Chapter 12 Gravitation

Goals for Chapter 12 To study Newton’s Law of Gravitation To consider gravitational force, weight, and gravitational energy To compare and understand the orbits of satellites and celestial objects To explore the existence and nature of black holes (beyond science fiction)

Introduction Looking at the picture of Saturn, we see a very organized ring around the planet. Why do the particles arrange themselves in such orderly fashion? From Copernicus and Galileo to Hubble and NASA, centuries of scientists have struggled to characterize gravitation and celestial motion.

Newton’s Law of Gravitation The gravitational force is always attractive and depends on both the masses of the bodies involved and their separations.

Henry Cavendish determines G Gravitational forces were relative until 1798 when Henry Cavendish made the sensitive measurement to determine a numerical value for the constant G.

Calculate gravitational variables Example 12.1 leads us through an example of the gravitational force between two masses. Example 12.2 leads us to an acceleration that will result from a gravitational force. Example 12.3 reminds us that gravitational forces are vectors and are all active in a physical situation. See Figure 12.5 below.

Weight (skip Weight Watchers, just climb upward) Gravity (and hence, weight) decreases as altitude rises.

Gravitational force changes densities below sea level Just as it’s interesting to remember that all gravitational forces are calculated from the center of the planet, it’s interesting to follow the density as one proceeds from crust to mantle to core. “Want to get away”? Consider Example 12.4 to calculate gravity on Mars.

Gravitational potential energy Objects changing their distance from earth are also changing their potential energy with respect to earth.

Jules Verne had no way to know… To escape from the earth, an object must have escape velocity (not a small number). Follow Example 12.5 and Figure 12.12.

Satellite motion

Consider satellite orbits Several images of things in orbit to consider are shown below. Follow Example 12.6.

Kepler’s laws for planetary motion Each planet moves in an eliptical orbit with the sun at one focus. A line connecting the sun to a given planet sweeps out equal areas in equal times. The periods of the planets are proportional to the 3/2 powers of the major axis lengths in their orbits.

Orbital questions Consider Conceptual Example 12.7 about orbital speeds. Refer to Example 12.8 about Keppler’s Third Law. Example 12.9 examines the orbit of Halley’s Comet.

Spherical mass distributions Newton delayed the publication of his gravitational work until he was certain he could treat each planetary object from its center. Consider Example 12.10 and Figure 12.25.

Spherical mass distributions II

A visit to a black hole Refer to Example 12.11 and Figures 12.29 and 12.30.