The Speed of Planets in their Orbits

The answer is that the speed of the outer planet must be slower than the speed of the inner planet. A simple mathematical solution is as follows:

g = due to gravity, c = centripetal, p = of the planet, s = of the sun

F(g) = F(c)

m(p)a(g) = m(p)a(c)

Gm(s) / r² = v(p)² / r

So v(p) = [Gm(s) / r]½

So v(p) ~ 1 / r½, since G and m(s) are constants.

For the outer (o) and inner (i) planets, r(o) > r(i)

As r increases, v(p) decreases, so the outer planet (with a larger r) must have a v(p) that is smaller than the inner planet.

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