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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 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 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: 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 Example: Example: Example: Example: