1. Evolving perspectives - a historical prologue

Moving points of light

The ancient wanderers

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There are seven objects that move with varying speeds against the background of fixed stars. Ranked in order of greatest apparent brightness, they are the Sun, Moon, Venus, Jupiter, Saturn, Mercury and Mars. Our ancestors called them planets, the Greek word for "wanderers"; a designation we still use for all but the Sun and Moon. For much of recorded history, astronomy has been mainly occupied with describing and predicting the movements of these ancient wanderers.

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The Sun does not rise at precisely the same point on the horizon each day. Instead, the location of sunrise drifts back and forth along the horizon in an annual cycle that is tied to the seasons. Ancient astronomers used monuments to line up the limits of these excursions. The length of the Sun’s arc across the sky also changes with a yearly rhythm. The Sun rises highest in the sky every summer, with its longest trajectory and the most daylight hours.

Circles and spheres

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The Moon repeats its motion around the Earth on a monthly cycle, periodically changing its appearance. Once each month, the Moon comes nearly in line with the Sun, vanishing into the bright daylight. On the next night the Moon has moved away from this position, and a thin lunar crescent is seen. The crescent thickens on successive nights, reaching the rotund magnificence of full Moon in two weeks. Then, in another two weeks, the Moon disappears into the glaring Sun, completing the cycle of the month and providing another natural measure of time.

Even the earliest sky-watchers must have noticed that the wanderers are confined to a narrow track around the sky, known as the zodiac from the Greek word for "animal". The Sun’s annual path, called the ecliptic, runs along the middle of this celestial highway. The paths of the other wanderers also lie within the zodiac. Its narrowness is a sign that the planets move almost like marbles on a table because the planes of their orbits are closely aligned with each other.

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It was obvious to astronomers from the earliest times that the wanderers do not move at uniform speeds or follow simple paths across the sky. When Mars, Jupiter and Saturn shine brightly in the midnight sky, each planet will gradually come to a stop in its eastward motion, move backward toward the west, and then turn around again and resume moving toward the east. Although these planets travel eastward in the "prograde" direction most of the time, they sometimes appear to move in the westward "retrograde" direction before continuing on in their eastward course. Ancient and modern explanations of this looping, retrograde motion differ in their perspective on the locations and motions of the planets.

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In arguments used by the Pythagoreans, and subsequently recorded by Aristotle (384-322 BC), it was shown that the Earth is a sphere. During a lunar eclipse, when the Moon’s motion carries it through the Earth’s shadow, observers at different locations invariably saw a curved shadow on the Moon. Only a spherical body can cast a round shadow in all orientations. The curved surface of the ocean was also inferred by watching a ship disappear over the horizon; first the hull and then the mast disappear from view.

In the Greek geocentric model, the central spherical Earth was supposed to be bounded by a much greater sphere, the imaginary celestial sphere of fixed stars. It wheeled around the central Earth once every day, with uniform circular motion and perfect regularity, night after night and year after year. Such a celestial sphere would also explain why people located at different places on Earth invariably saw just half of all the stellar heavens.

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Combinations of uniform circular motion were additionally required to account for the looping, or retrograde, paths of the planets. Each planet was supposed to move with constant speed on a small circle, or epicycle, while the center of the epicycle rotated uniformly on a large circle, or deferent. In this way Ptolemy, in his Mathematical Compilations, or Almagest, written about 145 AD, was able to predict the motions of every one of the seven wanderers, compounding them from circles upon circles.

In Ptolemy’s model, the Earth was located to one side of the center of the deferent circle. An imaginary point, called the equant, was symmetrically positioned on the opposite side of the center, and each planet was supposed to move uniformly with respect to the equant point. By selecting suitable radii and speeds of motion, Ptolemy could use this system of uniform motion around two circles to reproduce the apparent motions of the planets with remarkable accuracy. He succeeded so well that his model was still being used to predict the locations of the planets in the sky more than a thousand years after his death.

The Earth moves

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The Sun might not be moving across the bright blue sky each day, for the Earth’s rotation could produce this motion. Every point on the surface of a spinning Earth can be carried across the line of sight to an unmoving Sun, from sunrise to sunset, producing night and day. Such a perspective involves a certain amount of detachment – the ability to separate yourself from the ground and use your mind's eye to look down on the spherical, rotating Earth, like a spinning ball suspended in space.

