Comets, Predicting

When comets are first seen through a telescope, they are faint, "fuzzy" patches of light at the limit of visibility. A few years ago, most comets were discovered by amateur astronomers who looked for comets as a hobby.* To find comets takes enormous patience and many nights of scanning the sky through huge binoculars or wide angle telescopes. To save time, amateur comet hunters also memorize large areas of the sky, so that they can immediately recognize when something new appears. Recently, professional astronomers have discovered many comets. Professionals normally do not spend much time looking for comets, because time on modern research telescopes is typically considered too valuable to spend on projects that are as uncertain as comet seeking. However, many research projects involve capturing long exposure electronic images of large areas of the sky for other purposes, and comets often appear in these images.

*If you find a new comet, it will bear your name!

What Are Comets?

Aristotle thought that comets were atmospheric phenomena, since they changed appearance. Aristotle's cosmology divided the universe into various spheres. The spheres below the Moon (Aristotle's sublunary spheres) were the only spheres that could change. The unchangeable heavens included the Moon and everything beyond. However, Tycho Brahe demonstrated that comets must be farther from Earth than the Moon. If the Moon is observed from different places on Earth, its position in the sky will change slightly due to parallax . By measuring the angular change in the position of the Moon and knowing the distance between the observing locations on Earth, the distance to the Moon can be measured. The distance between the observing positions is the base of an isosceles triangle with the vertex on the Moon. The appearance of the Great Comet of 1577 (which is now known as Halley's comet) gave astronomers the opportunity to measure its parallax. According to Tycho's parallax measurements, it was six or seven times farther than the Moon was from Earth.

A comet consists of a core of frozen material. This core is only a few kilometers across, far too small to be seen as more than a tiny point. The core contains frozen methane, ammonia, and water ice. Dust is mixed in with the ice, so the comet core resembles a "dirty" snowball. A comet has a temperature of only a few kelvins. However, as this frozen material nears the Sun it warms up and begins to sublimate (pass directly from solid to gas). The gas and dust then form a halo around the core. It is this halo that is initially seen by astronomers. As the comet gets closer still to the Sun and warms up even more, the rate of sublimation increases and the solar wind blows the material away from the comet, forming the long "tails" that are the hallmark of comets. The gas is blown straight away from the Sun and ionized by the solar radiation, forming a bluish, glowing ion tail. The dust that is released when the gas sublimates drifts more slowly away, forming the whitish or yellowish, curving dust tail.

The Origin and Movement of Comets

Comets probably originate far out on the edges of the solar system in a cloud of material left over from the formation of the solar system. When this cloud of material, called the Öort cloud , is disturbed by some gravitational influence, such as a nearby star, clumps of material begin to fall in toward the Sun. Hundreds of thousands (or even millions) of years later, a few of these objects approach the Sun and begin to warm up. Eventually, the objects swing around the Sun and head back out into space.

Most comets have orbital periods of thousands or millions of years. These "long period" comets are unpredictable. Even when the orbit of one is calculated, in a thousand or more years it will be impossible to tell if the same comet has returned or not. This unpredictability does not hold for "short period" comets (periods of less than 200 years).

Comets can approach the Sun from any direction. This suggests that the Öort cloud is spherical. Occasionally, a comet will approach the Sun along a path that takes it close to one of the large planets in the solar system. These gravitational encounters can alter the path of the comet and convert a long period comet into a short period comet. Halley's comet is probably the most famous of the short period comets. It is expected to return to the inner solar system in 2061. We know this, because comets follow the same laws of physics as other objects in our solar system.

All comets obey the same rules of motion that hold for the planets. Johannes Kepler first proposed these rules in the early part of the seventeenth century. Kepler's rules are usually stated in the form of three empirical laws :

1. All planets move in elliptical orbits with the Sun at one focus ;
2. A line drawn from the Sun to the planet sweeps out equal areas in equal times; and
3. The square of a planet's orbital period is proportional to the cube of its semi-major axis .

If the period (P ) is measured in years and the semi-major axis (a ) is given in astronomical units , Kepler's third law can be written as P ² = a ³. (One astronomical unit is the semi-major axis of Earth's orbit, which is also the average distance from Earth to the Sun.)

