Chapter 13 Gravitation ► 13-1 What Is Physics? ► 13-2 Newton's Law of Gravitation ► 13-3 Gravitation and the Principle of Superposition ► 13-4 Gravitation Near Earth's Surface ► 13-5 Gravitation Inside Earth ► 13-6 Gravitational Potential Energy ► 13-7 Planets and Satellites: Kepler's Laws ► 13-8 Satellites: Orbits and Energy ► 13-9 Einstein and Gravitation 13-1 What Is Physics? ► Understand the gravitational force-the force that holds you to Earth, holds the Moon in orbit around Earth, and holds Earth in orbit around the Sun. ► The gravitational force also reaches across intergalactic space, holding together the Local Group of galaxies. ► The gravitational force also reaches across intergalactic space, holding together the Local Group of galaxies. ► This force is also responsible for some of the most mysterious structures in the universe: black holes. 13-2 Newton's Law of Gravitation 13-3 Gravitation and the Principle of Superposition Example: 13-4 Gravitation Near Earth's Surface Example: Example: The Earth: ► 1. Earth's mass is not uniformly distributed. ► 2. Earth is not a sphere. Earth is approximately an ellipsoid, flattened at the poles and bulging at the equator. ► 3. Earth is rotating. ► At equator: Example: Shell Theorem: ► A uniform shell of matter attracts an external particle as if all the shell's mass were concentrated at its center. Example: Gravity Force Inside a Spherical Shell 13-5 Gravitation Inside Earth 13-6 Gravitational Potential Energy ► Potential energy and force: Gravitational Field: 13-7 Planets and Satellites: Kepler's Laws The Second Law: The Third Law: 13-8 Satellites: Orbits and Energy Example: All Earth geosynchronous orbits, whether circular or elliptical, have a semi-major axis of 42,164 km (26,199 mi). Scape Speed: Example: 13-9 Einstein and Gravitation ► Einstein's View of Gravitation Einstein pointed out that gravitation and acceleration are equivalent. This principle of equivalence led him to a theory of gravitation (the general theory of relativity) that explains gravitational effects in terms of a curvature of space. Curvature of space Gravitational Lensing Dark Matter Example: Example: Example: Example: .