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The Moon’s nightly motion from horizon to horizon could also be neatly explained by the rotation of the Earth, and the Moon’s monthly circuit against the background stars could be ascribed to its slower orbital motion around the Earth. This would also account for the Moon’s varying appearance. The Moon borrows its light from the Sun, and the Sun illuminates first one part of the Moon’s face and then another as the Moon orbits the Earth. On any given night, all observers on Earth will see the same phase of the Moon as our planet's rotation brings it into view.

The globe on which we live might not only spin on its axis; it could also be whirling endlessly around the Sun, completing one circuit each year. This notion was presented by the Polish cleric and astronomer Mikolaj Kopernik (1473-1543), better known as Nicolaus Copernicus. Since the orbits of Venus and Mars lie inside that of Earth and closer to the Sun, these planets are only seen around dawn or dusk. In contrast, the orbits of Mars, Jupiter and Saturn lie outside that of the Earth, so they are visible throughout the night.

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The Sun-centered view also provides a simple explanation of the occasional backward, or retrograde, motions that were so hard to reproduce using an Earth-centered, or geocentric, model. Most of the time we see Mars, Jupiter and Saturn moving around the Sun in the same direction as the Earth, but during the relatively short time that the Earth overtakes one of these planets, that planet appears to be moving backward. Moreover, one could confidently predict when a planet’s apparent motion would come to a halt and turn around, and for how long it would seem to move backwards.

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We now realize that the seasons can be explained in the heliocentric model by the tilt of the Earth’s rotational axis and the annual orbit of the Earth about the Sun. As the Earth orbits the Sun, its rotational axis points toward the same direction in the sky, at the star Polaris, but the northern and southern hemispheres are tilted toward or away from the Sun by up to 23.5 degrees. The greatest sunward tilt in a given hemisphere occurs in summer when the Sun is more nearly overhead and its rays strike the surface more directly. Winter occurs when that hemisphere is at its greatest tilt away from the Sun.

The harmony of the world

In the hope of developing a more precise description of planetary motions, the Danish astronomer Tycho Brahe (1546-1601) amassed a great number of observations that were more accurate and complete than any previous ones. This was before the days of telescopes, and he used ingenious measuring instruments that resembled large gun sights with graduated circles. These data were eventually interpreted by Tycho’s assistant and successor, Johannes Kepler (1571-1630), who was able to determine precise mathematical laws from them.

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Since circular motions could not describe Tycho’s accurate observations of the planets, Kepler concluded that non-circular shapes were required. In 1605, after four years of computations, Kepler found that the observed planetary orbits could be described by ellipses with the Sun at one focus. This ultimately became known as Kepler’s first law of planetary motion.

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A planet speeds up when it approaches the Sun, and slows down when it moves away from the Sun, and that accounts for the varying planetary speeds observed from Earth. Kepler was able to state the relationship in a precise mathematical form that can be explained with the help of the Figure. Imagine a line drawn from the Sun to a planet. As the planet swings about its elliptical path, the line (which will increase and decrease in length) sweeps out a surface at a constant rate. This is also known as the "law of equal areas". During the three equal time intervals shown, the planet moves through different arcs because its orbital speed changes, but the areas swept out are equal.

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Kepler investigated arithmetic patterns between the periods and sizes of the planetary orbits, discovering the harmonic relation that is now known as Kepler’s third law. It states that the squares of the planetary periods are in proportion to the cubes of their average distances from the Sun. If Pp denotes the orbital period of a planet measured in Earth years, and ap describes its semi-major axis measured in AU, then Kepler’s third law states that Pp3 = ap2, where the subscript "p" denotes the planet under consideration. This expression is illustrated in Figure 1.13, for the major planets and for the brighter moons of Jupiter. The mean orbital velocity of each planet is proportional to the ratio ap/Pp, so the velocity varies inversely with the square root of the distance or as (ap)-1/2.

