The law of universal gravitation

Now let us consider the motion of bodies in this upper atmosphere, and in the space beyond.

If we throw a stone or cricket ball up into the air it goes up to a certain height, stops, and then comes down again. If we throw it vertically upwards it comes down on the same spot as that from which we threw it and, if we neglect the effects of air resistance, it returns with the same velocity down­wards as that with which we threw it upwards. Moreover, again neglecting air resistance, we can easily calculate how high it will go because we know that (at first, at any rate) it loses velocity as it travels upwards at the rate of 9.81 m/s or, very roughly, lOm/s every second, and gains it again at the same rate as it comes downwards.

But we ought to know better by now than to neglect air resistance? Yes, we certainly ought to know better, but unfortunately it wasn’t only air resistance that we were neglecting in the simple examples in Chapter 1 – though, in fair­ness, that was our worst error, and our other omissions really were negligible in the circumstances that we were then considering. This is no longer true of the circumstances of this chapter for some of which air resistance really can be neglected, but other things that we calmly assumed most certainly cannot.

Newton would probably have been less surprised than we were when arti­ficial satellites began to circle the globe – for these are but examples of the laws he enunciated.

When he saw the apple drop – assuming that story is true – he wondered why it did so, and eventually decided that it was because there was a mutual force of attraction between the apple and the earth; so it wasn’t just a case of the apple dropping, it was the apple and the earth coming together, due to this mutual force of attraction, when there was no longer anything to hold them apart. And if the apple and the earth, why not any mass and any other mass? And so eventually, by observing the facts, and by reasoning, he came to realise that there is a force of attraction between any two masses, and that this force is proportional to the product of the masses, and inversely proportional to the square of the distance between them. This is the law of universal gravitation, perhaps the most important of all the physical laws, the law that governs the movement of bodies in space (whether they be natural or artificial), the law that Newton enunciated 300 years ago.