[Kryptid (OP)]

Has sufficient information been gained, either from geological evidence or from computer models, to determine the distance of the Moon from the Earth over its 4.51 billion year history? That is, can we reasonably make a graph of distance versus time for the Earth-Moon system?

I know that the rate of recession has changed over time, both speeding up and slowing down at times. It changes depending on the arrangement of the continents and the Earth's rotation rate, for example. Numbers that I pulled from Wikipedia suggest that the Moon was about 206,000 miles away from Earth 2.5 billion years ago and 15,000 miles away when it initially formed. Tidal rhytmites have given some data about this over geological history. How complete is this information?

[evan_au]

over geological history. How complete is this information?

I'm afraid our geological and fossil record is rather fragmentary.

To be preserved with a readable history on a scale of days to years, rocks must be formed from fine sediments, buried at a steady rate over a long period.
- They can't stay too near the surface, or they will be eroded by the next flood
- They can't be buried too deep, or they will be melted into the mantle, and lose any visible structure
- They have to be close enough to the surface today for us to be able to find them (since there is no economic value in rhythmites, this typically means exposed in a quarry or road cutting)

I have heard of another source of evidence on the recession of the Moon, and that was around fossilized corals that show both daily and annual growth rings, allowing researchers to deduce the number of days per year, and hence the rate at which the Earth's rotation is slowing. This angular momentum is transferred to the Moon, and indicates how much the Moon has receded.

For more tasty sedimentary deposits like an animal carcass, the odds are very much stacked against leaving a complete record.

[guest4091]

The current rate:
The Moon is spiraling away from Earth at a rate of 3.8 cm per year.[9] This rate has been described as anomalously high.
en.wikipedia.org/wiki/Lunar_Laser_Ranging_experiment
see also:
nasa.gov/mission_pages/LRO/multimedia/lroimages/lroc-20100413-apollo15-LRRR.html
The history of the earth-moon system is far too complex and unknown to find a simplistic relation.

[jeffreyH]

The earth/moon system is not a straightforward 2 body problem. It is complicated by the other bodies in the solar system.

[evan_au]

This rate has been described as anomalously high.

Astronomers think the average rate of recession is lower than the current rate.

They suspect that the current rate is due to the present distribution of continents, which presents several large North-South barriers to tidal circulation (North/South America and Africa/Europe), increasing tidal drag and causing the Moon's recession to increase.

At other times, the Earth's continents were clustered in a supercontinent, which might have provided less of an impediment to tides, and the Moon's recession rate would have been lower.
See: https://en.wikipedia.org/wiki/Supercontinent