why does a comet spend so little time in the inner solar system?
To answer this question you have to observe Kepler's laws of planetary motion:
http://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion
Carefully read the second one. Then observe one of the images there:
http://en.wikipedia.org/wiki/File:Kepler-second-law.svg
Note that the arch closer to the sun is much longer then the other arch which means traveling in higher speed.
The question is answered if you recall that a comet trajectory is a very thin ellipse:
http://epoxi.umd.edu/3gallery/comet_orbits.shtml
or:
http://epoxi.umd.edu/3gallery/EPOXI_Mission_Trajectory.shtml
So this happens not only to comets but also to planets… and to spaceships:
http://en.wikipedia.org/wiki/Slingshot_effect
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