$$\require{cancel}$$

# 8.12 Asteroids

Ceres, the largest asteroid in the asteroid belt. Click here for original source URL

Asteroid Ida with its tiny moonlet Dactyl. Click here for original source URL

The asteroid belt (shown in white) is located between the orbits of Mars and Jupiter. This diagram also shows the location of the Trojan and Greek asteroids, located at two Lagrangian points of the Sun-Jupiter system. Click here for original source URL

Asteroids are rocky and metallic interplanetary bodies. They appear throughout the Solar System, but are most abundant in the main belt, a region between the orbits of Mars and Jupiter. Asteroids lack enough ice to give off gas like comets. The largest, Ceres, is about 1000 kilometers (600 miles) across, while the smallest are only a few meters across. Detailed images from passing spacecraft show that asteroids smaller than 100 kilometers or so are irregularly-shaped cratered objects, while larger ones are probably spherical due to their own self-gravity.

Giuseppe Piazzi. Click here for original source URL.

Astronomers discovered asteroids while looking for a new planet. After Uranus was discovered in 1781, some astronomers felt that there might be a planet in the large empty zone between Mars and Jupiter. This was suggested by the roughly geometric spacing of the planets (Bode’s rule). Astronomers set out to find the "missing planet.” Instead, Ceres was discovered on the first night of 1801 by the Sicilian monk Giuseppe Piazzi. Ceres was located at 2.8 AU from the Sun — right between Mars and Jupiter, where they had expected to find a planet.

Arthur C. Clarke, the famous science fiction writer, has noted an interesting fact about this discovery. Ceres was found just after the philosopher G.W.F. Hegel had "proved" philosophically that there could be no more than the seven then-known planetary bodies, Mercury through Uranus. As you can see, the scientific method of going out and looking tells us more about the physical nature of the universe than the philosophical method of sitting at home speculating!

Between 1802 and 1807, three more small, planet-like bodies turned up between 2.3 and 2.8 AU from the Sun. Because of their small size, they came to be called minor planets, or asteroids. All of them are too dim to be seen with the naked eye, but some can be seen with a small telescope. Photographic searches began in 1891, and more are discovered each year using modern electronic detectors. As of 2002, almost 40,000 of these bodies had been cataloged in the main asteroid belt, and modern CCD survey over wide field have increased that number to several hundred thousand. Depending on the lower size cutoff the total number is tens of millions. We have probably detected most asteroids larger than 100 km, and over 200 are cataloged, but the small ones are a lot harder to detect from Earth. Astronomers estimate almost a million asteroids larger than one kilometer orbit within the main belt.

After an asteroid’s orbit has been accurately identified, it is given a number (indicating the order of discovery) and a name (chosen by the discoverer). Ceres is thus more properly called 1 Ceres, and the second-discovered asteroid is 2 Pallas. The names are sometimes Latinized and they cover a wide range of human interests, including cities, mythology (Quetzalcoatl, Odysseus), politicians (Hooveria), celebrities (Zappafrank), family members, and lovers. (One form of astronomical amusement involves making sentences using only asteroid names. A favorite is "Rockefellia Neva Edda McDonalda Hamburga.")

Joseph Louis Lagrange. Click here for original source URL.

A diagram showing the five Lagrangian points in a two-body system with one body far more massive than the other (e.g. the Sun and the Earth). In such a system, L3?L5?will appear to share the secondary's orbit, although in fact they are situated slightly outside it. Click here for original source URL.

Several subgroups of asteroids do not orbit in the main belt. The Trojan asteroids, for example, orbit the Sun in two swarms that lie in Jupiter’s orbit, 60° ahead of and 60° behind the planet. These locations are called Lagrangian points, after the French astronomer Joseph Louis Lagrange. Lagrange discovered that an object at that location would be stable due to the combination of gravitational forces from the Sun and Jupiter. The name Trojan comes from the tradition of naming these particular asteroids after heroes in Homer’s epic poem of the Trojan War. More than 1500 Trojan asteroids are known. A few dozen of them are bigger than 50 kilometers across. Astronomers estimate that the two Trojan swarms contain nearly as many asteroids as the main asteroid belt, but most Trojans are too far away to see easily. The largest Trojan is 624 Hektor, estimated to be 100 km wide and 300 km long, tumbling end over end in Jupiter’s orbit.

Some asteroids come close enough to be of special interest to Earth-dwellers. These objects have been perturbed by gravitational encounters into the inner solar system. Their orbits have been disturbed or deviated slightly, so they take a new trajectory. This occurs any time a small body is affected by the gravity of a larger body, and there are many examples in the Solar System.

Perhaps the best sense of the distribution of asteroids in the Solar System comes from a map showing the actual positions of thousands of cataloged asteroids on a specific, randomly chosen date. In such a map, the main belt stands out clearly, along with the two swarms of Trojans in Jupiter’s orbit, and a scattering of Earth-approaching asteroids among the terrestrial planets. A plot of the radial distribution of asteroids from the Sun shows a lot of structure. The regions that are almost free of asteroids are called Kirkwood gaps, after their discoverer. The gaps are caused by gravitational resonances with mighty Jupiter, in exactly the same way that Mimas clears out regions of Saturn’s rings. There are gaps at the primary harmonics of 2:1, 3:1, and 4:1, but they also occur at other ratios like 5:2 and 7:2. The same gravitational physics occurs in the asteroid belt, on a scale 3,000 times larger than Saturn’s rings!

This histogram clearly shows the primary Kirkwood gaps in the asteroid main-belt. These gaps (labeled "3:1", "5:2", "7:3", "2:1") are caused by mean-motion resonances between an asteroid and Jupiter. For example, the 3:1 Kirkwood gap is located where the ratio of an asteroid's orbital period to that of Jupiter is 3/1 (the asteroid completes 3 orbits for every 1 orbit of Jupiter). The effect of these mean-motion resonances is a change in the asteroid's orbital elements (particularly semi major axis) sufficient to create these gaps in semi major axis space. Click here for original source URL.

The asteroid belt is not a crowded place — distances are vast, and asteroids are small. If you were cruising in the asteroid belt, you would rarely see another asteroid passing close by, contrary to Hollywood versions of the belt as a dangerous forest of rocks. Several unmanned spacecraft have already flown through the belt with no serious consequence, though they did experience more impacts by dust grains.