1. 14
The Law of Gravity

2. C h a p t e r O u t l i n e
14.1 Newton’s Law of Universal Gravitation
14.2 Measuring the Gravitational Constant
14.3 Free-Fall Acceleration and the Gravitational Force
14.4 Kepler’s Laws
14.5 The Law of Gravity and the Motion of Planets
14.6 The Gravitational Field
14.7 Gravitational Potential Energy
14.8 Energy Considerations in Planetary and Satellite Motion
14.9 (Optional) The Gravitational Force Between an Extended Object and a Particle
14.10 (Optional) The Gravitational Force Between a Particle and a Spherical Mass

3. 14.1 Newton’s Law of Universal Gravitation
every particle in the Universe attracts every other particle with a force that is
directly proportional to the product of their masses and
inversely proportional to the square of the distance between them.

4. Properties of the gravitational force
Because the force varies as the inverse square of the distance between the particles, it decreases rapidly with increasing separation.
the gravitational force exerted by a finite-size, spherically symmetric mass distribution on a particle outside the distribution is the same as if the entire mass of the distribution were concentrated at the center.

5. 14.2 Measuring the Gravitational Constant
The universal gravitational constant G was measured in an important experiment by Henry Cavendish (1731–1810) in 1798.

6. EXAMPLE : Billiards, Anyone?

7. Solution

8. 14.3 Free-Fall Acceleration and the Gravitational Force

10. 14.4 Kepler’s Laws
1. All planets move in elliptical orbits with the Sun at one focal point.
2. The radius vector drawn from the Sun to a planet sweeps out equal areas in equal time intervals.
3. The square of the orbital period of any planet is proportional to the cube of the semimajor axis of the elliptical orbit.

11. 14.5 The Law of Gravity and the Motion of Planets

12. Kepler’s Third Law

14. Kepler’s Second Law and Conservation of Angular Momentum
the radius vector from the Sun to a planet sweeps out equal areas in equal time intervals.

15. 14.6 The Gravitational Field

16. 14.7 Gravitational Potential Energy
the gravitational force is conservative.
a central force is always directed along one of the radial segments, therefore, the work done by F along any radial segment is
any central force is conservative

18. Three interacting particles

19. 14.8 Energy Considerations in Planetary and Satellite Motion

20. The total mechanical energy is negative in the case of circular orbits.
The kinetic energy is positive and equal to one-half the absolute value of the potential energy.
both the total energy and the total angular momentum of a gravitationally bound, two-body system are constants of the motion.

21. Escape Speed

23. 14.9 (Optional) The Gravitational Force Between an Extended Object and a Particle

24. 14.10 The Gravitational Force Between a Particle and a Spherical Mass