Gravitational Fields, Circular Orbits and Kepler’s Laws

Gravitational Field The Force of gravity per unit of mass at a given point It is the same as “local gravity” for a planet

Finding g (0,100m) m = 10,000 kg What is g at the origin?

Tycho Brahe

https://www.youtube.com/watch?v=7QDvKzY4aqA

Johannes Kepler

Kepler’s First Law of Planetary Motion The orbit of a planet/comet about the Sun is an ellipse with the Sun's center of mass at one focus http://home.cvc.org/science/kepler.gif

Ellipse vs. Circle

This occurs because angular momentum is conserved Kepler’s Second Law of Planetary Motion A line joining a planet/comet and the Sun sweeps out equal areas in equal intervals of time This occurs because angular momentum is conserved http://home.cvc.org/science/kepler.gif

Kepler’s Third Law of Planetary Motion The squares of the periods of the planets are proportional to the cubes of their semi-major axes

Kepler’s 3rd Law for Circular Orbits

If the distance R is measured in AU and the period T is measured in years then the third law for orbits about the Sun becomes

Comet Axis? What is the length of the semi-major axis of the orbit of a comet that takes 76 years to revolve around the sun?