Equations of motion when masses move according to Newton's law of gravity. In general relativity, rotational motion is described by the relativistic angular momentum tensor, including the spin tensor, which enter the equations of motion under covariant derivatives with respect to proper time. The Mathisson–Papapetrou–Dixon equations describe the motion of spinning objects moving in a gravitational field. Unlike the equations of motion for describing particle mechanics, which are systems of coupled ordinary differential equations, the analogous equations governing the dynamics of waves and fields are always partial differential equations, since the waves or fields are functions of space and time. For a particular
Kepler's laws of planetary motion "θ" by Kepler's first law: Using the relation above between "θ" and "E" the final equation for the distance "r" is: Kepler's laws of planetary motion In astronomy, Kepler's laws of planetary motion are three scientific laws describing the motion of planets around the Sun. Most planetary orbits are nearly circular, and careful observation and calculation are required in order to establish that they are not perfectly circular. Calculations of the orbit of Mars, whose published values are somewhat suspect, indicated an elliptical orbit. From this, Johannes Kepler inferred that other bodies in the Solar System, including those farther away