Category: Gravitation

Principle of Equivalence Albert Einstein once said: “I was . . . in the patent office at Bern when all of a sudden a thought occurred to me: ‘If a person falls freely, he will not feel his own weight.’ I was startled. This simple thought made a deep impression on me. It impelled me…

As a satellite orbits Earth in an elliptical path, both its speed, which fixes its kinetic energy K, and its distance from the center of Earth, which fixes its gravitational potential energy U, fluctuate with fixed periods. However, the mechanical energy E of the satellite remains constant. (Since the satellite’s mass is so much smaller than Earth’s mass, we…

The motions of the planets, as they seemingly wander against the background of the stars, have been a puzzle since the dawn of history. The “loop-the-loop” motion of Mars, shown in Fig. 13-12, was particularly baffling. Johannes Kepler (1571–1630), after a lifetime of study, worked out the empirical laws that govern these motions. Tycho Brahe (1546–1601),…

In Section 8-4, we discussed the gravitational potential energy of a particle–Earth system. We were careful to keep the particle near Earth’s surface, so that we could regard the gravitational force as constant. We then chose some reference configuration of the system as having a gravitational potential energy of zero. Often, in this configuration the particle…

Newton’s shell theorem can also be applied to a situation in which a particle is located inside a uniform shell, to show the following:  A uniform shell of matter exerts no net gravitational force on a particle located inside it. Caution: This statement does not mean that the gravitational forces on the particle from the various elements of the shell magically disappear.…

Let us assume that Earth is a uniform sphere of mass M. The magnitude of the gravitational force from Earth on a particle of mass m, located outside Earth a distance r from Earth’s center, is then given by Eq. 13-1 as If the particle is released, it will fall toward the center of Earth, as a result of the gravitational…

Given a group of particles, we find the net (or resultant) gravitational force on any one of them from the others by using the principle of superposition. This is a general principle that says a net effect is the sum of the individual effects. Here, the principle means that we first compute the individual gravitational forces that…

Physicists like to study seemingly unrelated phenomena to show that a relationship can be found if the phenomena are examined closely enough. This search for unification has been going on for centuries. In 1665, the 23-year-old Isaac Newton made a basic contribution to physics when he showed that the force that holds the Moon in…

What monster lies at our galaxy’s center? The answer is in this lesson. This is an image of the stars near our Milky Way galaxy’s center, which is marked with a small cross. Note that nothing shows up exactly at the center, but slightly off center (at the 8:00 position) there is a small circle.…