How long will it take for the moon to spiral out of orbit?

Can someone do the math on this?

Depends how you define "out of orbit"
Are you referring to the Moon's "current" orbit, or a "range of orbits" or any orbit at all?

In the first case: it happens all the time, since the Moon is not yet in a "stable" orbit. It moves away from us at the rate of ~3.8cm/year.
In the last case: it will never really happen, because when the Sun dies in roughly 5 billion years, the Moon will still be in orbit around Earth.


But since this is the entertainment forum, I want to highlight another severe! problem the impact is creating!

It is widely overlooked, that NASA hit the moon on the south pole, not on the equator. This means that the inclination of the Moon's orbit around the Earth will slowly increase over the years and since the moon is the major factor that stabilizes the Earth's rotational axis, it too will tilt over time!

In the end, the Earth (with the Moon) will "roll" along its orbit around the Sun, just like Uranus does. The Earth's northern hemisphere will face the Sun for half a year and the southern hemisphere during the other half. Of course this will be the end of nearly all life on Earth!

I'll bet I had you until you saw that it was in the entertainment forum!

Incorrect.
The impact has occurred already. Whatever effect it has on the inclination of Lunas orbit will be seen in the next month. It will not have an ongoing cumulative effect on the inclination of Lunas orbit. The asymmetry in the density of Luna has led to its tidal lock with Earth over a long period of time. This asymmetry will quickly negate any effect that the LCROSS impact has on the moons rotation or inclination.

The orbit of Luna will have a small ongoing cumulative effect of the orbit of Earth due to its tidal influence. However there is already an effect like this since the moon does not orbit the barycenter of the Earth/Luna system in the same plane as the Earths equator. The precession of the poles is already an understood and documented variation in Earths inclination. I assume that the orbit of Luna is a contributing factor to this phenomenon.

johno

Well... I have to admit that this was indeed the case!

The moon is slowly spiraling outwards to larger orbit, longer period due to Earth rotation and tidal friction giving a small, persistent forward force.

There is not enough rotational momentum in the Earth to drive the moon entirely free. It will progress outward till the orbit is over 600,000 km compared to 400,000 today and with a period of about 60 days, and one face of Earth will face the moon. They will be "tidally locked" just as the moon became locked to Earth already (the Earth is about 80 times the mass of the moon).