Kepler’s 3 Laws
- Kepler I : Orbits are ellipses, with Sun at one focus
- Ellipse : equidistant from 2 points (focii)
- cf. circle, equidistant from 1 point
- draw on blackboard, string and chalk
- focii close -- circle
- focii apart -- eccentric -- ellipse
- a conic section (circle, ellipse, parabola, hyperbola)
- all orbital motions follow one of the conic sections
- proved by Newton (law of gravity and calculus)
- What is at the other focus?
- nothing!
- see Kepler II to find a dark “sun”, i.e. a black hole
- Kepler II: Planets sweep equal areas in equal times
- Planets velocity not uniform
- speed up near perhelion blackboard ellipse
- focus near fastest speed is sun (black hole)