1 / 9

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

toni
Télécharger la présentation

Celestial Mechanics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related