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Research Topic: Unstable Moon

By Ian Mander BSc, 12 September 1999, updated 28 December 2004. For Allan.

Question: If man-made satellites like Skylab fall out of the sky after only a few years, how come the moon stays up?

Answer: The moon only seems stable because it's much bigger than man-made satellites, which makes it less affected by things that satellites are affected by, so its orbit takes longer to change. But it's still changing.

Note: I mostly use "the moon" rather than "Moon" throughout this article becoz it just seems righter.

Man-Made Satellites

Reasons for a man-made satellite's orbit becoming too unstable/deteriorated for the satellite to stay up include:

  • They weren't put up very well in the first place, and so have a reasonably predictable decay built in. This is a good idea to prevent space junk littering the area immediately around Earth clogging all the most useful orbits.
  • Tidal effects and gravitational irregularities pulling a satellite around in its orbit, or more correctly, continually changing its orbit, making it very hard to get the orbit very accurately to begin with.
  • Atmosperic drag - only a problem for very low satellites at times of extreme solar flares etc. Lightning related discharges (elves) have been observed as high as 70 km.
  • Things like sputtering and the Poynting-Robertson effect are really too small to affect objects as large as satellites in the timeframe we're talking about, but I mention them for interest's sake. Sputtering is photons hitting small (orbiting) particles such as dust and breaking off small bits of matter, in time destroying the particles. The Poynting-Robertson effect is pressure from sunlight slowing objects down as they orbit around a larger body. The slowing effect is directly related to the mass of the object being slowed. When sufficiently slowed, the particles fall toward whatever they are orbiting. (A good example is the rings around Saturn, with the implication that these two effects mean that the rings are either relatively young or being refreshed, either continuously or periodically.)

The Moon

The distance between Earth's centre and the moon's centre is about 385,000 kilometres, with the centre of gravity of the two (from memory) about 1600 km beneath Earth's surface (and I'll bet you didn't know that).

Using special mirrors left by Apollo 11 (and three other manned and unmanned missions), laser pulses are precisely timed for an Earth-Moon-Earth round trip. This has given us the information that our dear moon is slowly departing us at 3.8 cm/year.*

*Dividing the distance 385,000 kilometres by 3.8 cm/year gives about 10 billion years, but tidal forces would have ripped at least the moon apart (and possibly Earth as well) if it had been anywhere near that close. (If, of course, the moon was really that old and the rate of recession has been constant, etc.) This would mean that Earth would have had a good ring for a few years, and we would have had no tides - with serious consequences for life on Earth.

28/12/2004: FWIW I've found a mention that the Roche Limit where the moon would have been ripped apart by tidal forces is 18,500km - seems actually quite close.

Incidently, according to the American Institute of Physics, "Three decades of lunar laser ranging (bouncing light off reflectors placed on the Moon) show that the Moon and the Earth fall toward the Sun with the same acceleration to within half a part in a trillion (10^12)." So there.

Tides - a related subject

A tide is caused by a fluid or semi-fluid body being exposed to a gravitiational field gradient changing in periodic fashion. [Nup. Sounds way too complicated - try again.]

Gravity gets weaker with increased distance. This means satellites in a high orbit only need to orbit slowly to counteract the gravitational field of Earth, but low-orbit satellites need to go really fast to orbit.

The reason we get a tide on Earth is that the moon's gravity gets noticeably weaker over the thickness of Earth. That is, the moon's gravitational field is stronger on the side of Earth facing the moon than it is on the side of Earth facing away from the moon. So the near side of Earth is more strongly attracted to the moon that the other side. Earth is pretty solid, so it deforms only a little, and carries on in its orbit. (Changes in the moon's and Earth's shapes due to these tidal forces have been measured, but are much smaller than the water tides.)

However, Earth's liquid oceans are a different matter, since they are more-or-less free to be attracted more strongly on the near side and more weakly on the other. ("More-or-less" due to continents getting in the way.) Because Earth is moving fast enough to stay in orbit (as a whole Earth-Moon system), this has the net effect of meaning the water on the near side is pulled more toward the moon while the water on the far side is flung away from the moon (by centrifugal force, if you like). Basically, we have a net pull on the near side and a net push on the other.

The sun also affects the tides, but the effect the sun has is much smaller than the moon has, because although the sun is much bigger than the moon, due to its greater distance the change in gravitational force across Earth's thickness is much smaller. Jupiter's tidal effect on Earth is only about a millionth as big as the sun's effect with the other planets having an even smaller effect; we don't need to worry about planetary alignments causing earthquakes.

28/12/2004: Some figures for maximum tidal forces from various bodies in the solar system, from Thompson (1981):

Body Solacentric Lunacentric
Moon 2.21 1
Sun 1 0.45
Venus 0.000 113 0.000 051
Jupiter 0.000 013 1 0.000 005 9
Mars 0.000 002 3 0.000 001
Mercury 0.000 000 7 0.000 000 32
Saturn 0.000 000 5 0.000 000 23
Neptune 0.000 000 002 0.000 000 000 9
Uranus 0.000 000 001 0.000 000 000 45

0.000 000 000 000 1

0.000 000 000 000 045

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