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Celestial Mechanics

Physics 201 Lecture 10. Celestial Mechanics. Newton’s triumph was to derive Kepler’s three laws of planetary motion. Kepler’s three laws: The orbit of every planet is an ellipse with the Sun at one of the foci

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Celestial Mechanics

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  1. Physics 201 Lecture 10 Celestial Mechanics

  2. Newton’s triumph was to derive Kepler’s three laws of planetary motion • Kepler’s three laws: • The orbit of every planet is an ellipse with the Sun at one of the foci • A line joining a planet and the Sun sweeps out equal areas during equal intervals of time • The square of the orbital period is proportional to the cube of the orbital size • Newton showed how these laws all follow from

  3. Everything you must know about ellipses – and nothing more Orbitalparameters Eccentricity Orbitalperiod Geometricparameters

  4. Polar components of kinetic energy lead to the “effective potential” Kinetic energy “Effective potential”

  5. Using the effective potential makes this a one-dimensional problem The trajectory of the particle does not depend on its mass – to make things a bit simpler, both energy and angular momentum will be implicitly divided by mass.

  6. Planning a trip in space? Manage your Δv budget “Get to low-Earth orbit, and you’re halfway to anywhere in the solar system” – Robert A. Heinlein The Hohmann transfer orbit Longest time of transit Minimum Δv budget

  7. Gravitational slingshot can be a huge source of Δv – e.g., Cassini probe to Saturn Venus 1 Flyby Venus 2 Flyby EarthFlyby JupiterFlyby TargetingManeuver

  8. No return Escape orbit Elliptical orbit Circular orbit Escape velocity and unbound orbits • Adding speed increases energy and makes the orbit more linear • If total energy is positive, the orbit will not return • Five probes will escape our solar system… Semi-latusrectum

  9. Is there a future in space? Phase 1 : 1950 – 1980 “The Glory Days” Phase 2 : 1980 – 2010 “No Nonsense” Phase 3 : 2010 – 2040 “Divide & Conquer” http://upload.wikimedia.org/wikipedia/commons/8/82/Orbitalaltitudes.jpg

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