| MadSci Network: Astronomy |
Hi,
Thanks for your question! There are a lot of things to say about the orbit of the Moon around the Earth. For instance, it's a good question whether the orbit of the Moon changes on it's own or not, without external influences. Then, we can look at whether it can change due to external influences, and also how big these influences need be. To start off, we'll begin at the beginning-the formation of the Moon.
Interestingly enough, it is not known with certainty how the Moon was formed1. There are several theories about how it was formed. The most probable theory is that an object the size of Mars struck the Earth, and that the ejected mass formed the Moon. This proto-moon (a colossal ball of molten slag) probably was ejected to some 20.0002,3 kilometers above the Earth's surface. This sounds like quite a lot, but it's in fact only a 5% of the current distance of the Earth from the Moon. Imagine a Moon with 400 times the apparent area flying through the sky! Furthermore, you would have to go to bed early-days lasted a mere 5.3 hours3! The Moon also revolved around the Earth much more rapidly.
Nowadays, days last a lot longer and the Moon is further away. So, the orbit of the Moon hasn't been the same since the formation of Earth and Moon, some 4.5 billion years ago. What has happened is that the Earth and Moon have dissipated energy due to the tides. The Moon attracts the Earth, and this causes the oceans (and to a lesser extend the ground) to rise and fall periodically4. This generates energy, that you can see in crashing waves on the shores. In fact, power harnessed from the tides is one of the more important forms of clean power5.
In physics, there is no free lunch, and this power is coming from something. In the Earth-Moon system, the rotation of the Earth is slowing down, the Moon is taking longer to revolve around the Earth, and the Moon is getting further away from the Earth. The first and second effect liberate energy, while the third effect consumes it. The net effect, however, is a liberation of energy6. At this moment, the Moon moves 3.8 cm away from the Earth each year1, releasing most of the colossal amounts of energy generated in the tides.
Having seen how much energy a small move in the Moon's position liberates, we get an idea how much energy it would take to nudge the Moon back to the Earth. One issue we should look at is what would happen if we were to knock the Moon closer to the Earth, say by a huge asteroid impact. What would happen is that the Moon would be knocked closer to the Earth, but it would still have its orbital velocity. This means that it would still be shooting forward, an in effect "missing" the Earth. It would then continue in an elliptic orbit.
What we could do to get some number is compute the amount of energy that would be needed to stop the Moon dead in its tracks around the Earth. If this were to happen, it should theoretically fall and crash into the Earth. The energy needed to stop the Moon is equal to the kinetic energy of the Moon which is given by one half the mass times the velocity times the velocity. Now, the velocity of the Moon is 1022 meter per second. This is roughly equal to the maximum velocity of the SR-71 "Blackbird" spyplane7. Unlike the Blackbird, the Moon has a mass 7.3477×1022 kg. The total energy we need to generate is 3.8e28 J of energy. This is slightly less than 10 trillion megatonnes of TNT8.
In reality, we have oversimplified quite a bit in the last paragraph, as we not only need to provide the kinetic energy to stop the Moon, but also enough momentum. In practice, this means a small, ultra-high velocity projectile such as an asteroid isn't as efficient as you would think, and it would need several more orders of magnitude of energy than our estimate to stop the moon. In fact, it would probably shatter the Moon rather than move it.
In short, we can say that the orbit of the Moon changes in time, but that it is quite stable, and that currently, small variations are accompanied by very large energy flows. We would need a massive amount of energy indeed to knock the Moon out of orbit. Hope this answers your question.
Regards,
Bart Broks
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