbit somehow adjust automatically to the velocity of the object? It would seem intuitively that this can't be true, and that any orbiting object is in a metastable orbit that is actually slowly spiraling either inward or outward. So what's the answer?

Not quite sure what you mean by "stable."

The Earth tides lead the Moon thereby transferring additional angular momentum to the Moon causing the diameter of the Moon's orbit to slowly spiral out about 3 meters in the last 75 years. The Moon automatically adjusts to a slightly slower (~0.145 m/hr) velocity.

So what's the question, Bob?

[Chris Peterson]

After 75 years, this question has just now occurred to me......why are moon orbits stable for millions or even billions of years? Doesn't this require that the orbital velocity be exactly correct forever? Or does the diameter of the orbit somehow adjust automatically to the velocity of the object? It would seem intuitively that this can't be true, and that any orbiting object is in a metastable orbit that is actually slowly spiraling either inward or outward. So what's the answer?

The tides leave patterns in silt that sometimes survive in sedimentary rock. We have Cambrian rock that shows there were close to 500 days in a year a billion years ago. The rotation rate of the Earth is slowing down as rotational angular momentum is transferred to orbital angular momentum of the Moon, pushing its orbit outwards. This is confirmed by fossil shell growth patterns that show the changing length of the lunar month.

Bodies in our Solar System have orbits that evolve over time, and occasionally experience chaotic shifts (because no natural system of three or more bodies is perfectly stable).

[Tallahassee Bob]

So, is there a calculable terminal diameter of moon orbit when the moon eventually rotates in geo-synchrony with the Earth and no longer appears to move in the sky?

[Chris Peterson]

So, is there a calculable terminal diameter of moon orbit when the moon eventually rotates in geo-synchrony with the Earth and no longer appears to move in the sky?

It's not a well constrained problem. For one thing, a major component of the angular momentum transfer involves the tidal motion of Earth's oceans. But those oceans will have evaporated away in 1-2 billion years, which is long before the rotational period of the Earth will match the orbital period of the Moon. Most calculations suggest that tidal locking will not be complete before the Sun expands into a red giant with a radius greater than 1 AU, and the question becomes irrelevant.

[neufer]

So, is there a calculable terminal diameter of moon orbit when the moon eventually rotates in geo-synchrony with the Earth and no longer appears to move in the sky?

It's not a well constrained problem. For one thing, a major component of the angular momentum transfer involves the tidal motion of Earth's oceans. But those oceans will have evaporated away in 1-2 billion years, which is long before the rotational period of the Earth will match the orbital period of the Moon. Most calculations suggest that tidal locking will not be complete before the Sun expands into a red giant with a radius greater than 1 AU, and the question becomes irrelevant.

Were there time to be allowed for that to happen, however, the terminal diameter of moon orbit would be about 50% greater than it is now and the geo-synchronous month/day would be around 2 (current) months long.

[Tallahassee Bob]

Thanks to all!

Bob