Pedagoguery

When Isaac Newton formulated the laws of universal gravitation, it was believed that the orbits of the planets could be predicted with perfect accuracy. If the Sun were the only gravitating body in the solar system, then that would in fact be the case. However, the planets exert small gravitational tugs on each other, and those tugs can sometime add up to devastating effect.

Recent observations of other planetary systems have demonstrated this. For example, the start Upsilon Andromedae has three known planets. The outer two planets have highly eccentric orbits (meaning they are highly elliptical) which can be explained by the gravitational ejection of a fourth planet at sometime in the past. In fact, calculations find that the two planets return to the configuration that existed just after the disaster every 8000 years.

The key to understanding potential orbital instabilities is the concept of resonances. These are circumstances where two bodies have a simple ratio of orbital periods. For example, Neptune and Pluto have a 3:2 resonance: Neptune makes three orbits for every two of Pluto's. In this case, it is has a stabilizing effect – it ensures that neither body is anywhere near the other when Pluto crosses Neptune's orbit.

Another example is the Galilean moons of Jupiter. The innermost three, Io, Europa, and Ganymede, have a 4:2:1 resonance with each other. The net result of this is that Io's orbit is distinctly elliptical, resulting in a great deal of tidal heating. The result has made Io the most volcanically active body in the solar system. However, the eccentricity of the orbits of those three moons has other effects. Take, Io, for example. Io's gravity raises a tidal bulge on Jupiter. Due to Jupiter's fast rotation in comparison to Io's orbit (10 hours as compared to 42 hours), the tidal bulge exerts a gravitational pull on Io that tends to accelerate it in its orbit, causing the orbit to spiral outward. A similar effect exists with the Earth and the Moon. However, Jupiter also raises a tidal bulge on Io, and since Io rotates at the same 42 hour period as its orbit around Jupiter, this tidal bulge falls behind, pulling Io backward in its orbit and causing it to spiral inward. As it turns out, the latter effect predominates for Io, but the former effect dominates for Europa and Ganymede. As a result, the satellites are gradually falling out of resonance. When that happens, Io's orbit will circularize, lessening the effect of the spiraling inward effect and causing it to move outward again. At that point, it could fall back into resonance with Europa and Ganymede, perhaps starting the whole cycle over again.

These two examples are stable. However, there is a chance of a highly unstable resonance. It also involves Jupiter, but the second body is Mercury. Mercury has a modestly eccentric orbit. Jupiter's orbit is also eccentric, but less so. Currently, the lines of apsides of the two planets do not line up. The line of apsides is the line between the perihelion (the closest point in the orbit to the sun) and the aphelion (the furthest point). If the lines were start to align, and the precession of Mercury's orbit makes this a possibility, successive tugs by Jupiter on Mercury would cause Mercury's orbit to get more and more eccentric. If this were to continue, Mercury's orbit would eventually cross that of Venus. If that happens, all bets are off. The chance of a close encounter between Venus and Mercury is quite high, and it is anybody's guess what would happen, up to and including a planet getting thrown in Earth's direction.

It wouldn't even necessarily need to be a direct hit to doom life on Earth. A close enough near miss would result in enough tidal heating of Earth to completely melt the mantle and crust, turning Earth into a world of lava.

The chances of such an event are small; current calculations put it at less than 1%, but when considered over the course of billions of years, such numbers can add up. The problem is that because the orbital interactions are chaotic (in a mathematical sense), no one can predict them with any certainty. All we can do is monitor the situation.

Next time, a new generation of neutrino telescopes.