January is something of a bumper month for notable birthdays, with two great English physicists born this month – Isaac Newton and Stephen Hawking. The former climbed to the zenith of classical physics while the latter achieved fame investigating the origins of the cosmos and extending Roger Penrose’s theorem of a space-time singularity in the centre of black holes to the entire universe. (See our separate blog about Hawking for further information.)

It seems, however, even in Newton’s day that time could be confusing. Depending on which calendar you adhered to – either the “old style“ Julian calendar in protestant and Orthodox regions, including Britain, or the Gregorian “new style“ calendar in Roman Catholic Europe, which was ten days ahead – that he was either born on Christmas Day 1642 or 4 January 1643!

Originally undistinguished in his studies (there’s hope for us all!) he went on “to distinctly advance every branch of mathematics then studied” and to develop theories of calculus. He is generally credited with the generalised binomial theorem and numerous other mathematical discoveries. He also studied optics – constructing a reflecting telescope – and was perhaps ahead of his time by suggesting that light is composed of particles or “corpuscles”, which were refracted by accelerating into a denser medium. That said, today’s quantum mechanics, photons and the idea of wave-particle duality bear only a minor resemblance to Newton’s understanding of light.

He was also interested in alchemy: after his death, examination of the great scientist’s hair showed it to contain mercury – probably the result of his alchemical pursuits. Well known for causing bizarre behaviour – and captured in the phrase “mad as a hatter” because milliners often succumbed – mercury poisoning could be an explanation for Newton’s eccentricity during his later years.

Nonetheless, Newton is probably best known for his advances in the study of celestial mechanics and gravitation. Like many of us today, he was fascinated by the appearance of a comet (one was visible over the winter of 1680-81); he established a proof that the elliptical form of planetary orbits would result from a centripetal force inversely proportional to the square of the radius vector. Among the many famous scientists with whom he communicated was the renowned astronomer Edmond Halley.

Newton expanded his thoughts in his most famous work, the *Philosophiae Naturalis Principia Mathematica* *Principia*, which was backed by Halley and published on 5 July 1687. In it, he stated the three universal laws of motion that were to stand for over 200 years and still underpin much of physics at this scale. He used the Latin word for weight – *gravitas* – for the effect that would become known as gravity, and defined the law of universal gravitation.

There’s not enough room here to describe the full scale of this work but, suffice to say, that it brought unprecedented accuracy to the calculation of planetary orbits and motion of celestial bodies such as comets. Most importantly, the *Principia* contains Newton’s three famous laws of motion:

1) The law of inertia;

2) The second law, which states that an applied force on an object equals the rate of change

of its momentum with time, most often expressed in the well-known form F = ma (force equals mass times acceleration); and

3) The third law which is often expressed as “for every action there is an equal and opposite reaction”. The SI unit for force is named the “newton” in honour of his work.

One story that is inextricably linked with Newton is the story of an apple falling from a tree in his garden as the genesis of his theory of gravity. Famous French author Voltaire was taken with the story of Newton and the apple and wrote in his 1727 *Essay on Epic Poetry*: “Sir Isaac Newton walking in his gardens, had the first thought of his system of gravitation, upon seeing an apple falling from a tree.”

And it seems that the story has some basis in fact, albeit that the fruit didn’t actually land on Newton’s head! William Stukeley recalls in his *Memoirs of Sir Isaac Newton’s Life* a conversation he had in Kensington, London on 15 April 1726. Newton pondered on “why should that apple always descend perpendicularly to the ground”, asking “why should it not go sideways, or upwards, but constantly to the earth’s centre?” Assuredly, for Newton, the reason was: “That the earth draws it – there must be a drawing power in matter and the sum of the drawing power in the matter of the earth must be in the earth’s centre.” Therefore, the apple falls towards the centre of the earth. Furthermore, Newton suggested: “If matter thus draws matter, it must be in proportion of its quantity. Therefore the apple draws the earth, as well as the earth draws the apple.”

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