Equations of motion modification consistent with conservation of momentum, see variable-mass system. It may be simple to write down the equations of motion in vector form using Newton's laws of motion, but the components may vary in complicated ways with spatial coordinates and time, and solving them is not easy. Often there is an excess of variables to solve for the problem completely, so Newton's laws are not always the most efficient way to determine the motion of a system. In simple cases of rectangular geometry, Newton's laws work fine in Cartesian coordinates, but in other coordinate systems can become dramatically complex. The
Kepler's laws of planetary motion 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 from the Sun, also have elliptical orbits. Kepler's work (published between 1609 and 1619) improved the heliocentric theory of Nicolaus Copernicus,