Kepler orbit led to Johannes Kepler working on his celestial mechanics. He later became known as the father of calculus. In 1601, Johannes Kepler acquired the extensive, meticulous observations of the planets made by Tycho Brahe. Kepler would spend the next five years trying to fit the observations of the planet Mars to various curves. In 1609, Kepler published the first two of his three laws of planetary motion. The first law states: More generally, the path of an object undergoing Keplerian motion may also follow a parabola or a hyperbola, which, along with ellipses, belong to a group of curves known
Stellar dynamics from the collisionless Boltzmann equation. This was originally developed by Ludwig Boltzmann to describe the non-equilibrium behavior of a thermodynamic system. Similarly to statistical mechanics, stellar dynamics make use of distribution functions that encapsulate the information of a stellar system in a probabilistic manner. The single particle phase-space distribution function, formula_16, is defined in a way such that formula_17 represents the probability of finding a given star with position formula_18 around a differential volume formula_19 and velocity formula_20 around a differential volume formula_21. The distribution is function is normalized such that integrating it over all positions and velocities will equal