The Significance of Halley's Comet

Kepler's laws are now known to be a direct consequence of Isaac Newton's laws of motion and his law of universal gravitation. In 1705, the British astronomer Edmund Halley realized that Kepler's laws (as extended by Newton) could be applied to comets. He deduced that a comet seen in 1682 was orbiting the Sun like a planet and had probably been seen many times before. By examining previous sightings of what he thought to be the same object, he calculated its orbit and determined its period was 76 years and its semi-major axis was 18 astronomical units. This orbit took the comet past the orbit of Neptune, to the edge of the solar system where it cannot be seen by telescopes. Halley predicted that the same comet would return to the inner solar system again in 1758. Although Halley did not live to see the return of the comet, his prediction was correct: That particular comet was seen again in 1758. His successful prediction was a triumph of Isaac Newton's theories of gravity and motion. The comet was named in Halley's honor, starting a tradition of naming comets after their discoverers.

Since astronomers knew the period of Halley's comet, they were able to determine when it had previously appeared in the inner solar system and became visible. By putting together records from the Chinese and other ancient peoples, astronomers have determined that Halley's comet has been observed at every passage since 240 b.c.e. Halley is usually a spectacular sight, with its tail stretching out at least one astronomical unit. The tail can stretch many degrees across the sky.

In a real sense, a comet falls towards the Sun, accelerating as it descends. Its movement is most rapid as it passes near the Sun (as predicted by Kepler's second law). Then it moves away from the Sun, but the Sun's gravity is trying to pull it back. So it slows down as it moves away. At its maximum distance from the Sun, it is moving most slowly. So Halley's comet actually spends most of its time far from the Sun out past the orbit of Neptune.

The most recent appearance of Halley's comet, in 1986, was not ideal for viewing from Earth. However, a fleet of spacecraft was able to visit the comet. A Soviet spacecraft, Vega 2, traveled through the comet's coma and returned accurate information about the position of the nucleus. This allowed the Giotto spacecraft launched by the European Space Agency (ESA) to navigate within 600 km of the nucleus.* Moving this close was risky, because dust from the comet could (and did) damage the spacecraft. However, before the spacecraft was damaged, it was able to send pictures back to Earth. One picture returned by the Giotto spacecraft showed the actual core of the comet shrouded in dust.

*Giotto was named after an Italian artist who saw the comet in 1301 and painted it into a nativity scene.

The nucleus was larger than expected. It was about 15 km long and 10 km wide. It was also extremely dark, about the color of powdered charcoal, due to the thick layer of dust on its surface. The dust remains behind as the ice sublimates. Since Giotto passed very close to the nucleus of Halley's comet, ESA engineers were able to calculate its mass. It has a surprisingly low mass and a low density of about 0.1 g/cm³. This figure is probably because much of the frozen gas has already escaped, leaving behind a very "fluffy" residue. The comet will continue to lose material every time it swings close to the Sun. It loses as much as 30 tons per second. This loss of material will completely destroy the comet in about 40,000 years or after 5,000 orbits.

Although astronomers know Halley's comet will return sometime in 2060 or 2061 to the vicinity of Earth, the moment it first becomes visible cannot be predicted accurately. The orbits of all comets are somewhat unpredictable. This is due in part to the gravitational forces of the planets that act on them as they pass through the solar system. Also, each time a comet passes by the Sun, jets of evaporating gas spew out of the surface. These jets act like rockets and change the orbit of the comet slightly. As a result, no one knows exactly when Halley's comet will return. So keep your eyes open in 2061. Who knows, you may be the first person to see its return!

see also Astronomy, Measurements in; Solar System Geometry, Modern Understandings of.

Elliot Richmond

Bibliography

Chaisson, Eric, and Steve McMillan. Astronomy Today, 3rd ed. Upper Saddle River, NJ: Prentice Hall, 1993.

Giancoli, Douglas C. Physics, 3rd ed. Englewood Cliffs, NJ: Prentice Hall, 1991.

Sagan, Carl. Cosmos. New York: Random House, 1980.

Sagan, Carl, and Ann Druyan. Comet. New York: Random House, 1985.

WHAT ARE EMPIRICAL LAWS?

Empirical laws are mathematical summaries of observations. They do not attempt to explain things, but they are very good at predicting the results of experiments.