Discovery of new worlds

Galileo, the telescope, and the unseen cosmos

One of the most fascinating and lively books in astronomy, Sidereus Nuncius or Starry Messenger, was published in 1610. In it, the Italian astronomer and physicist Galileo Galilei (1564-1642) described how he turned the newly devised telescope toward the heavens, bringing the sky down to Earth and the Earth into the sky. In 1609 he found craters, rugged mountains and valleys on the Moon, perceiving another Earth-like world hanging unattached in space. Galileo next used his rudimentary telescope to show that the Earth is not the only object with a satellite, our Moon, accompanying its motion through space. In 1610 he discovered four satellites that circle Jupiter. This meant that there was more than one center of motion in the Universe, and it contradicted Ptolemy's theory in which all astronomical objects move around the central Earth.

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Early telescopic observations by Galileo were also used to show that Venus goes through a complete sequence of Moon-like phases, from new to full, appearing at times as a thin crescent and thickening at other times into a round disk. This meant to Galileo that Venus had to circle the Sun. If nearby Venus orbited the Earth inside the Sun’s orbit, then it could never appear completely illuminated, but Venus could appear in all its phases if it orbited the Sun. Of course, Venus might orbit the Sun while the Earth remained at rest, so Galileo’s persuasive evidence did not provide definite proof of the complete Copernican model.

Telescopes to extend our vision

Astronomical telescopes, which have been in use for about four hundred years, have enabled us to detect previously unknown objects, or to see known ones in greater detail, transforming our perception of the planets and their satellites.

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There are two kinds of telescopes, the refractor, used by Galileo, and the reflector, initiated by Isaac Newton. As the names suggest, the refractor uses a lens to focus light, employing the principle of refraction, while the reflector uses a mirror to reflect and focus light. Modern refractors consist of a lens and a detector. The parallel light rays from a distant object are bent by refraction at the curved surface of a convex lens, known as the objective or the object-glass. The objective lens brings the incoming light to a focus, where the light rays meet and an image is formed. A detector placed at the focal plane, parallel to the objective lens, is used to record the image.

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Unfortunately, the objective lens in a refractor does not bring all parallel rays of light to a unique focus. As shown by Isaac Newton, sunlight is a mixture of all the colors seen in the prismatic display of a rainbow or in sunlight reflected by the crystals of new-fallen snow. Each color has a definite wavelength, from the long red waves to the short violet ones. When sunlight passes through a glass lens, each wavelength or color is bent or refracted through a slightly different angle. This unequal refraction, known as chromatic aberration, produces a blurred image. In 1668, Newton got around the problem by building an entirely different kind of telescope, the reflector, that uses a primary, concave mirror with a parabolic shape to gather the parallel light rays of a distant object and focus them to a point. Light does not pass though a mirror, as it does through a lens, and the mirror concentrates light of all colors to the same focus, producing a sharp image.

The serendipitous discovery of Uranus

The first planet to be discovered since the dawn of history was found accidentally, by a professional musician and self-taught amateur astronomer, William Herschel (1738-1822), using a home-made reflecting telescope in a systematic study of the stars from his home in Bath, England. While surveying the heavens on the night of 13 March 1781, Herschel came across an unusual object that was definitely not a star. It showed a disk, which no star can do, and it moved slowly from one night to another across the background of distant stars. This meant that it belonged to our solar system. After some controversy, the new planet was instead named Uranus, after the Greek personification of the sky.

When he found Uranus, Herschel was apparently unaware of a numerical sequence that predicted its relative distance from the Sun. Known as the Titius-Bode law, after the last names of the first persons to state it, the sequence describes the regular spacing of the planets, suggesting that the next planet beyond Saturn would be located at 19.6 AU, or at about twice Saturn’s distance. The so-called “law” also indicated a missing planet at 2.8 AU, in the gap between Mars and Jupiter, and suggested that another unknown planet would be located at 39 AU, or about twice the distance of Uranus. As it turned out, the asteroids were next discovered in the gap, and Neptune was eventually found close to the most distant location.

The ubiquitous asteroids

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Most of the asteroids with well-determined orbits lie in a great asteroid belt between the orbits of Mars and Jupiter, at distances of 2.2 to 3.3 AU and with orbital periods of 3 to 6 Earth years. The asteroids are so little, and distributed across such a large range of distances, that the asteroid belt is largely empty space. This leaves plenty of room for spacecraft to pass though to the giant planets, undamaged by collision with any asteroid.

