Posted by **Claire** on Tuesday, July 22, 2008 at 12:52pm.

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

- physics -
**Damon**, Tuesday, July 22, 2008 at 2:53pm
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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