Posted by Claire on .
It takes Pluto a longer time to travel around the sun than the Earth because Pluto:
a. has farther to go
b. goes slower
c. a and b
d. none of these
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
Mplanet v^2/r = G Msun Mplanet/r^2
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)
as r goes up, T goes up
and as r goes up, v goes down
it goes further, and it goes slower.