celestial mechanics
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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 - PowerPoint PPT PresentationTRANSCRIPT
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Celestial Mechanics
Physics 201 Lecture 10
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• 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
Newton’s triumph was to derive Kepler’s three laws of planetary motion
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Everything you must know about ellipses – and nothing more
Orbitalparameters
Geometricparameters
Eccentricity
Orbital period
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Polar components of kinetic energy lead to the “effective potential”
Kinetic energy
“Effective potential”
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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.
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Planning a trip in space? Manage your Δv budget
The Hohmann transfer orbitLongest time of transitMinimum Δv budget
“Get to low-Earth orbit, and you’re halfway to anywhere in the solar system” – Robert A. Heinlein
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Gravitational slingshot can be a huge source of Δv – e.g., Cassini probe to Saturn
Venus 1 Flyby Venus 2
Flyby
EarthFlyby
TargetingManeuver
JupiterFlyby
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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…
No return
Escape orbit
Elliptical orbit
Circular orbit
Semi-latus rectum
Launch date
Distance (AU)
Speed (AU/yr)
Working?
Pioneer 10 Mar 1972 107 2.54 no
Pioneer 11 Apr 1973 86.8 2.40 no
Voyager 2 Aug 1977 100 3.26 yes
Voyager 1 Sep 1977 122 3.60 yesNew
Horizons Jan 2006 24.8 3.21 yes
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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