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Orbital Mechanics Mike Rodning 27 April 2005

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Introduction Survey of interesting celestial mechanical phenomena and techniques Types of Earth Orbits Coriolis effect Lagrange points Interplanetary mechanics

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Types of Earth Orbits Geosynchronous orbits Polar orbits: Inclination of 90 degrees. Polar orbits are useful for satellites that carry out mapping and/or surveillance operations Walking orbits: Uses external gravitational influences to induce a precession in the satellite's orbital plane. The resulting orbit is called a walking orbit, or processing orbit. Sun synchronous orbits: Are walking orbits whose orbital plane processes with the same period as the planet's solar orbit period. Useful if a satellite is carrying instruments which depend on a certain angle of solar illumination on the planet's surface. Molniya orbits are highly eccentric Earth orbits so the satellite remains above the northern hemisphere. Hohmann transfer orbits

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Coriolis Effect A force (2w x v) that exists in a rotating coordinate system when a particle has a velocity anti-parallel to the axis of rotation A particle dropped from 100 m on Earth at 45 deg lat would fall E 1.55 cm Fire a projectile parallel to horizon East it will deflect south Effects long range artillery and rockets

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Lagrange Points Points where a light third body can sit "motionless" relative to two heavier bodies that are orbiting each other L-points are “potential hilltops” of gravitational fields, points with equal but opposite forces L1, L2, and L3 are unstable L4 and L5 are stable and tend to collect stellar junk SOHO and Genesis satellites have orbited around L1, WMAP orbited around L2

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Genesis Orbit

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Gravitational Assist Using Gravity and the momentum of a planet a spacecraft can increase its energy Only needs to enter planets sphere of influence Can also be used to slow a space probes velocity

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Cassini Grand Tour

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Interplanetary Superhighway System Transfer between unstable L-points with almost no energy “Petit Grand Tour” could go to multiple locations with low energy Manned solar service station at E-M L1

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