1. Gravitation Chapter 7

2. Kepler’s Laws  In the 1600s Johannes Kepler proposed three laws of planetary motion based on observational data. The laws are:  The path of the planets about the sun is elliptical in shape, with the center of the sun being located at one focus. (The Law of Ellipses)  An imaginary line drawn from the center of the sun to the center of the planet will sweep out equal areas in equal intervals of time. (The Law of Equal Areas)  The ratio of the squares of the periods of any two planets is equal to the ratio of the cubes of their average distances from the sun. (The Law of Harmonies)

3. Law of Ellipses  The path of the planets about the sun is elliptical in shape, with the center of the sun being located at one focus. (The Law of Ellipses)

4. Law of Equal Areas

5. Law of Harmonies PlanetPeriod (years)Avg. Distance (AU) Mercury0.2410.390.98 Venus0.6150.721.01 Earth1.00 Mars1.881.521.01 Jupiter11.85.200.99 Saturn29.59.541.00 Uranus84.019.181.00 Neptune16530.061.00 Pluto24839.441.00

6. Example Problem  69. Every 74 years Halley’s comet is visible from Earth. Find the average distance of the comet from the Sun in astronomical units (AU).

7. Kepler’s Laws Activities  Planetary Orbit Simulator Planetary Orbit Simulator  Which planet has the most eccentric orbit?  Which planet’s orbit is closest to circular (e = 0)?  At which point is each planet going fastest? Slowest?  Kepler’s 2 nd Law Interactive Kepler’s 2 nd Law Interactive  Orbits and Kepler's Laws Orbits and Kepler's Laws

8. Universal Gravitation

9. Example Problem  55. Tom has a mass of 70 kg and Sally has a mass of 50 kg. Tom and Sally are standing 20 m apart on the dance floor. Sally looks up and sees Tom. She feels an attraction. If the attraction is gravitational, find its size. Assume that both Tom and Sally can be replaced by spherical masses.

10. Satellite Motion around the Earth

11. Motion of Planets Orbiting the Sun

12. The Relation Between G and g

13. Example Problem  46. Jupiter has about 300 times the mass of the Earth and about 10 times Earth’s radius. Estimate the size of g on the surface of Jupiter.

14. Gravitation Videos  How to Think About Gravity How to Think About Gravity  Gravitation Tutorial Gravitation Tutorial

15. Today’s Lab  Projectile Simulator Projectile Simulator  Planetary Orbit Simulator Planetary Orbit Simulator  Which planet has the most eccentric orbit?  Which planet’s orbit is closest to circular (e = 0)?  At which point is each planet going fastest? Slowest?