A creationist website makes this argument for the 6,000 year old earth. I'm embarrassed to say I don't know how to do the math to evaluate the claim myself. However, the time scales involved seems to lend some credence to this argument. "The Moon is slowly drifting away from the Earth. If it is getting further, at one time it was much closer. The Inverse Square Law dictates that if the Moon were half the distance from the Earth, its gravitational pull on our tides would be quadrupled. 1/3 the distance, 9 times the pull. Everything would drown twice a day. Approximately 1.2 billion years ago, the Moon would have been touching the Earth. Drowning would be the least of our concerns! - See more at: http://www.allaboutcreation.org/how-old-is-the-earth.htm#sthash.LSHK4GQk.dpuf"
Extrapolation is as likely to produce meaningless results when done into the past as when done into the future.
The most widely accepted theory for how the Earth-Moon system was formed is the Giant impact hypothesis: around 4.5 billion years ago, the (then itself still very new) Earth was nearly destroyed by a collision with another planet roughly the size of Mars. This created a huge cloud of debris orbiting the Earth, much of which coalesced into the moon.
So the moon first formed at a certain distance from the Earth, and that distance has since then grown due to tidal braking (and the same effect is steadily increasing the length of the day on Earth).
An interesting detail about your quote is that their extrapolation of 1.2 billion years is much shorter than the time since the impact, but without any indication of how that number was computed, it means nothing. It is not a linear extrapolation of the current distance (384,000km) and rate of increase (3.8cm/a) because that yields over 10 billion years. But the rate of increase really cannot be meaningfully extrapolated because it depends on the magnitude of friction caused by tidal forces, and that depends on what the Earth looks like. After the impact, the Earth was probably mostly liquid for some time, which would cause much more tidal friction and thus a much more rapid increase in distance.
But the creationists are correct about one thing: Drowning would, indeed, be the least of our concerns back then!
63,360 x 238,900 = 15,136,704,000(inch now) (1.5inch x 4,000,500,000 = 6,000,750,000) 15,136,704,000 - 6,000,750,000 (inch then ) = 9,135,954,000 inches. 9,135,954,000/63360=144,191.19318181 (converting it back to miles)
Roughly 144,000 miles 4.5 billion years ago
But due to the tidal friction, caused by the tidal bulge, the earth loses energy and is given to the moons orbit at a slower and slower rate as time goes by so it was much less than 144,000 miles.
The rate of the moons movement (away from earth) decreases as the moons distance (away from earth) increases.
I just stumbled across this more than two years after the fact. Interesting conversation.
One thing that the creationist website and the answers I've seen in this forum have failed to address, is that the increased tidal action would not be the only effect of a closer Moon. The farther back we look in time the less chance the moon would be able to escape the Earth's gravity. It should be getting closer today and yet it is moving away instead.
For the sake of argument let's assume that the aforementioned idea that the moon was caused by a collision of another Celestial body with the primordial Earth is indeed what occurred. That leaves us with a contradiction.
With an exponential increase in gravity the closer the Moon and Earth are to one another, in order to maintain the proper balance to sustain its orbit until now, the moon would also have to be going exponentially faster the further back in time. That being the case, the debris from the Collision could never have coalesced into the moon in the first place. (These same factors, also mean the death of the capture Theory.)
Assuming such exponential speeds were not present at the time of the Collision, means the debris that would have coalesced into the Moon, would need to have accelerated dramatically once it had. This again would not have happened.
Further, through observation, we know that objects in space that break apart within the gravitational field of a planet, do not coalesce back into a localized Mass. Instead, due to the influence of the nearby gravitational field, they remain a debris field because the field exerts greater influence on the individual bits of debris than they can exert on one another.
This does not even consider heat pressure; another force working against coalescence. This, among other reasons, is the same reason nebula are coming apart rather than coalescing into new stars.