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By Root 715 0

the Lucasian Professor of Mathematics in October 1670 (a post recently held by Stephen Hawking and currently held by string theorist Michael Green – both of whom continue to work on the problem of the nature of gravity). Newton spent the next twenty years lecturing and working in a diverse range of scientific and pseudo-scientific endeavours, including alchemy and predictions of the date of the apocalypse. The economist John Maynard Keynes said of Newton that he was not ‘the first in the age of reason, but the last of the magicians’. This is not entirely accurate, but then what can one reasonably expect from an economist? Newton lived on the cusp of pre-scientific times and the modern age and did more than most to usher in the transition. His greatest contribution to modern science was the publication in 1687 of the Philosophiæ Naturalis Principia Mathematica, otherwise known as the Principia. This book contains an equation that describes the action of gravity so precisely that it was used to guide the Apollo astronauts on their journey to the Moon. It is beautiful in its simplicity and profound in its application and consequences for scientific thought.

This time-lapse image neatly illustrates the concept of gravity. The feather and ball are here seen falling at the same speed in a vacuum, proving that any two objects of different mass will accelerate at identical rates when at the same gravitational potential. The reason that this does not happen on Earth is because of the air resistance that is present, which is, of course, absent in a vacuum. This principle was also proved correct when an Apollo astronaut dropped a feather and a hammer on the Moon (which has no atmosphere) and saw them fall at the same rate.

This is the mathematical expression of Newton’s Law of Universal Gravitation. In words, it says that the force (F) between two objects is equal to the product of their masses (m1 and m2), divided by the square of the distance between them. G is a constant of proportionality known as the gravitational constant; its value encodes the strength of the gravitational force: The force between two one-kilogramme masses, 1 metre (3 feet) apart, is 6.67428 x 10-11 newtons – that’s 0.000000000667428 N, which is not a lot. For comparison, the force exerted on your hand by a 1kg bag of sugar is approximately 10 N. In other words, the gravitational constant G is 6.67428 x 10-11 N (m.Kg)2. The reason why G is so tiny is unknown and one of the greatest questions in physics; the electromagnetic force is 1036 times stronger – that’s a factor of a million million million million million million.

There are many reasons why Newton’s Law of Universal Gravitation is beautiful. It is universal, which means it applies everywhere in the Universe and to everything not in the vicinity of black holes, too close to massive stars or moving close to the speed of light. In these cases, Einstein’s more accurate theory of General Relativity is required. For planetary orbits around stars, orbits of stars around galaxies and the movements of the galaxies themselves, it is more than accurate enough. It has also applied at all times in the Universe’s history beyond the first instants after the Big Bang. This is not to be taken for granted, because the law was derived based on the work of Johannes Kepler and the observations of Tycho Brahe, who were concerned only with the motion of the planets around the Sun. The fact that a law that governs the clockwork of our solar system is the same law that governs the motion of the galaxies is interesting and important. It is the statement that the same laws of physics govern our whole universe, and Newton’s law of gravitation was the first example of such a universal law.

It is also profoundly simple. That the complex motion of everything in the cosmos can be summed up in a single mathematical formula is elegant and beautiful, and lies at the heart of modern fundamental science. You don’t need to sit down with a telescope every night and use trial and error to find the positions of the planets and moons