How close was the Moon to the Earth when it formed?
Answers
The Moon is thought to have formed when an object roughly the size of Mars hit the Earth. The impact was so violent that it threw large amounts of the Earth's mantle into orbit. This material evenually coalesced and formed the Moon.
It is not easy to estimate how far away from the Earth the Moon was when it formed, but simulations suggest is was about 3-5 times the radius of the Earth, or about 20 to 30 thousand kilometers. (The Moon is currently about 384,000 km or 60 Earth radii away from Earth, which is about fifteen times further away than it was when it first formed.) The Moon probably couldn't have formed closer than 3 Earth radii because tidal forces from the Earth would just pull it apart again, and it is unlikely that the impact could have ejected material further than 5 Earth radii. It's not a totally easy questions to answer though as it depends a lot on the (unknown) details of the impact and how the hot material behaved in space.
The exact rate of the Moon's movement away from Earth has varied a lot over time. It depends both on the distance between the Earth and the Moon, and the exact shape of the Earth. The details of continents and oceans moving around on Earth actually change the rate, which make it a very hard thing to estimate. The rate is currently slowing down slightly, and it is estimated that in about 15 billion years the Moon's orbit will stop increasing in size.
While our two celestial bodies remain locked in orbit, the moon is slowly — very slowly — inching away from Earth, at a rate of about 3.8 cm a year. Right now the moon is more than 238,000 miles from Earth, but when it formed, it was just 14,000 miles away.