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.
In 1661, Robert Boyle, called the father of modern chemistry, defined an element as a substance that cannot be further decomposed. He distinguished an element from both a mixture, which is easily separable, and a compound, which is not easily separable. He used an air pump he developed and a glass jar to create a confined vacuum space for experiments to find the properties of heat, light, and sound. He noted that burning objects such as candles and coal, when placed in the receiver of his air pump, went out after a time although air was still present. He opined that animals were dependent upon a fresh supply of air to live. He studied the relationship between the volume, density, and pressure of air and gases. He proved by experiment that the volume of a gas at a constant temperature varies in inverse proportion to the pressure applied to the gas. Since gas is compressible, he opined that gases must be composed of discrete particles separated by void, and also that basic physical properties were due to motions of particles, or atoms, which was an ancient Greek conjecture. This cast doubt on the long-held belief that everything was composed from four basic elements: air, water, fire, and earth. Boyle's laboratory at Oxford was denounced by the Oxford clergy as destroying religion. In 1679, the steam pressure cooker was invented by Denis Papin from France. He invented the atmospheric engine in 1690.
Robert Hooke helped Boyle build his air pump. Hooke was thirteen when his father, a minister, died. Hooke was a genius with innate mechanical skill and was an able mathematician. He applied a spiral spring to regulate the balance of watches. A lord financed him as a Gresham lecturer of geometry for 50 pounds a year. In 1666, he used a pendulum to measure the force of gravity and showed that the center of gravity of the earth and moon is a point describing an ellipse around the sun. In 1667, he explained the twinkling of the stars by irregular atmospheric refractions. He formulated the theory that light is composed of pulses. Hooke's Law states that the amount an elastic body such as a spring stretches out of shape is in direct proportion to the force acting on it: its tension. He invented the odometer, a wheel to measure distances. He constructed an arithmetical machine. He invented the universal joint, which can move in many angles. His book of drawings of microscopic animals is a classic. He proposed that fossils can be used as a source of information about the earth's history. Hooke became rich from his inventions, but this was not known until his death, when thousands of pounds were found in his iron chest.
In 1668, Wallis postulated the correct theory of impacts of inelastic bodies, based on the principle of conservation of momentum. In 1685, he introduced the first graphical representation of complex numbers.
Royal astronomer and genius Edmond Halley, the son of a soap maker, studied tides, magnetism, and the paths of comets and stars. He went on voyages to study the heavens from different positions, thereby laying the foundations of physical geography. He showed that the stars change in position in relation to each other. With Newton's help, he calculated the orbit of a comet he saw in 1682 to be elliptical rather than parabolic and then proved it was the same comet that had appeared in 1531 and 1607, indicating it's regularity; it was then named "Halley's comet". However, the Church of England still embraced the idea that comets and eclipses were evidence of God's wrath. Greenwich Observatory was built in 1675. Halley used a barometer to measure the density of the atmosphere and related its readings to elevations into the atmosphere and to weather. He determined that the cause of the tropical trade winds was the sun warming the tropical air at the equator, causing it to rise and move north as it was replaced by cooler air from the north. This body of air was deflected by the rotation of the earth. He illustrated the tropical winds with the first meteorological map. He made a descent in a diving bell, which was used to try to reach wrecked treasure ships. He studied fossils and perceived them as remnants of living beings that had died long ago, and imagined a succession of living things. Halley surveyed the tides and coasts of the British Channel for the king in 1701.