# The Naked Scientists Forum

### Author Topic: How far can we predict the Earth-Moon system?  (Read 866 times)

#### chiralSPO

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##### How far can we predict the Earth-Moon system?
« on: 29/11/2015 18:30:52 »
I was thinking about the tidal acceleration of the Earth-Moon system (https://en.wikipedia.org/wiki/Tidal_acceleration#Earth.E2.80.93Moon_system)

We know that the Earth's day is getting ever-so-slightly longer, and will eventually equal the lunar month, such that the system is doubly tidally locked. We can also predict times and locations of lunar eclipses with reasonably high accuracy and precision very far into the future.

Can we predict where on the surface the moon will essentially always appear to be full (the points closest the moon), and where it will remain a thin sliver, or even never visible (the far side of the Earth)?

Is the system chaotic on the timescale of the billions of years it would take to achieve tidal locking, or is it closer to a clock winding down, and we can just predict it to the end, or is there some innate asymmetry in the system (like a weighted coin) that will favor a specific alignment and we don't even need to know when it is achieved to know where it will be?

#### evan_au

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##### Re: How far can we predict the Earth-Moon system?
« Reply #1 on: 29/11/2015 21:16:43 »
Quote from: ChiralSPO
Can we predict where on the surface (of the Earth) the moon will essentially always appear to be full?
The terms "full" and "thin sliver" refer to the illumination of the Sun, not the Earth-Moon system itself.

So if the Lunar Month is a lot longer than it is now (say, 2 months), and the Earth is tidally locked with a "day" that is 2 months long, then the Moon will still change phases from "Full", half-Moon, New Moon, etc, but each cycle will now take 2 months in stead of 29 days like it does now.

Every point on Earth that can see the Moon will see the same phases.

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Can we predict where on the surface (of the Earth) the moon will never be visible (the far side of the Earth)?
This is asking where the sub-Lunar point will be on the Earth.

I see this system as like a ball bouncing around a roulette wheel, gradually losing energy, until it settles down into a local minimum of energy. Picking the final resting position is about as easy as winning at roulette.

It will probably be affected by the motion of the tectonic plates on Earth, which will be in an entirely different location by that stage, so current points of reference on the Earth's surface will be somewhat meaningless.

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is there some innate asymmetry in the system (like a weighted coin)
I understand that the near and far sides of the Moon have quite different appearance, so the Moon is quite asymmetrical. Some astronomers have suggested that the Moon initially formed in two pieces that later mashed together in a relatively low-velocity impact. This may have weighted the coin.

However, the interior of the Earth is still being actively stirred by convection, so it is currently quite evenly balanced.

Around the time the Sun goes into red-giant phase, the Moon's orbit will shrink, and it may well turn into a temporary ring system.

#### chiralSPO

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##### Re: How far can we predict the Earth-Moon system?
« Reply #2 on: 30/11/2015 18:24:08 »
The terms "full" and "thin sliver" refer to the illumination of the Sun, not the Earth-Moon system itself.

So if the Lunar Month is a lot longer than it is now (say, 2 months), and the Earth is tidally locked with a "day" that is 2 months long, then the Moon will still change phases from "Full", half-Moon, New Moon, etc, but each cycle will now take 2 months in stead of 29 days like it does now.

Every point on Earth that can see the Moon will see the same phases.

Ah yes, of course! I wrote this post in a fairly sleep-deprived state, and now feel somewhat foolish...

When tidally locked, the different locations on Earth will see the moon go through the phases, but the moon will appear fixed in the sky, right?

#### evan_au

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##### Re: How far can we predict the Earth-Moon system?
« Reply #3 on: 30/11/2015 19:39:49 »
Quote from: ChiralSPO
When tidally locked, the different locations on Earth will see the moon go through the phases, but the moon will appear fixed in the sky, right?
Yes, the Moon will be in a fixed position above a point on the Earth (perhaps wobbling a bit North & South over a month or so, if the Moon's orbit is not exactly aligned with Earth's equator, or a bit East & West if the orbit is slightly elliptical).

Every point on Earth in the hemisphere around the sub-Lunar point will be able to see the Moon, at a fairly fixed position in the sky.

When doubly tidally-locked, the phases of the Moon will be the opposite of the illumination at the sub-Lunar point. So when it is:
- midnight at the sub-Lunar point, it will be a full Moon
- Sunrise or sunset at the sub-Lunar point, it will be a half Moon
- noon at the sub-Lunar point, the Moon will be lost in the brightness of the Sun

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##### Re: How far can we predict the Earth-Moon system?
« Reply #3 on: 30/11/2015 19:39:49 »