# Newton's Law of Gravity

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## Video Clips

#### Universal Gravitation

RealVideo®
5:57 minutes (31:11 - 37:08)

Work when g varies; statement of law of universal gravitation; calculation of g.

Instructor: Prof. Walter Lewin
Prior Knowledge: Gravitational Work (13:04 of V11)

#### Gravitational Potential Energy

RealVideo®
8:29 minutes (37:08 - 45:37)

Derivation of formula, with U=0 at ∞ comparison with earlier formula.

Instructor: Prof. Walter Lewin
Prior Knowledge: Universal Gravitation (31:11 of V11)

#### Gravitational Potential Energy Continued

RealVideo®
7:00 minutes (0:00 - 7:00)

Formulas for U and F; graph of U vs. r; explanation of difference in potential energy.

Instructor: Prof. Walter Lewin
Prior Knowledge: Gravitational Energy (37:08 of V11)

#### Force and Potential Energy

RealVideo®
7:56 minutes (7:00 - 14:56)

Proof that dU/dx=-F using mass on a spring; statement in 3D; application to gravity.

Instructor: Prof. Walter Lewin
Prior Knowledge: Mass on a Spring (1:20 of V10), Gravity (31:11 of V11)

#### Earth-Sun Gravitational System

RealVideo®
6:53 minutes (32:37 - 39:30)

Law of universal gravitation; velocity, potential, and kinetic energy for Earth's orbit; escape velocity for Earth.

Instructor: Prof. Walter Lewin
Prior Knowledge: Gravitation (31:11 of V11)

## Lecture Notes

#### Law of Universal Gravitation

PDF - 1.6 MB#
Page 1 to page 6

Newton's law of gravity; gravitational potential energy; principle of superposition; potential energy of a spherical shell and a particle; cavendish experiment and the gravitational constant.

Instructor: Prof. Stanley Kowalski
Prior Knowledge: Newton's Laws, Potential Energy, Torque

#### Gravitational Forces

PDF - 1.6 MB#
Page 1 to page 3

Potential energy of a sphere and particle; gravitational force between spherically symmetric objects; gravitational forces on extended objects; tidal forces; weight and gravitational force.

Instructor: Prof. Stanley Kowalski
Prior Knowledge: Lecture 27

#### Gravitational Force

PDF - 1.3 MB#
Page 2 to page 4

Newton's law of gravity defined; universal gravitation constant; definition of weight; comparison of inertial mass and gravitational mass; principle of equivalence. Includes accelerating elevator and satellite examples.

Instructor: Prof. Stanley Kowalski
Prior Knowledge: Newton's Third Law

#### Law of Universal Gravitation

PDF - 1.2 MB#
Page 1 to page 14

Newton's law of gravity; gravitational potential energy; principle of superposition; potential energy of a spherical shell and a particle; cavendish experiment and the gravitational constant.

Instructor: Prof. Stanley Kowalski
Prior Knowledge: Newton's Laws, Potential Energy, Torque

#### Gravitational Forces

PDF#
Page 1 to page 9

Potential energy of a sphere and particle; gravitational force between spherically symmetric objects; gravitational forces on extended objects; tidal forces; weight and gravitational force.

Instructor: Prof. Stanley Kowalski
Prior Knowledge: Lecture 27

#### Gravitational Force

PDF#
Page 4 to page 11

Newton's law of gravity defined; universal gravitation constant; definition of weight; comparison of inertial mass and gravitational mass; principle of equivalence. Includes accelerating elevator and satellite examples.

Instructor: Prof. Stanley Kowalski
Prior Knowledge: Newton's Third Law

#### Gravity

PDF
Page 1

Gravitational constant defined; equation for gravitational force between two bodies; circular orbits and escape velocity; potential energy due to gravity, with equation.

Instructor: Dr. George Stephans
Prior Knowledge: Force and Potential Energy

#### Universal Gravitation

PDF
Page 13 to page 17

Universal law of gravitation defined; double star system example; gravitational field of a spherical shell of matter.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: Lecture 9

#### Harmonic Oscillator Problem Solving

PDF
Page 1 to page 6

Modeling the motion of a simple harmonic oscillator; gravitational field of a spherical shell of matter; gravitational force inside uniform sphere.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: Lecture 16

## Practice Problems

#### Calculating Work Integrals

PDF
Problem 20c

Work done by the inverse square gravitational force.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Escape Velocity on Asteroid

PDF
Problem 22

Escape velocity for an object on the surface of an asteroid.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Journey to the Center of the Earth

PDF
Problem 22

Finding the time it takes for an object to traverse a hole through the earth.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Work on a Comet

PDF
Problem 2

Work done on a comet moving in a hyperbolic orbit away from the sun.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Planetary Rotation

PDF#
Problem 5

Finding maximum rotation period for planet from density; calculating periods.

Instructor: Prof. Walter Lewin
Prior Knowledge: None

#### Slingshot Encounter

PDF#
Problem 2

Gain in mechanical energy from looping around a planet; finding new velocity and energy.

Instructor: Prof. Walter Lewin
Prior Knowledge: None

## Exam Questions

#### Gravitational Force

PDF#
Problem 1

Motion of celestial bodies due to gravitational force.

Prior Knowledge: None

#### Binary Star System

PDF#
Problem 12b

Gravitational forces acting on a small mass in a binary star system.

Instructor: Dr. George Stephans
Prior Knowledge: None

#### Escape Speed of Moon

PDF
Problem B6

Finding the escape speed of a rocket from the moon.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None