The main bodies of the Solar System are the bun and, in orbit round it, the nine major planets. In order of increasing distance from the Sun these are Mercury, Venus, Earth, Mars, Jupiter, Saturn (all known since antiquity), Uranus, Neptune and Pluto. Sir William Herschel discovered Uranus in 1781 during a review of the entire sky which was so systematic as to be virtually certain to reveal any such object. A planet more distant from the Sun than Uranus was predicted independently by John Adams hi 1843 and by Urbain Le Verrier in 1846. These predictions enabled Johann Galle and Heinrich d’Arrest to find and identify the planet which is now known as Neptune. In 1915 Percival Lowell published calculations predicting another planet beyond Neptune; this ninth planet was found hi 1930 by Clyde Tombaugh and named Pluto.

Several of the planets have systems of satellites, or moons, in orbits round them which in several ways mimic the system of Sun and planets. There is also a whole host of lesser objects: minor planets or asteroids, comets, meteoroids, and dust, as well as the solar wind.

The word planet is derived from the Greek noun (planetes) which means wanderer. This name arose because of the way in which the planets wander against the backcloth of distant stars. According to Ptolemy, the Earth lay at rest at the centre of the Universe, while the Moon, Sun and planets moved in orbits around it. This view was generally accepted until the middle of the sixteenth century when Nikolaus Copernicus argued that it was the Sun which should ho at the centre. This view was bitterly opposed at the time but gradually became accepted. Copernicus followed Ptolemy’s views in one respect: he built planetary orbits up from circles. The theories of both Copernicus and Ptolemy suffered from a great defect: they did not predict the positions of the planets with suffiicient accuracy. The true nature of planetary orbits was eventually elucidated by Johannes Kepler in the early seventeenth century when he published three relationships describing planetary motion. These are usually referred to as KEPLER’S LAWS. The first of these laws is Kl: Each planetary orbit is an ellipse with the Sun at one focus.The SEMI-MAJOR AXIS, a, determines its size and the ECCENTRICITY, e, its shape. The eccentricity is less than one for elliptical orbits; if it is zero we have a circle with both foci at the centre. As e increases towards one, the ellipse becomes more elongated and the foci move further from the centre.

Kepler’s second law is K2: The line joining any one planet to the Sun sweeps out equal areas in equal times. This constant rate of sweeping out area is different for each planet.

It follows from this law that the speed of a planet varies along its orbit . It is greatest at PERIHELION, the point at which the planet is nearest to the Sun, and least at APHELION, at which it is furthest away. Our Earth is at its perihelion about 2 January each year; the near coincidence with the start of the calendar year is fortuitous.

Kepler’s third law, K3 can be expressed thus: For any pair of planets, the squares of the periods are proportional to the cubes of the semi-major axes of their orbits. As a result the further a planet is from the Sun, the longer it takes to go once round its orbit.

The Earth’s orbit lies in a plane which passes through the Sun and which is called the ECLIPTIC. The orbit of each one of the other planets also lies in such a plane which is inclined at a small angle to the ecliptic. Because this angle is small, but not zero, a planet passes above and below the ecliptic as it moves around its orbit, but by only a relatively small amount. Each planet goes around its orbit in the same direction as the Earth does.

The Earth’s rotation axis is not perpendicular to the ecliptic but is tilted by an angle of 23° 27′; this angle is called the OBLIQUITY OF THE ECLIPTIC. The axis points in a direction which is almost fixed in space as the Earth moves round its orbit. We can see that during the year this causes the Sun to appear to move northwards and southwards relative to Earth . The SUMMER SOLSTICE is the time of the year (22 June) when the Sun appears at its most northerly position. It is then overhead at a latitude of 23° 27′ N; the line joining all points with this latitude is called the TROPIC OF CANCER. Six months later, at the WINTER SOLSTICE (22 December) the Sun is at its most southerly and is overhead at a latitude of 23° 27’S (TROPIC OF CAPRICORN). Twice a year the Sun appears overhead at the equator; these occasions are the VERNAL EQUINOX on 21 March and the AUTUMNAL EQUINOX of 23 September. It is customary to use each of the terms Summer Solstice etc. to describe both a particular time, as above, and the position of the Earth in its orbit at that time. In particular the vernal equinox, or more precisely, the direction from the Earth to the Sun at the vernal equinox, is used as a standard direction in many astronomical coordinate systems. This direction is also called the direction of the FIRST POINT OF ARIES.

