Posted by Claire on Tuesday, July 22, 2008 at 12:52pm.
Assume circular orbits.
Now let me see
F = Mplanet a where a is v^2/r, the centripetal acceleration with speed v and orbit radius r
F = G Msun Mplanet /r^2
so
Mplanet v^2/r = G Msun Mplanet/r^2
or
v^2 r = G Msun for every planet around sun (I am calling Pluto a planet :)
circumference of orbit = 2 pi r
so time around T = 2 pi r/v
but v = sqrt(G Msun/r)
SO
as r goes up, T goes up
and as r goes up, v goes down
SO
it goes further, and it goes slower.
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