Tycho Brahe (TK–TK) spent years meticulously recording astronomical data. Johannes Kepler (TK–TK), studying Brahe’s data, formulating the following three laws to describe how the planets orbit our Sun.
- The orbit of a planet is an ellipse with the sun at one of the two foci.
- A line segment joining a planet and the sun sweeps out equal areas during equal intervals of time.
- The square of a planet’s orbital period is proportional to the cube of the length of the semi-major axis of its orbit.
These laws were only concluded empirically based on data; there was still the question of why these laws were true. It wasn’t until Isaac Newton, in Principia Mathematica (1687) proved that Kepler’s laws follow from his own more general laws about gravity, the Second Law of Motion and the Law of Universal Gravitation.
\(\displaystyle \bm{F} = m\bm{a}\)
\(\displaystyle \bm{F} = -G\frac{m_1 m_2}{r^3}\bm{r}\)