# Useful Formulae

26 KEPLERSNEWTONSLAWS bodies in motion Johannes Kepler discovered three laws describing planetary motion. They hold true for all orbiting bodies in space. 1 Planets move in ellipses with the sun at one focus. 2 A line drawn from the sun to the planet sweeps out equal areas in equal times. 3 The square of the time which a planet takes to orbit the Sun divided by the cube of its major semiaxis see page 4 is a constant throughout the solar system. Using Keplers discoveries, Isaac Newton deduced his Law of Universal Gravitation see page 28, and then went on to deduce his general laws of motion 1 An object at rest or in motion will remain in such a state until acted upon by some force. 2 The acceleration produced by a force on a given mass is proportional to that force. 3 A force exerted by A on B is always accompanied by an equal force exerted by B on A,in the same straight line but in the opposite direction. Einstein discovered that at velocities approaching that of light, Newtons Laws require significant modification. 27