👕 The Laws of Planetary Motion

Tycho Brahe’s accurate observations of planetary positions provided the data used by Johannes Kepler to derive his three fundamental laws of planetary motion.
Kepler’s laws describe the behavior of planets in their orbits as follows:

(1) planetary orbits are ellipses with the Sun at one focus;

(2) in equal intervals, a planet’s orbit sweeps out equal areas; and

(3) the relationship between the orbital period (P) and the semimajor axis (a) of an orbit is given by 

P² = a³ 

(when a is in units of AU and P is in units of Earth years).

Newton’s law of universal gravitation

For two bodies having masses m and M with a distance r between their centers of mass, the equation for Newton’s universal law of gravitation is

F = G mM /r²,

where F is the magnitude of the gravitational force and G is a proportionality factor called the universal gravitational constant.
G is a universal gravitational constant—that is, it is thought to be the same everywhere in the universe.
It has been measured experimentally to be
G = 6.674×10⁻¹¹N⋅m²  / kg²
in SI units.

Note that the units of G are such that a force in newtons is obtained from F = G mM /r², when considering masses in kilograms and distance in meters.