Newton discovered that colors arose from the separation, rather than a modification, of white light, that is natural sunlight. He did this using a prism to dissect the white light into its spectrum of constituent colors and then using a prism and lens to recombine the colors to reconstitute white light. The spectrum was the same as that of a rainbow. He determined the angle of refraction of each color by beaming white light through a prism, and then through a hole in a board which isolated one color, to another prism. When he discovered that all colors reflect from a mirror at the same angle, he invented and built the reflecting telescope, which used a parabolic concave mirror and a flat mirror instead of a convex lens, thereby eliminating the distortions and rainbow coloring around the edges that resulted from the refraction of different colors at different angles. He deemed a ray of light to consist of a rapidly moving stream of atomic particles, rather than Robert Hooke's pulses or Christian Huygens' waves, because shadows showed a sharp boundary between the light and the absence of light. He reasoned that if light was made up of pulses or waves, it could spread around obstacles or corners as sound seemed to do. He approximated the speed of sound by timing echoes in corridors of various lengths.
Newton was methodical and combined the inductive and deductive methods of inquiry, first making observations, and then generalizing them into a theory, and finally deducing consequences from the theory which could be tested by experimentation. This was the first clear expression of the basis of the "scientific method". He carried mathematization of data from experiments as far as possible.
Newton theorized that the same gravity force that pulled an apple down from a tree extended out to the moon to hold it in its orbit around the earth. He saw a connection between these movements by imagining a cannon on a mountain shooting a series of cannonballs parallel to the earth's surface. The first shot has only a tiny charge of explosive, and the cannonball barely makes it out of the muzzle before falling to the ground. The second shot is propelled by a larger charge, and follows a parabolic arc as it falls. The next shots, fired with increasingly more propellant, eventually disappear over the horizon as they fall. Lastly, with enough gunpowder, a speeding cannonball would completely circle the earth without hitting it. By extrapolating from these ever faster projectiles, he opined that the moon was held in its orbit by the same earth force that operated on the projectiles. He correlated the moon's orbit with the measured acceleration of gravity on the surface of the earth. He put various substances with different masses and weights into the shell of a pendulum and observed that the pendulum had the same period [time for one oscillation] and fell at the same rate as free-falling objects. Then he formulated the idea that the ultimate agent of nature was a force acting between bodies rather than a moving body itself. Gravity did not act in proportion to the surfaces of bodies, but in proportion to quantity of matter. Gravity penetrated to the very center of all bodies without diminution by the body. Gravity's force extended to immense distances and decreased in exact proportion to the square of the distance.
Newton opined that an object moves because of external forces on it rather than by forces internal to the object. These are his three laws of motion. 1) He connected the concepts of force and acceleration with a new concept, that of mass. Mass is a quantity intrinsic to an object that determines how it responds to forces, such as the force of gravity. The greater the mass of a body, the stronger the force of gravity on it, and the more difficult it is to get it moving. He found that the acceleration of a body by a force is inversely proportional to its mass, and formulated the equation that force equals mass multiplied by acceleration. So if a force acts on a planet, it produces a change in velocity that is proportional to the force and in the same direction as the force.2) His law of inertia is that any body, persists in its state of rest or of uniform motion in a straight line, unless affected by an outside force. 3) His next law is that when a body A exerts a force on a body B, then B also exerts a force on A which is equal in amount but opposite in direction. This means that forces that operate between different parts of a planet produce no net force upon the whole planet, so that the mass of a planet can be treated as if it is concentrated at a point.
