Orbital Mechanics

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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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Questions?