Asteroids in the Inner Solar System

The inner solar system is a crowded place, filled with gravitational interactions between the planets and the Sun. Asteroids traveling through the inner solar system are seldom in stable orbits because they are constantly being deflected by the gravitational fields of planets. Asteroids in unstable orbits will not trace the same path over and over again but will experience gradual deflections that cause their orbits to wander, until they experience a larger gravitational pull and impact a planet, fall into the Sun, or, less likely, are expelled into the outer solar system. In addition, all small bodies in the solar system, except those locked into special stable orbits, slowly spiral toward the Sun under the influence of a force called the Poynting-Robertson effect. This is caused by reflecting and reradiating solar radiation, which slows the body by tiny, tiny amounts, gradually causing its orbit to decay to be closer to the Sun.

With so many effects making orbits unstable, most asteroids in the inner solar system have only a limited life span here. Over time, some small bodies are added to the inner solar system from the outer solar system, but many more are lost into the Sun, impact planets, or are flung into the outer solar system. The population of small bodies in the inner solar system might be expected to be much smaller so long after the solar system began, except that there are specific regions where their orbits are stable. The two major ways that asteroids can safely orbit near planets are through resonance of orbits, and by orbiting at Lagrange points.

Orbital periods can differ from each other by an integer multiple. For example, the period of one orbit is two years and the other six, differing by a multiple of three; this means that every three years the two bodies will have a close encounter. Even asteroidal orbits that differ by an integral multiple from the orbit of the large planet are usually cleared of asteroids by the gravitational field of the large planet. However, some special integral multiples of orbits actually stabilize the orbits of the asteroids, maintaining them in place indefinitely. These stabilizing multiples are called resonances, and the unstable multiples eventually are depopulated of asteroids, creating gaps.

The Jupiter system has good examples of both resonances and gaps. One group of Jovian asteroids, the Trojans, are at 1:1 (meaning that their orbit and Jupiter's are the same). Another group, the Hildas, are at 3:2 (meaning that they orbit the Sun three times for every two Jupiter orbits), and the asteroid Thule orbits at 4:3. There are gaps at 1:2,2:3, 1:3, 3:1, 5:2, 7:3, 2:1, and 5:3. Gaps in the asteroid belt that are cleared out by gravitational interactions with Jupiter have the special name of "Kirkwood gaps" because they were first observed in 1886 by Daniel Kirkwood, a professor of mathematics at Indiana University.

The second type of stable orbit is named for its discoverer, JosephLouis Lagrange, a famous French mathematician who lived in the late 18th and early 19th centuries. He calculated that there are five positions in an orbiting system of two large bodies in which a third small body, or collection of small bodies, can exist without being thrown out of orbit by gravitational forces. More precisely, the Lagrange points mark positions where the gravitational pull of the two large bodies precisely equals the centripetal force required to rotate with them. In the solar system, the two large bodies are the Sun and a planet, and the smaller body or group of bodies, asteroids.

Of the five Lagrange points, three are unstable over long periods, and two are permanently stable.The unstable Lagrange points, L1, L2 and L3, lie along the line connecting the two large masses.The stable Lagrange points, L4 and L5, lie in the orbit of the planet, 60 degrees ahead and 60 degrees behind the planet itself (see figure on page 80).

The L4 and L5 points are stable orbits so long as the mass ratio between the two large masses exceeds 24.96. This is the case for the Jupiter-Sun, Earth-Sun, and Earth-Moon systems and for many other pairs of bodies in the solar system. Objects found orbiting at the L4 and L5 points are often called Trojans after the three large asteroids Agamemnon, Achilles, and Hektor that orbit in the L4

and L5 points of the Jupiter-Sun system. (According to Homer, a Greek historian and writer from the eighth or ninth century B.C.E., Hektor was the Trojan champion slain by Achilles during King Agamemnon's siege of Troy.)

There are hundreds of Trojan-type asteroids in the solar system. Most orbit with Jupiter, but others orbit with Mars. The first Trojan-type asteroids for Mars were discovered in 1990 and named 5261 Eureka. Saturn has co-orbital asteroids as well, and Uranus is suspected to have its own Trojans. Neptune has recently discovered Trojans, including 2001 QR322 , which is in a particularly stable and long-lived orbit. No large asteroids have been found at the Trojan points of the Earth-Moon or Earth-Sun systems. However, in 1956, the Polish astronomer Kazimierz Kordylewski discovered dense concentrations of dust at the Trojan points of the Earth-Moon system.

There are at least two regions of resonance in the inner solar system where, theoretically, long-lived stable belts of asteroids can orbit the Sun without being disrupted by the gravitational pulls of planets. One theoretical belt lies between the Sun and Mercury and is named Vulcan, after the mythical planet once thought to orbit there. This region is theoretically stable for asteroids, but none have yet been found.The Vulcanoid region extends from 0.09 to 0.20 AU, with gaps at 0.15 and 0.18 AU that correspond to destabilizing resonances with Mercury and Venus. Here debris left over from the solar nebula may still orbit, perhaps along with material knocked off Mercury by large impacts. N. Wyn Evans and Serge Tabachik, researchers at Oxford University, have estimated that the largest Vulcanoids likely orbit between 0.16 and 0.18 AU, and they recommend sky searches in that area to locate larger asteroids. Other scientists are searching for Vulcanoids by scanning photos taken by fighter planes at high altitudes at dusk and dawn. Discovery of Vulcanoids may need to wait for the MESSENGER mission to Mercury, launched in 2004 and expected to reach Mercury in 2008.There also may be stable orbits between the Earth and Mars (at least one scientist has suggested that, according to physical calculations, a planet should have formed there).

Most of the asteroids that potentially threaten the safety of Earth are in unstable orbits and are classified according to their distance from the Sun.Those that have orbits crossing the orbits of other planets, particularly the Earth, are of special interest.These asteroids have

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