Asteroids, comets and meteors

Every year around 12 August the Perseid meteors streak across the night sky, up to about a hundred an hour from a dark site, all seeming to fly out of one small patch of sky in Perseus. They are grains of dust shed by the comet Swift–Tuttle, which crosses Earth's orbit once every 133 years, and Earth ploughs through its trail at the same point of its orbit each August. Comets, asteroids and the dust and rock they leave behind are the small bodies of the Solar System. They are too small to be planets, but they record how the planets formed, and olympiad problems use them to test orbits, brightness and the geometry of the sky.

6.6.1Asteroids

Most asteroids, small rocky or metallic bodies, go round the Sun between Mars and Jupiter, from about 2.1 au to 3.3 au, in the main belt. The largest, Ceres, is about 940 km across, and most are much smaller. The belt is not evenly filled. At certain distances there are almost no asteroids, the Kirkwood gaps. They lie where an asteroid's period would be a simple fraction of Jupiter's period of 11.87 years. An asteroid there meets Jupiter at the same points of its orbit again and again, and the repeated tugs build up until its orbit is changed, much as a swing goes higher when it is pushed at the same point of each swing.

By Kepler's third law (3.2), an asteroid that goes round $p$ times while Jupiter goes round $q$ times has $a=a_{\text{J}}(q/p{)}^{2/3}$. With $a_{\text{J}}=5.2028$ au, the 3:1, 5:2, 7:3 and 2:1 resonances fall at 2.50 au, 2.82 au, 2.96 au and 3.28 au, which are the main Kirkwood gaps. Not every resonance clears a gap. At Jupiter's own distance, the Lagrange points L4 and L5 of Section 3.9 hold thousands of Trojan asteroids that share Jupiter's orbit, 60° ahead of it and 60° behind.

An asteroid is usually too small to show a disc, so its size has to come from its brightness. In Section 6.3 we found that the absolute magnitude fixes the product of the albedo and the square of the radius. Writing it for the diameter $D$ gives the formula used for every asteroid.

6.6.2Comets

A comet is a body of ice and dust a few kilometres across, its nucleus. Far from the Sun it is frozen and dark. Within about 3 au of the Sun, where the sunlight is more than a ninth as strong as at Earth, the water ice begins to turn straight to gas. The gas and the dust it carries swell into a glowing cloud around the nucleus, the coma, which can be wider than the Sun.

Two forces then pull the coma out into tails. The gas is ionised by sunlight and swept away by the solar wind, so the ion tail points straight away from the Sun, whatever the direction the comet is moving. The dust is pushed outwards more gently by the pressure of sunlight, and it lags behind along the orbit, so the dust tail curves. On the way out from the Sun, a comet travels tail first.

Comets come from two great reservoirs. Short-period comets, with periods of less than 200 years, mostly come from the Kuiper belt, a ring of icy bodies beyond Neptune, from about 30 au to 50 au. Long-period comets fall in from the Oort cloud, a vast shell tens of thousands of au across, and many visit the inner Solar System only once (Section 3.4). Halley's comet has an orbit with $a=17.83$ au and $e=0.967$, so its period is 75.3 years and it ranges from 0.59 au, inside Venus's orbit, to 35.1 au, beyond Neptune. By the vis-viva equation (3.5) it races past the Sun at 54.4 km/s and creeps round its far end at 0.91 km/s. It last came by in 1986 and returns in 2061, 75 years later.

Comet Encke, with a period of 3.30 years, swings from 0.34 au to 4.09 au and moves at 69.8 km/s at perihelion. Running it shows the comet spending most of its time far out and slow, then rushing round the Sun in a few weeks with its tails swinging round to stay pointed away from the Sun.

6.6.3Meteors

A meteoroid is a grain or rock in space. When one hits the upper air, at around 100 km height, friction heats it and the air around it until both glow, and we see a meteor. Most are grains smaller than a grain of sand, but they arrive so fast that a single gram at 60 km/s carries $1.8\times {10}^6$ J, the energy of about 430 g of TNT. A piece that survives to reach the ground is a meteorite.

How fast a meteoroid can strike follows from energy. The slowest arrive at Earth's escape speed, 11.2 km/s, because even a body at rest near Earth falls in at that speed. The fastest are on orbits just bound to the Sun, which at 1 au move at the Sun's escape speed there, $\sqrt{2}$ times Earth's orbital speed, 42.1 km/s.

In the evening we are on the side of Earth facing backwards along its orbit, and only meteoroids that catch us up can reach us. After midnight we face forwards and sweep up meteoroids from ahead, like the front windscreen of a car in rain, so more meteors are seen before dawn, and faster ones.

The meteoroids of a meteor shower come from a comet's trail and move on nearly parallel paths. Parallel lines seen in perspective seem to spread out from one point, as railway tracks seem to meet in the distance, so the meteors of a shower appear to fly away from one point of the sky, the radiant. The shower is named after the constellation of its radiant, such as Perseus for the Perseids. Since each meteor moves along a great circle away from the radiant, tracing two meteor trails backwards until they cross finds the radiant.