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The asteroids are scattered around their orbits in a haphazard fashion, much like runners near the end of a long race on a small track. So, at first glance, the asteroids appear to fill the belt quite uniformly. But, if the asteroids could be arranged along a line outward from the Sun – as though they had been placed on the starting line – a different pattern would emerge. Not all distances from the Sun are equally well represented. There are a few prominent gaps, and these are named the Kirkwood gaps after the American astronomer, Daniel Kirkwood (1814-1895), who discovered them in 1866. A careful comparison with the period of Jupiter, 11.56 Earth years, shows that the missing periods are rational fractions of it. Asteroids with these orbits always come nearest Jupiter in the same point of their orbit, so Jovian gravitational perturbations recur repeatedly at the same orbital position. The recurring gravitational jolts dislodge the asteroids from their orbits, but the details depend on modern concepts of chaos.

Neptune’s discovery, triumph of Newtonian gravitational theory

Neptune's discovery was no accident, in contrast to those of Uranus and the first asteroid. It was a direct consequence of precise mathematical calculations of Uranus' motion. A large, unknown world, located far beyond Uranus, was evidently producing a gravitational tug on Uranus, causing it to deviate from the expected location. Two astronomer-mathematicians, John Couch Adams (1819-92) in England and Urbain Jean Joseph Le Verrier (1811-77) in France, independently took on the challenge of locating that planet by a mathematical analysis of the wanderings of Uranus. Neptune is located at a mean distance of 30.07 AU, at 1.6 times the distance of Uranus and fairly close to the 38.8 AU predicted by the Titius-Bode law. Remote Neptune takes so long to travel around the Sun, about 165 Earth years, that it has not made a full orbit since it was discovered in 1846.

Physical propeties of the Sun and planets

Distance to the Sun

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How far away is the Sun from the Earth, and how fast is the Earth moving through space? Kepler’s model of planetary motion only provided a scale model for the relative distances of the planets from the Sun, and for a long time no one knew exactly how big the solar system was. The crucial unit of distance for the planets is the mean Sun-Earth distance, known as the astronomical unit and designated AU for short. It can be determined by first estimating the distance between Earth and a nearby planet, and then inferring the Sun-Earth distance from geometry and Kepler's third law. The planetary distances are themselves determined by triangulation from different points on the Earth.

The AU was established with increasing accuracy in the 19th and 20th centuries, by determining the distances of Mars and the nearby minor planet 433 Eros during their closest approaches to the Earth. The results converged toward a solar parallax of 8.80 seconds of arc.

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The quest for accuracy in the mean distance of the Sun from the Earth culminated in the 1960s, when radar (radio detection and ranging) was used to accurately determine the distance to Venus. The round-trip travel time, T, for a radio pulse to travel from the Earth to Venus and back – about 276 seconds when Venus is closest to the Earth – was precisely measured. The distance to Venus was then obtained by multiplying half the round-trip time, T/2, by the speed of light, c = 2.99792458 x 108 m s-1. The radar measurements have determined the mean distance between the Sun and the Earth to an accuracy of about 1,000 meters.

Mass, radius and mass density of the Sun and major planets

Once an accurate value for the mean distance between the Earth and the Sun is known, one can use it with the orbital period of the Earth to infer the mass of the Sun from Newton’s formulation of Kepler’s third law. The precise distance to a planet can also be combined with the angular separation of one of its satellite to determine the orbital distance of that satellite from its planet, which can then be combined with the satellite’s orbital period to establish the planet’s mass using a similar mathematical expression. When the mass of the Sun and planets are thus determined, we find that the Sun doesn’t just lie at the heart of our solar system, it dominates it. Some 99.866 percent of all the matter between the Sun and halfway to the nearest star is contained in the Sun.

Ingredients of the Sun and planetary atmospheres

The ingredients of the Sun and planetary atmospheres can be determined when the intensity of their radiation is shown as a function of its wavelength. Such a display is called a spectrum, and the study of spectra is known as spectroscopy. Each chemical element or compound produces a unique set, or pattern, of spectral signatures at certain specific wavelengths and only at those wavelengths. They resemble a barcode or a fingerprint that can be used to identify the element or compound.

