Newton's professional work can be summed up in the
following categories:
Optics:
In 1664, while still a student, Newton started reading
works on optics written by other English physicists, Robert Hooke and
Robert Boyle. He was very interested in this subject and so he
started to investigate the refraction of light by a glass prism;
developing a series of increasingly elaborate experiments. By
conducting these experiments, Newton discovered that white light is a
mixture of infinitely varied coloured rays, each ray is definable by the
angle at which it enters or leaves the prism (or any other medium) and
also there exists mathematical patterns in the colours of light.
When he first expressed his findings nobody believed him, he was
criticized because before Newton's findings, colour was thought to be
modified forms of white light. Newton expressed his finding in Opticks, written in 1692, but
waited to publicize it until all the critics were dead. The book
was imperfect, but still served as a model of theory with quantitative
experimentation.
Mathematics:
Newton made considerable contributions to all areas of math,
but his more famous contributions were in analytical geometry and
calculus. He discovered differentiation (lines tangent to curves)
and integration (area underneath a curve) and found that they are
inverse of each other. He also found ways to resolve problems of
curvature by a method of fluxions. He used the term fluxion
because he thought of a quantity flowing from one value to
another. Newton's work on math wasn't publicized until 1704.
Newton wasn't alone in finding these "discoveries," Leibniz claimed he
independently came up with the first ideas about differential
calculus. This sprung up a huge fight between both men which
didn't end even upon Leibniz's death. Today they are jointly
ascribed in the honor of first inventing calculus.
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Universal Law of Gravitation:
According to the well-known story of Newton seeing an apple fall from a
tree, Newton conceived that the force on the moon must be the same as
the force on the apple. He calculated the force that it takes to
hold the moon in orbit and then compared it to the force pulling the
apple to the ground. He also calculated the centripetal force
needed to hold a stone in a sling as well as the relationship between
the length of a pendulum and the time of its swing. Through
corresponding with Hooke (another physicist/mathematition) Newton
corrected some of the problems he ran into. And from this he came
up with an equation and explanation of gravitational force.
F=G* (m1 * m2)/r^2
This equation states that every object in the universe attracts every
other object with a force directed along the line of centers for the two
objects that is proportional to the product of their masses and
inversely proportional to the square of the separation between the two
objects.
This principle was published into a book Principia, which isn't only
Newton's masterpiece, but it is also the fundamental work that modern
science is built on. The book was separated into three
volumes. The first stated the foundations of the science of
mechanics while mathematically developing them, also gravity was stated
in this book as the cause of controlling the motions of celestial
bodies. Book two examines the theory of fluids, while book three
shoes the law of gravitation at work in the universe.
Laws of Motion:
The Principia rested
on Newton's three laws of motion:
1. A body remains in its state of rest unless it is
compelled to change that state by a force impressed on it.
2. The change of motion (change in velocity multiplied by
the mass) is proportional to the force impressed.
3. That every action has an equal and opposite reaction.