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

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

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

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

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

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.

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

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.

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.

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

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.

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

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

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

Work done by the inverse square gravitational force.

Solution (PDF)

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

Solution (PDF)

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

Solution (PDF)

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

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

Solution (PDF)

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

Solution (PDF)^#

Motion of celestial bodies due to gravitational force.

Solution (PDF)

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

Solution (PDF)

Finding the escape speed of a rocket from the moon.

Solution (PDF - 2.0 MB)^#

Finding escape velocity of a rocket launched from a planet.

Solution (PDF)