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The technique of astronomical spectroscopy was first developed using the bright light of the Sun. When its spectrum is examined carefully, with fine wavelength resolution, numerous fine, dark absorption lines are seen crossing the rainbow-like display. The separate colors of sunlight are somewhat blurred together when coarser resolution is used, and the dark places are no longer found superimposed on its spectrum.

We now know that hydrogen accounts for 92.1 percent of the number of atoms in the Sun, and that hydrogen is the most abundant element in most stars, in interstellar space, and in the entire Universe. Helium, the second-most abundant element in the Sun, is so rare on Earth that it was first discovered in the Sun. The next-most abundant elements in the Sun are carbon, nitrogen and oxygen, as well as the inert element, neon.

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Strong red and infrared absorption lines were also detected in early spectroscopy of the giant planets. They were interpreted in the 1930s as absorption by methane, CH4, and ammonia, NH3. The presence of methane and ammonia would be expected if the planets formed together with the Sun. The massive giant planets would then approximate the solar composition, which would explain their low mean mass densities. The overwhelmingly abundant hydrogen, H, would combine with the abundant carbon, C, nitrogen, N, and oxygen, O, in the low-temperature environment far from the Sun, to form stable molecules of methane, CH4, ammonia, NH3, and water vapor, H2O. Nevertheless, the exact composition of the atmospheres of the giant planets had to await space-age infrared spectroscopy, which showed that Jupiter and Saturn are mainly composed of hydrogen.

Satellites, rings and small distant objects

Discovery of satellites and rings

For nearly half a century, the only satellites known in the solar system were the Earth’s Moon and Jupiter's four largest satellites, discovered by Galileo in 1610 and now often called the “Galilean satellites” in his honor. They are named after four of Jupiter’s lovers. Io is the innermost of the four Galilean satellites, succeeded by Europa, Ganymede, and Callisto.

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In 1655 the Dutch astronomer-physicist, Christiaan Huygens (1629-95), discovered Titan, the largest satellite of Saturn, named after Saturn's older brother. Within a few decades Gian Domenico Cassini (1625-1712), at the Paris Observatory, had discovered four more moons circling Saturn; they are named Iapetus, Rhea, Tethys and Dione.

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Huygens turned his telescope toward Saturn itself, and explained its mysterious handle-like appendages. Galileo had noticed that the planet was not round, but had blurry objects on each side. When these objects disappeared two years later, Galileo wondered if Saturn “had devoured his own children”. In 1656 Huygens, then only 27 years old, realized that the planet was surrounded by “a thin flat ring, nowhere touching it, and inclined to the ecliptic”. Because the ring is tipped with respect to the plane of the Earth’s orbit around the Sun, it changes its shape when viewed from Earth, slowly opening up and then turning edge-on as Saturn makes her slow 29.5-year orbit around the Sun. When the ring is opened up, it resembles handle-like appendages, but when it is viewed edge-on the ring virtually disappears.

In the meantime, more planetary satellites had been found, and for the next three centuries their discovery progressed more or less in tandem with the development of increasingly powerful telescopes.

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Jupiter has eight small outer moons in eccentric tilted orbits that are so far from the planet that the Sun competes for their gravitational control. These eight outer moons fall into two widely separated groups. The innermost four move in the same direction as the planet rotates, but in highly inclined orbits that are not in the plane of the planet's equator. The outermost four circle Jupiter in the backward, or retrograde, direction. The Sun’s gravitational perturbations would have dislodged the outermost satellites if they had direct orbits.

Pluto - a small world with an oversized companion

The discovery of Neptune in 1846 resulted from a mathematical study of the differences between the predicted and observed positions of Uranus, attributed to the gravitational pull of the then unknown planet. Astronomers hoped that similar irregularities in Neptune's motion would lead to the discovery of another remote planet; but because of Neptune's long 165-year orbit there were insufficient observations. Prediction of another unknown planet therefore had to be based upon perturbations in Uranus' motion, after corrections for the gravitational effects of Neptune.

The most ambitious search for the trans-Neptunian planet was directed by Percival Lowell, at his observatory in Flagstaff, Arizona, but no new planet was found at a variety of predicted locations between 1905 and 1919. The search from the Lowell Observatory continued a decade later using a new 0.33-meter (13-inch) photographic telescope. Once three photographs had been taken at intervals of several days, they were set in pairs in a blink microscope that would show the apparent motion of a planet, asteroid or comet against a background of nearly half a million stars on each photograph.

