Question
If a small planet were discovered whose orbital period was twice that of
Earth, how many times farther from the Sun would this planet be?
Earth, how many times farther from the Sun would this planet be?
Answers
Steve
consider that T^2 = kr^3
That means that T^2/r^3 is constant
T^2/r^3 = (2T)^2/(xr)^3 = 4T^2/x^3r^3
So, 4/x^3 = 1, and x = ∛4
That is, our small planet's orbital radius is ∛4 times earth's.
That means that T^2/r^3 is constant
T^2/r^3 = (2T)^2/(xr)^3 = 4T^2/x^3r^3
So, 4/x^3 = 1, and x = ∛4
That is, our small planet's orbital radius is ∛4 times earth's.