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# Chapter 12: Gravitation

Gravitational forces describe how massive objects are attracted to each other. As a consequence of its range, the gravitational force is an extremely important force for massive objects. But is the force responsible for the motion of the planets (a celestial gravitational force) the same force responsible for the motion of objects near the surface of the earth (terrestrial gravitational force)? Yes! In 1685 Newton proposed the idea of universal gravitation, a unification of celestial and terrestrial gravity.

# Table of Contents

## Illustrations

- Illustration 12.1: Projectile and Satellite Orbits.
- Illustration 12.2: Orbits and Planetary Mass.
- Illustration 12.3: Circular and Noncircular Motion.
- Illustration 12.4: Angular Momentum and Area.
- Illustration 12.5: Kepler's Second Law.
- Illustration 12.6: Heliocentric vs. Geocentric.

## Explorations

- Exploration 12.1: Different x
_{o}or v_{o}for Planetary Orbits. - Exploration 12.2: Set Both x
_{o}and v_{o}for Planetary Orbits. - Exploration 12.3: Properties of Elliptical Orbits.
- Exploration 12.4: Angular Momentum and Energy.

## Problems

- Problem 12.1: Determine the unknown mass.
- Problem 12.2: Determine the mass of the star.
- Problem 12.3: Determine the mass of the orbiting planets.
- Problem 12.4: Determine the mass of the star.
- Problem 12.5: Could this animation of a planetary orbit depict a physical situation?
- Problem 12.6: Kepler's laws.
- Problem 12.7: Determine the speed for circular orbit.
- Problem 12.8: Determine the mass of the star.
- Problem 12.9: Determine the acceleration.
- Problem 12.10: Tunnel through the earth.