Newton explains Kepler’s Laws
Newton was able to show mathematically
(using his calculus), that for inverse square forces, the orbits are
ellipses and obey Kepler’s laws. He realized this must apply to all celestial
bodies. In particular, he could show that the period and size of an
orbit are
given by:
Where P is period, a is
semi-major axis, M is central mass, and G is the “gravitational
constant” that expresses the strength of gravity (in the right units, of course).
Thus, this law (or Kepler’s Third Law) can
be used to find the mass of any body in which an
orbiting body’s period and distance can be measured (starting with the
Earth-Moon system).