Keplers laws according to Newton
- For circles, the required acceleration and hence force is easy to derive
- Newton used this to derive law of gravity
- Newton was able to show if the velocity was less or greater than the circular velocity, the orbit would be an ellipse
- Not an easy problem
- One of the triumphs of his master work the Principia
- Richard Feynman -- famous 20th century physicst
- gave independent “elementary” derivation in a lecture to the 1964 freshman class of Cal Tech
K II -- equal areas in equal times draw on board
- Implied angular momentum was constant
- In absence of torques (i.e. spinning forces) angular momentum is conserved
- demo with orbiting ball and adjustable string length
- equal areas in equal times implies that if the string radius is cut in half, the period should be cut in four