1. 1 Class #23 Celestial engineering Kepler’s Laws Energy, angular momentum and Eccentricity

2. 2 Kepler’s 1 st, 2 nd and 3 rd laws (1610) 1 st Law – Planets move in ellipses with sun at one focus 2 nd law is direct consequence of momentum conservation “Equal areas are swept out in equal times” True for ALL central forces Third law demonstrated previously relates period to semi-minor radius

3. 3 Kepler’s 3 rd law

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5. 5 Converting I

6. 6 Converting II

7. 7 Converting III

8. 8 Properties of ellipses :30

9. 9 E, L and Eccentricity The physics is in E and L. Epsilon is purely a geometrical factor. Epsilon equation applies to ALL conic sections (hyperbolae, ellipses, parabolas).

10. 10 Energy and Eccentricity EccentricityEnergyOrbit E<0 Circle E<0 Ellipse E=0 Parabola E>0 hyperbola

11. 11 E, L and Eccentricity The physics is in E and L, and it transfers to quantum mechanics.