Kepler’s Laws

Each planet’s orbit around the Sun is an ellipse, with the Sun at one focus; Newton
proved that this implies r
2
gravitational force.

A planet moves along its orbit with a speed
(incomplete)
Orbital Paths

Extending Kepler’s Law #1, Newton found that ellipses were not the only orbital paths

Possible orbital paths
Ellipse(bound)
Parabola(unbound; E=0)
Hyperbola(unbound)
Angular Momentum
Angular momentum – the momentum involved in spinning/circling = mass x velocity x radius
Torque – Anything that can cause a change in an object’s angular momentum (twisting force)
Conservation of Angular Momentum

In the absence of a net torque, the total angular momentum of a system remains
constant.
Torque

Torque is a twisting force – moving a door on hinges

Depends on not only how much force is used but where you apply the force
Universal Law of Gravitation

Between every two objects there is an attractive force along a line between them; thus
there is NO TORQUE and ANGULAR MOMENTUM is conserved.
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 Winter '08
 HARTMANN,BERGIN
 Angular Momentum, Celestial mechanics

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