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The next challenge was to find an explanation for Kepler's laws. Although Galileo conducted numerous experiments into the effects of gravity, he did not realize the full significance of his discoveries. This was left to an Englishman, Isaac Newton, who was born in 1642, the year that Galileo died.

One anecdote attributes Newton's discovery of universal gravitation to him observing an apple falling from a tree. Whatever the truth, by 1684 Newton was able to explain planetary motions. His law of gravitation stated that all objects attract each other, and that the strength of this gravitational attraction is proportional to their mass (see Chapter 8).

Clearly, since the Sun has nearly all the mass in the Solar System, it should pull all of the other bodies into it. Newton explained that this did not happen because their orbital velocities are just sufficient to counteract the Sun's gravity. The result is that the planets fall towards the Sun in such a way that the curve of their fall takes them completely around it (Figure 1.6). This is sometimes known as free fall. (This same explanation, of course, applies to artificial satellites.)

Figure 1.6 (a) If a spacecraft does not accelerate to orbital velocity, it will fall back to the planet's surface. (b) If it reaches orbital velocity, it will remain in a closed path (orbit) around the planet under free fall conditions. (c) If the spacecraft reaches escape velocity, it will be able to break free from the planet's gravitational pull and travel to another planet. The same rules apply to planets and spacecraft in orbit around the Sun.

(NASA)

Newton's law also stated that the strength of gravitational attraction decreases with distance. For example, if planet A is twice as far from the Sun as planet B, then the gravitational force exerted by the Sun on planet A is one quarter that exerted on planet B.

In practical terms, this means that a satellite in low Earth orbit must travel at 8 km/s, whereas the Moon only has to circle the Earth at 1 km/s in order to avoid crashing into our planet. Similarly, planets further from the Sun are able to move more slowly around their orbits than those in the inner Solar System. Newton's law also explained why a planet's orbital speed increased as it approached perihelion (closest point to the Sun) and slowed near aphelion (furthest point from the Sun).

From this time on the orbital mechanics of the Solar System were very well understood. With the exception of Mercury, whose orbital motion refused to obey Newton's law (see Chapter 5), the only significant problems involved minor variations in orbits caused by gravitational interactions between the planets, particularly those involving massive Jupiter. Careful study of unexpected changes in the orbital velocity of Uranus may even have enabled the position of an unknown planet, Neptune, to be successfully calculated (see Chapter 11) – although there are those who consider the discovery to be pure chance.