Chapter 13 Gravitation - Sharifsharif.edu/~rahimitabar/pdfs/L13.pdf · Chapter 13 Gravitation 13-1 What Is Physics? 13-2 Newton's Law of Gravitation 13-3 Gravitation and the Principle

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: