1. Chapter 13: Gravitation

2. Newton’s Law of Gravitation A uniform spherical shell shell of matter attracts a particles that is outside the shell as if all the shell’s mass is concentrated at its center! G = 6.67  10 –11 N m 2 /kg 2 Superposition Principle

3. Gravitation Near Earth’s Surface Gravitational acceleration 1. 1.Earth is not uniform. 2. 2.Earth is not a sphere. 3. 3.Earth is rotating. Mean Earth surface (0 km, 9.83 m/s 2 ), Mt. Everest (8.8 km, 9.80 m/s 2 ), highest manned balloon ( 36.6 km, 9.71 m/s 2 ), Space Shuttle orbit (400 km, 8.70 m/s 2 ), and communications satellite (35,700 km, 0.225 m/s 2 )

4. Kepler’s Laws 1. 1.The Law of Orbits: All planets move in elliptical orbits, with the Sun at one focus. 2. 2.The Law of Areas: A line that connects the planet to the Sun sweeps out equal areas in the plane of the planet’s orbit in equal times, i.e., the rate dA/dt at which it sweeps out area A is constant. 3. 3.The Law of Periods: The square of the period is proportional to the cube of the semimajor axis of its orbit.

6. Potential and Kinetic Energy Potential Energy Kinetic Energy Total Energy

7. Einstein and Gravitation

8.  Sample Problems 13-4, 13-5, 13-6