His law of gravitation explains how the whole universe is held together. This law holds that every object in the universe attracts every other object with a single gravitational force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. Newton had at first accepted the Cartesian system of celestial vortices of aether that swirled the planets and comets around their orbits. He determined that Kepler's law that areas were swept out in equal times implied that gravity acts in the direction of a line between the planet and the sun. The gross features of the universe and Kepler's observations led to his recognition that the attraction between two bodies decreases inversely in proportion to the square of the distance between them. Only one kind of force would satisfy Kepler's requirement that the sun was a focus of an ellipse and still be consistent with Kepler's law that the square of a planet's period was proportional to the cube of its mean distance from the sun; that was the inverse square law. Then he came to accept Robert Hooke's hypothesis that planets are kept in their orbits by the combination of an attractive power of the sun and of motion in a straight line that was tangential to their orbits. From astronomical data, he calculated this centripetal acceleration of each planet towards the sun to be proportional to the inverse square of its distance from the sun. He also calculated the "centrifugal" accelerations in a straight line. His experiments showed that the centripetal force in a circular orbit was equal to the mass of the body multiplied by the square of its velocity, all divided by the radius of the circular path. He used calculus and differential equations to determine centripetal forces of elliptical orbits, where the distance from the sun, the velocity, and the acceleration were variables.
Newton showed that his single gravitational force could account for the way free-falling objects descend to the ground, the parabolic trajectory of projectiles, the path of the moon in its orbit around the earth, the course of the tides every twelve hours, the lower densities of the earth's atmosphere at greater heights, the paths of Jupiter's moons, the paths of comets, and the elliptical paths of the planets in their orbits around the sun. This determination discredited the previous belief that invisible angels moved the planets. Newton proved from his law of gravitation and his three laws of motion the truth of Kepler's laws of elliptical planetary motion. Newton demonstrated from data collected from the comet of 1680 that comets moved according to his law of gravitation. He showed that the path of a body traveling within the gravitational force of the sun is a circle, an ellipse, a parabola, or a hyperbola. He used the concept of a common center of gravity as a reference point for other motions. The fact that the center of gravity of the solar system was within the body of the sun verified that the sun was indeed at the center of the solar system.
Newton deduced that the tides were created by the rotation of the earth with bulges of water on the earth's surfaces that were closest and farthest from the moon. The moon "pulled" the water nearest to it with a greater force than average. It "pulled" the water farthest from it with a force weaker than average. These two moving bulges created two tides a day.
Newton's "Principia Mathematica Philosophiae Naturalis", was published in 1687. The established church denounced it as being against the scripture of the Bible. Newton did not agree with the established church on many points, such as the trinity, and was considered a heretic. He had his own interpretations of the Bible and doubted the divinity of Jesus. But it was accepted for dissenters like Newton to qualify for full civil rights by maintaining an outward conformity and taking the sacrament in the established church once a year. Newton was given a royal dispensation from taking holy orders as prescribed by the rules for tenure of fellows of his college at Cambridge University. He did believe in a God who created the universe and who had a ubiquitous presence in all space. When Catholic King James II tried to have a Catholic monk admitted to the degree of a Master of Arts at Cambridge University without taking the oath of adherence to the established Protestant church, so that he could participate in the business of the university, Newton was active in the opposition that defeated this attempt. As a result, he was elected to Parliament by Cambridge.
When Olaus Roemer, a Danish astronomer, was applying Newton's laws to the paths of the moons of Jupiter to make a table of eclipses of Jupiter's moons for use in determining one's longitude, he noticed that the eclipses were five hundred seconds ahead of average time at that time of year when the earth and Jupiter were on the same side of the sun, and five hundred seconds behind average time six months later, when Jupiter was on the other side of the sun. He reasoned that this difference was due to the light from Jupiter's moons taking more time to reach the earth when Jupiter was farther from the earth, i.e. on the other side of the sun. He concluded that light does not travel instantaneously, but at a certain speed. From the fact that it took 1000 seconds for light to travel the diameter of the earth's orbit, he calculated its speed in 1676.
In 1668, Christian Huygens formulated the law of conservation of momentum [mass multiplied by velocity], which held that when objects collide, they may each change direction, but the sum of all their momenta will remain the same. Huygens also recognized the conservation of what was later called "kinetic energy", which is associated with movement. He developed laws of centrifugal force for uniform motion in a circle. He derived the formula for computing the oscillations of a simple pendulum. In 1690, he posited the theory that light consists of a series of waves. It states that all points of a wave front of light in a vacuum may be regarded as new sources of wavelets that expand in every at a rate depending on their velocities. He thought this a better explanation of bending and interference of light than Newton's particle theory.