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How can you prove by using Kepler's Law that the linear velocity of a planet varies as the square root of the mean distance from the Sun?
Wiki User
∙ 10y ago
It doesn't. It varies inversely as that square root.
Here's how I did it:
T = time for a planet's revolution
R = mean distance from the sun
K = some konstant, any konstant
V = planet's linear speed
Kepler's 3rd law: T2/R3 = K . . . . . T2 = K R3
But T = orbital circumference/V , so (2 pi R/V)2 = K R3 , and (2 pi/V)2 = K R
Divide ' 1 ' by each side:
(V/2 pi)2 = 1/K R or V2 = 1/K R (new konstant)
V = K sqrt( 1/R )
qed
Wiki User
∙ 10y ago
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