Yes, it is thought that the moon formed of the earth, so that would explain why it is moving away from us if it happened from a big impact. I'd have to say that it would be a hundred million years back at least before the earth would be uninhabitible for humans.

When the earth was still covered in magma some 100 billion years ago a planet collided with it and the remains that flew outside the atmosphere tightened together to form the moon. But the earth was unhabitable then also. There was never a time when the moon was too close to the earth that it made life impossible

you're making an incorrect extrapolation. Not counting some of the moon origin theories out there, there's no reason to think that the moon was ever in contact with the earth. It could very well have been such that it started X miles away, and is simply spiraling outward.

Never.Five hundred million years ago the nighty sky would have been I guess 10% brighter.As well the reflection during daylight hours must be factored in an equation of lunar influence on life in general.

It would be interesting to create an equation that predicts the height of the tides in relation to the distance of the moon from the earth. I'm assuming that the closer the moon is to the Earth, the greater effect it will have on the tides. Therefore, the opposite is probably true. I bet there was a time when the Earth's tides were 5 to 10 times greater than they are now.

1) "Several mechanisms have been suggested for the Moon's formation. The formation of the Moon is believed to have occurred 4.527 ± 0.010 billion years ago, about 30–50 million years after the origin of the Solar System." "The prevailing hypothesis today is that the Earth–Moon system formed as a result of a giant impact. A Mars-sized body (labelled "Theia") is believed to have hit the proto-Earth, blasting sufficient material into orbit around the proto-Earth to form the Moon through accretion." Source and further information: http://en.wikipedia.org/wiki/Moon#Origin_and_geologic_evolution 2) "The Roche limit (pronounced /ˈroʊʃ/), sometimes referred to as the Roche radius, is the distance within which a celestial body, held together only by its own gravity, will disintegrate due to a second celestial body's tidal forces exceeding the first body's gravitational self-attraction.[1] Inside the Roche limit, orbiting material will tend to disperse and form rings, while outside the limit, material will tend to coalesce. The term is named after Édouard Roche, the French astronomer who first calculated this theoretical limit in 1848." "The table below gives the Roche limits expressed in metres and in primary radii. The true Roche Limit for a satellite depends on its density and rigidity. Body | Satellite | Roche limit (rigid) | Roche limit (fluid) Earth | Moon | 9,496 1.49R | 18,261 2.86R" Source and further information: http://en.wikipedia.org/wiki/Roche_limit 3) "The evolution of the Earth-Moon system can be described by the dark matter field fluid model with non-Newtonian approach and the current data of the Earth and the Moon fits this model very well. At 4.5 billion years ago, the closest distance of the Moon to the Earth could be about 259000 km, which is far beyond the Roche’s limit and the length of day was about 8 hours. The general pattern of the evolution of the Moon-Earth system described by this model agrees with geological and fossil evidence. The tidal friction may not be the primary cause for the evolution of the Earth-Moon system. The Mars’s rotation is also slowing with the angular acceleration rate about -4.38 × 10-22 rad s-2." Source and further information: "The evolution of the Earth-Moon system based on the dark matter field fluid model" http://arxiv.org/ftp/arxiv/papers/0704/0704.0003.pdf (interesting is also "Figure 1, Moon's distance and the length of day of Earth change with the age of Earth-Moon system") 4) "If the time of Earth’s existence was condensed into a 24-hour clock, the moon formation event occurred just 10 minutes after the Earth was born. The Earth formed 4.56 billion years ago, and the Moon formed about 30 million years later. At that time, the Earth was a magma ocean. An impactor about the size of Mars struck the Earth at an oblique angle, and removed some of the magmatic mantle. This mantle was put in orbit around the Earth, together with some of the debris from the impactor itself, and this material eventually formed the Moon. When the Moon first formed, it was very close to the Earth. It was possibly only 20 to 30 thousands of kilometers away, and it would have looked extremely large in the sky, at least 20 to 10 times bigger. But there were no living creatures on the Earth at that time to witness this beautiful scene. The tidal effect of a body increases as a cube of the distance, so the effect of the Moon’s tidal forcing on the Earth was extremely high at this time, to the point that the early magma ocean was affected. " Source and further information: http://astrobio.net/news/modules.php?op=modload&name=News&file=article&sid=2507&mode=thread&order=0&thold=0