The Solar System. Kepler's laws of Planetary Motion

From times of antiquity, it was known that the heavens contained five wandering stars (the planets), the Sun and the Moon. Uranus. Neptune and Pluto are invisible to the naked eye and were discovered only alter the invention of the telescope.

In the 3rd century b. c. the Greek astronomer Aristarchus had ventured his opinion that the Earth revolves around the Sun. Five centuries later, however, the work of the Egyptian astronomer, Ptolemy, suggested a geocentric view of the Universe, in which till of the celestial objects were thought to orbit the Earth.

This theory held sway all the way through until the 16th century. It is important to note here that, in their attempts to understand the Solar System, which to them represented almost the entire Universe, the astronomers of years past were actually practising the science of cosmology.

We now know that the Solar System contains nine planets, a myriad of moons and an almost countless number of minor bodies, all in orbit around a single star, the Sun. The planets can be divided into two main categories: the rocky terrestrial planets and the gaseous Jovian worlds. Mercury. Venus, the Earth and Mars occupy the first category whilst Jupiter. Saturn. Uranus and Neptune populate the second. Pluto is something of an oddball and is best classified as being a member of the small icy worlds which make up a large proportion of the Jovian planets' moons.

The terrestrial planets are all relatively small, dense objects. They inhabit the inner regions of the Solar System and have tenuous atmospheres if, indeed, they have any at all. The predominant materials which make up the composition of these planets are silicate compounds and metals, especially iron and nickel.

The volatile substances, such as gaseous atmospheres and the water contained in Earth’s oceans, were probably deposited by colliding cornets after the planets had formed. Volatiles are substances which can change state easily, e.g. gas to liquid, solid to liquid. The asteroid belt marks the boundary between the inner and outer Solar System and represents a planet which was prevented from forming by the gravity of giant Jupiter.

The outer Solar System is the domain of the Jovian planets. These are gigantic worlds, many times larger and more massive than the terrestrial planets. Their compositions are very different and are predominantly light gases and volatiles. This means that, although the planets are very massive compared with the Earth, they are not very dense since their bulk is spread much more sparsely throughout their over-sized volumes. In point of fact, the average density of Saturn is less than that of water!

The further out into the Solar System one ventures the more prone to volatiles the worlds become. Uranus and Neptune, for instance, are gas giants with very high proportions of astronomical ices, e.g. water, methane, and ammonia.

Pluto, a tiny icy world with a similarly frigid moon, Charon, represents the start of the Kuiper Belt and the Oort Cloud. The Kuiper Belt is a flared disc which extends into a spherical cloud, the Oort Cloud, surrounding the Solar System. Together, they contain vast numbers of icy comets which are thought to be the remains of the material from which the Solar System was formed. Periodically, members of these ‘reservoirs’ fall inwards towards the Sun and their gases are boiled off by the heat. In general, however, they remain in the furthest reaches of the Solar System.

The motion of the planets was finally described in 1609 by Kepler when he presented his three empirical laws of planetary motion:

- The orbit of a planet about the Sun is an ellipse with the Sun at one focus.
- A line joining a planet and the Sun sweeps out equal areas in equal intervals of time.
- The squares of the sidereal periods of the planets are proportional to the cubes of their semi-major axes.

As yet, there were no theoretical foundations upon which his laws (see Fig. 1.1) could be based, yet their validity was beyond doubt because of the way they could be used in order to predict the motion of the planets. A theoretical framework within which these' laws could be hung was finally forth-coming in 1687 when Newton published his three laws of motion.

Fig, 1.1. Kepler’s laws of planetary motion represented one of the most fundamental advances of his time, (a) All orbits are ellipses with the Sun at one focus. Equal areas are swept out by the radius vector in equal times. The radius vector is an imaginary line joining the Sun and the orbiting body, (b) The squares of the sidereal periods are proportional to the cubes of the semimajor axes. (Adapted from Kaufmann, W.J., Universe, W.H. Freeman, 1987.)

Turning our attention back to the centre of the Solar System and to gain some kind of perspective on it, imagine if everything, except for the Sun, were placed on one side of a scale balance. The Sun is then placed on the other side. Despite grouping all the planets, moons, asteroids and comets together, the Sun would still outweigh them by over seven hundred times. In fact, the Sun contains 99.8 per cent of the mass contained within the Solar System. So, the matter which constitutes the planets cannot even be thought of as the icing on the Solar System cake!

The Sun itself is overwhelmingly composed of the two lightest gases in the Universe: hydrogen and helium. Therefore we must state that the Solar System, too, is overwhelmingly composed of these two chemical elements. We have to disregard what our eyes tel! us from looking around the Earth and recognise that our entire world, plus everything it contains, is made up of nothing more than the cosmic flotsam produced, as we shall see, as a by-product of stellar evolution.

Our theories of star formation suggest that stars are produced by the gravitational collapse of giant clouds of gas. As the collapse proceeds, the central concentration of matter becomes a star. Other factors, such as the orbital motion of the cloud, mitigate to produce a disc of material around the central concentration. It is in these discs that planets form. Just recently there have been a number of extra-solar planets detected.

These have ranged from the exotic pulsar planets to the more conventional ones surrounding the star 51 Pegasi. In short, planets can be predicted naturally out of star formation theories. Secondly, given the fact that the Sun, and hence other stars, are far more massive than any planets which may be in orbit around them, it would seem more sensible for cosmologists to switch their attention towards the stars in their attempts to understand the Universe.