1. Gravitational Fields, Circular Orbits and Kepler’s Laws

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

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

4. Tycho Brahe

6. Johannes Kepler

7. 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

8. Ellipse vs. Circle

9. 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

10. 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

11. Kepler’s 3rd Law for Circular Orbits

12. 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

13. 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?