How did newton map the orbits of the planets?

Law I. Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed theron.

In essence, a moving object won’t change speed or direction, nor will a still object start moving, unless some outside force acts on it. The law is regularly summed up in one word: inertia.

Law II. The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.

Newton’s second law is most recognizable in its mathematical form, the iconic equation: F=ma. The strength of the force (F) is defined by how much it changes the motion (acceleration, a) of an object with some mass (m).

Law III. To every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.

Eventually, however, Kepler noticed that an imaginary line drawn from a planet to the Sun swept out an equal area of space in equal times, regardless of where the planet was in its orbit. If you draw a triangle out from the Sun to a planet’s position at one point in time and its position at a fixed time later—say, 5 hours, or 2 days—the area of that triangle is always the same, anywhere in the orbit. For all these triangles to have the same area, the planet must move more quickly when it is near the Sun, but more slowly when it is farthest from the Sun.

This discovery (which became Kepler’s second law of orbital motion) led to the realization of what became Kepler’s first law: that the planets move in an ellipse (a squashed circle) with the Sun at one focus point, offset from the center.

If Kepler’s laws define the motion of the planets, Newton’s laws define motion. Thinking on Kepler’s laws, Newton realized that all motion, whether it was the orbit of the Moon around the Earth or an apple falling from a tree, followed the same basic principles. “To the same natural effects,” he wrote, “we must, as far as possible, assign the same causes.” Previous Aristotelian thinking, physicist Stephen Hawking has written, assigned different causes to different types of motion. By unifying all motion, Newton shifted the scientific perspective to a search for large, unifying patterns in nature. Newton outlined his laws in Philosophiae Naturalis Principia Mathematica (“Mathematical Principles of Natural Philosophy,”) published in 1687.

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