Over a period of 25 800 years the Earth’s axis sweeps out a cone; this motion is called PRECESSION. The obliquity remains very nearly constant while the direction of the axis varies. This has the interesting consequence that the pole star Polaris will only be over the Earth’s north pole for a few hundred years more. Relative to the stars, the equinoxes and the direction of the first point of Aries moves once round the Earth’s orbit in this time. As a result the TROPICAL YEAR of 365.24219 days, which is the time from one vernal equinox to the next is slightly shorter than the SIDEREAL YEAR of 365.25636 days, which is the orbital period of the Earth relative to a fixed direction in space.

To describe completely the orbit of a planet or other object round the Sun it is necessary to specify six parameters known as ORBITAL ELEMENTS. The choice of elements is not unique, but the set most commonly used for planetary orbits is the elements i and o determine the position of the orbital plane, ? the orientation of the orbit in the plane, a and e its size and shape and P and T the position of the planet in its orbit. The ASTRONOMICAL UNIT is denned to be equal to the semi-major axis of the Earth’s orbit.

The same elements can be used to describe the orbit of a comet when this is an ellipse. Some comets, however, move in orbits that cannot be distinguished from parabolas. In this case the eccentricity, €, is equal to one. The period, P, and the length of the semi-major axis, a, are both infinite and are not used. The size of the orbit can be specified by using q, the distance of the comet from the Sun at perihelion. This element, q, can also be used for elliptical orbits: in this case it is equal to a( 1 — e).

Kepler’s Laws are not laws in the sense of modern science. Rather they are a model, or set of rules, that give us a satisfactory account of how the planets move But why do they move in this way? The answer was given in the middle of the seventeenth century by Sir Isaac Newton who discovered laws of motion and of gravitation that explained why the planets have their observed motions. He was then able to predict theoretically that the planets would move very nearly in accordance with Kepler’s empirically-derived laws. The agreement is not exact because the planets have non-zero masses; this has two effects. First, the motion of the Sun, which is being tugged at by nine planets, must be taken into account. Second, the planets attract one another and these perturbations cause deviations from exact elliptical orbits. With modern computers it is possible to calculate the motions over long periods of time and to issue accurate predictions of the positions of planets and satellites. Comparison of such predictions with observations shows that Newtonian mechanics and gravitation give a very accurate description of motions in the Solar System,although the general theory of relativity has to be used in the case of Mercury’s orbit.

After the discovery of Uranus, astronomers found that irregularities in its motion could not be explained by perturbations caused by the* planets then known. It was the analysis of these discrepancies which led Adams and Le Verrier to predict another planet in a triumph for the gravitation theory. Later, more irregularities in the motion of Uranus were found which led Lowell to predict yet another planet beyond Neptune. This turned up in 1930 and was named Pluto. Although it was acclaimed at the time as yet another victory for theoretical astronomy, it is now considered that the discovery was mainly the result of good fortune.

Are there any more planets beyond Pluto? If there were a TENTH PLANET beyond Neptune and Pluto it would cause perturbations in the motions of the outer planets. These deviations would be very small. All observations of planetary positions have a small error and no discrepancy larger than these errors has been seen with any degree of certainty. It is also possible to use observations of certain comets, such as Halley’s comet, to make predictions of planets not yet seen but none of these calculations has resulted in the finding of a planet. Astronomers now consider that no further planets, comparable to those known, remain to be discovered.

One of the effects of the mutual perturbations of planets is to cause their orbits to rotate in their own plane so that there is a steady change in the direction of perihelion. For Mercury the observed PRECESSION OF PERIHELION per century is 574 arc sec. According to the Newtonian theory of gravitation, this shift should be only 532 arc sec, which leaves an unexplained discrepancy of about42 arc sec. Einstein’s general theory of relativity agrees very closely with Newton’s theory of gravitation, when applied to the Solar System, but it does also predict this extra shift. Within the accuracy of the measurements (about one second of arc per century) there is full agreement between observation and the predictions of the general theory of relativity. This result and the corresponding results for the smaller shifts of the perihelia of Venus and the Earth form one of the main experimental verifications of the general theory of relativity. For the Earth the total shift of the perihelion is 1165 arc sec per century, so that in 111270 years, perihelion moves once round the orbit. Of this shift only 3.8 arc sec per century is due to relativistic effects.

