The Theory of Gravitation

Law of Gravitation:

$F=G\frac{m{m}^{\prime }}{r^2}$

every object in the universe attracts every other object with a force which for any two bodies is proportional to the mass of each and varies inversely as the square of the distance between them

Kepler’s laws

1. Each planet goes around the sun in an ellipse, which is the locus of all points the sum of whose distances from two fixed points (the foci) is a constant
2. The radius vector from the sun to the planet sweeps out equal areas in equal intervals of time (the planets do not go around the sun at a uniform speed, move faster when nearer the sum and slower when farther from the sun)
3. The square of the periods of any two planets are proportional to the cubes of the semimajor axes of their respective orbits $T\propto a^{\frac{3}{2}}$.

Development of Dynamics

Galileo: The principle of inertia: if something is moving with nothing touching it and completely undisturbed, it will go on forever, coasting at the uniform speed in a straight line.
Newton: theory of motion: a force is needed to change the speed or the direction of motion of a body