= GEO via Construction Orbits =

=== Hohmann to GEO ===

The usual way to reach GEO is a launch into an elliptical Geosynchronous Transfer Orbit (GTO) followed by an apogee insertion burn.  GTO starting from launch loop altitude (80 km) to GEO will start with a perigee velocity of 10346 m/s (or 9875 m/s relative to the rotating Earth) and arrive at GEO radius (42164 km) with a velocity of 1585 m/s, 1490 m/s slower than 3075 m/s circular orbit velocity at GEO.

Escape velocity from GEO radius is 4348 m/s (in any direction, though downward trajectories at any velocity will impact the Earth).  Exhaust plume atoms leaving the vehicle at less than escape velocity, but faster than atmosphere-skimming velocities, will orbit the Earth, possibly for a very long time, until they intersect other atoms (or artificial satellites) in orbit.  Above 20,000 km radius, there is only a thin smattering of hydrogen, so exhaust plume molecules may orbit for decades or centuries until they hit that.  

|| Velocity Space Diagram - - - - - ~+'''The Rotten Apple''' +~ - - - - - download: [[ attachment:RottenApple.png | {{ attachment:RottenApple.png | | width = 540 }} ]] || This diagram describes a "velocity space" around a point in physical space above the Earth.<<BR>><<BR>>The center of the circle is zero velocity at that altitude.  The horizontal axis of the diagram represents tangential (east-west or north-south) velocity, the vertical axis represents radial velocity (up-down).  An object with a velocity vector in the "green zone" will intersect the atmosphere within one orbit time.  The radius of the circle is escape velocity;  an object with a velocity vector reaching into the blue zone escapes from the Earth, into solar orbit, or (for ''very'' large velocities) to solar escape. <<BR>><<BR>> In between, in the red '''Rotten Apple''' zone, objects go into Earth orbit.  At the blue edge of the Rotten Apple, tidal forces from the Sun and Moon may perturb them to escape, or deeper into the Rotten Apple.  At the green edge of the Rotten Apple zone, tenuous upper atmosphere will eventually slow the object and move it into the green atmosphere decay zone.  Objects in the center of the red zone may remain in orbit for years, perhaps centuries, '''until they hit something else''' (like an artificial satellite) also orbiting in that zone. ||

A particle with a small tangential (horizontal in the diagram) velocity will be at the apogee of a slow orbit, with a perigee inside the atmosphere.  Vertical velocity will bring it to the atmosphere sooner, and the orbit can have a little more tangential velocity and still graze the atmosphere.
  
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