Planetary Motion
Newton's law of gravitation explained the elliptical orbits of Kepler.
Kepler described the way that planets move in their orbits using three laws.
First, all planets orbit the Sun in ellipses. Before Kepler, everyone assumed that planetary orbits were composed of circular motions. By studying the orbit of Mars, Kepler realised that this was not true.
Second, planets move faster when they are closer to the Sun and slower when they are further away. The imaginary line between the planets and the Sun sweep out equal areas in equal times.
Third, the time it took for a planet to orbit the Sun depends on its distance from the Sun.
Today we realise that Kepler's Laws suggest that planets are being 'pulled' by the Sun, and that further away from the Sun, its pull gets weaker. However Kepler did not have the mathematics available to work this out.
Isaac Newton did—because he invented the mathematics. Newton realised that the Sun's gravity was pulling on the planets, while his mathematical brilliance allowed him to show how this force explained all of Kepler's laws.
With one equation, Newton could explain both the law of gravity described by Galileo, and the laws of planetary motion described by Kepler.
