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## EXERCISES & PROBLEMS

EXERCISES & PROBLEMS ssm Solution is in the Student Solutions Manual. www Solution is available on the World Wide Web at: http://www.wiley.com/coUege/hrw Ilw Solution is available on the Interactive LeamingWare. Newton’s law of Gravitation IE. What must the separation be between a 5.2 kg particle and a 2.4 kg particle for their gravitational attraction to have …

## REVIEW & SUMMARY

REVIEW & SUMMARY Tile Law of Gravitation Any particle in the universe attracts any other particle with a gravitational force whose magnitude. Gravitational Behavior  Uniform Spherical Shells  holds only for particles. The gravitational force. Superposition Gravitational forces obey the principle of superposition; that is, if n particles interact. Gravitational Acceleration The gravitational acceleration a. of a particle (of …

## Einstein and Gravitation

Einstein and Gravitation Albert Einstein once said 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 toward a theory of gravitation. Thus Einstein tells us …

## Satellites: Orbits and Energy

Satellites: Orbits and Energy As a satellite orbits Earth on its 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 …

## Sample Problem

Sample Problem Hunting a black hole. Observations of the light from star indicate that it is pan of a binary (two- star) system. This visible star has orbital speed . SOLUTION: Some of the Key Ideas in this challenging problem are as follows: I. The two stars are in circular orbits. not about each other, but about the center …

## Sample Problem

Sample Problem Comet Halley orbits about the Sun with a period of 76 years and. in 1986. had a distance of closest approach to the Sun. its perihelion distance . shows that this is  between the orbits of Mercury and Venus. (a) What is the comet’s farthest distance from the Sun. its aphelion distance Ru? SOLUTION:The Key idea comes …

## Planets and Satellites: Kepler’s Laws

Planets and Satellites: Kepler’s Laws 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 motion of Mars, was particularly baffling. Johannes Kepler (1571-1630), after a lifetime of study, worked out the empirical laws that govern these motions. 1 THE LAW OF ORBITS: All …

## Escape Speed

Escape Speed If you fire a projectile upward, usually it will slow, stop momentarily, and return to Earth. There is, however, a certain minimum initial speed that will cause it to move upward forever, theoretically coming to rest only at infinity. This initial speed is called the (Earth) escape speed. The escape speed does not depend on the …

## Potential Energy and Force

Potential Energy and Force We derived the potential energy function U(r) from the force function F(r). We should be able to go the other way-that is, to start from the potential energy function and derive the force function. This is Newton’s law of gravitation . The minus sign indicates that the force on mass m points radially inward, …