We are now in a position to discuss how astronomers have worked out the size of the Solar System. From Kepler’s third law and measurements of the orbital periods of the planets it is possible to calculate the relative sizes of planetary orbits; for example the semi-major axis of each orbit can be expressed in astronomical units. We can then use the theory of gravitation to predict the distance, in astronomical units, between any two planets at any time. Now if we can find just one such distance in kilometers , the length of the astronomical unit in kilometers can be obtained, and all distances in the Solar System are then known in kilometers. The modern method of making such a measurement is to use radar. A large radio telescope is pointed towards another planet (which in practice is Venus) and a pulse of radio waves is transmitted. Some of the radio waves are reflected by Venus back to the Earth where they are received several minutes after transmission. The time for the journey is measured and since the velocity of radio waves is known to be 299 792.458kms-1 the distance between the radio telescope and the surface of Venus can be calculated with great precision. A series of such observations is made over a period of several months. This produces a more accurate value of the astronomical unit than would a single measurement and enables other quantities, such as the radius of Venus, to be measured. The astronomical unit is now known to be 149 597 870 km.

Radar can also be used to measure the time that a planet takes to revolve on its axis. Because a planet is moving relative to the Earth, the reflected radio waves in a radar experiment suffer a doppler shift. The revolution of a planet about its axis causes this shift to be different for different parts of the planet’s surface, and the smearing of the returned radar pulse is used to calculate the period of revolution.

It is generally possible to determine the elements of the orbit of a planet or comet from its positions at three different and known times. The uncertainties in the positions inevitably result in uncertainties in the elements, but these can be reduced by using more than three positions spread over as long a time as possible. This has been done for all the. planets and their orbits are known with great accuracy. As mentioned above, each planet, as it moves around the Sun, suffers only small perturbations from the other planets which are relatively easy to allow for when making predictions of future planetary positions. The Moon presents a much more difficult problem, as its orbit around the Earth is affected so much by the Sun that the Sun cannot be considered a small perturbation. All three bodies, Moon, Earth and Sun, must be considered together; astronomers call this the THREE-BODY PROBLEM. The problem has no exact solution like the elliptical orbit of the two-body problem. Over the centuries, the theory of the lunar motion has improved but it has still not yet reached a completely satisfactory state from which the position of the Moon can be predicted as accurately as it can be measured.

In 1772 Johann Bode drew attention to a curious numerical relationship which had been discovered some years earlier by Titius. For many years this intriguing relationship was unfairly called Bode’s Law although recently the name TITIUS-BODE LAW has come into use. The law starts by taking the numbers, 0, 3, 6, 12, 24,48, 96,192 and 384. After 3 each of these is twice its predecessor. The value 4 is now added to each number. If the distance of the Earth from the Sun is taken as 10, this series of numbers gives the distances from the Sun of all the planets, except Neptune. In 1772 Uranus, Neptune and Pluto were unknown, but when Uranus was discovered in 1781 it fitted the law very well. Neptune does not fit but Pluto does if it is taken to follow Uranus. The law predicts a planet at a distance of 28 on the scale being used here. Such a planet was discovered by G.Piazzi on 1 January 1801, the first day of the nineteenth century. This was Ceres and on the scale of the Titius-Bode law its distance from the Sun was 27.7, in satisfactory agreement with the predicted value of 28. Later, many other objects at a similar distance from the Sun were found; they are now known as MINOR PLANETS because of their small size compared to the other, MAJOR PLANETS. Nobody has yet. devised a satisfactory explanation for the Titius-Bode law. It is most probably a mere coincidence. Although this may sound implausible we must bear in mind the fact that the ‘law’ has several degrees of freedom! The starting points 0 and 3 are chosen arbitrarily, then we choose the doubling law, then we decide to add 4 to each number. None of these choices is based on physical arguments. Even after playing about to find numbers that fit the inner planets we have trouble with Neptune which does not harmonize.

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