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After months of painstaking work, Clyde William Tombaugh (1906-1997) discovered, on 18 February 1930, the sharp, faint, moving image of the elusive quarry. The new object was named Pluto, for the Roman god of the underworld. It is a small frozen world at the outer fringe of the planetary system, with a highly-elongated orbit that carries it between 29.7 and 49.3 AU from the Sun.

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Pluto is now known to be a double object, with a companion that is half as big as Pluto is. This discovery was an accidental by-product of observations made for another purpose. In 1978, astronomers at the United States Naval Observatory were obtaining a series of photographs to improve the accuracy of Pluto's orbit, when several of the images appeared slightly distorted, from a round to oblong shape. The elongation seemed to disappear every few days, and careful examination showed that it is caused by another small world that orbits Pluto. The two objects are so close together and so far away that they remain blurred together when viewed with even the best telescopes on the ground, but they can be clearly resolved with the Hubble Space Telescope that orbits the Earth above its obscuring atmosphere. Pluto’s companion is named Charon, after the boatman who ferried new arrivals across the river Styx at the entrance to Pluto's underworld, Hades.

The announcement of this remarkable doubling was a happy surprise, for it permitted determining the mass of Pluto. Charon's slow revolution about Pluto is a result of Pluto's small mass - only 0.2 percent (0.002) of the Earth’s mass and only about one-sixth the mass of our Moon. This means that Pluto was not found because it was correctly predicted. Its mass is far too small to have noticeably influenced the past motions of Uranus.

Small cold worlds in the outer precincts of the planetary system

As it turned out, Pluto shares a similar orbit and composition with numerous small balls of ice and rock, forming a distant, flat ring just outside of Neptune's orbit. It is now known as the Kuiper belt in recognition of Gerard P. Kuiper's 1951 prediction of its existence. He argued that the dark outer edge of the planetary realm is not empty, but is instead full of small, unseen bodies created from the left-over debris of the formation of the giant planets. The low-density material in these distant regions would have been spread out into such a large volume, and moving in such slow, ponderous orbits around the Sun, that it could not gather or coalesce into a body any larger than Pluto.

Comet reservoirs

There are probably many more small objects than large ones in the Kuiper belt. Most of them have been hibernating in the deep freeze of outer space since the formation of the solar system. Yet, Neptune’s gravity slowly erodes the inner edge of the belt, within about 40 AU from the Sun, and gradually pulls some of its members closer to the Sun. The Kuiper belt is therefore a likely reservoir for a certain class of comets, called the short-period comets, that become visible when they emerge from cold storage and move toward the Sun. When a Kuiper-belt object has been launched into the inner solar system, within a few AU of the Sun, the increased solar heat vaporizes the object’s icy surface, forming an Earth-sized cloud of gas and dust that reflects enough sunlight to be seen as a short-period comet. The short-period comets have periods of less than 200 Earth years, typically 5 to 20 years, and conform somewhat to the pattern of planetary motion. They all move in the same prograde direction as the planets and their orbits are tilted only slightly from the orbital plane of the Earth, known as the ecliptic. This is consistent with an origin in the outer parts of the disk of the solar system, or in the Kuiper belt. The other class of comets, those with long periods greater than 200 Earth years, come into the planetary realm at every possible angle – their orbits are inclined at all angles to the ecliptic. Roughly half of them orbit the Sun in the retrograde direction, opposite to the motion of the planets. These long-period comets approach the Sun on very elongated orbits, coming from enormous distances of 50 thousand AU or more. The orientation and size of the orbits of long-period comets indicate an origin in a vast, remote spherical shell of icy objects, It surrounds the solar system and extends to interstellar distances of about 100 thousand AU, or up to one quarter the distance to the nearest star, Alpha Centauri at 250 thousand AU. This comet reservoir is named the Oort cloud, after Jan Hendrik Oort (1900-1992) who first postulated its existence in 1951.

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The random jostling of stars or giant molecular clouds passing near the Oort cloud can knock some of these icy objects from their stable orbits, sending them into the heart of the solar system where they can be seen as a long-period comet. When tossed near the Sun, these dirty balls of ice become vaporized and light up with long tails and changing shapes that have inspired awe for centuries.