Understanding Planetary Motion: Correcting a Common Misconception

[mormreed]

I just need an explanation of a formula, and I think part of it is wrong, so here is the formula:

$$(T_A/T_G)^2=(R_A/R_B)^3$$


so T is the period and $$T_A$$ is the period of planet A
then below it is what I think is wrong, $$T_G$$ G is the Kepler's constant, I'm not sure what that really is
=
[text]R_A[/tex] which is radius of planet A over radius of planet B cubed, this side is right, any help is appreciated thanks

 

[rock.freak667]

I comes from Kepler's third law which states that

$$T^2 \propto R^3$$


So if two planets have the same mass, in your case planet A and G.

then $T_A^2= k R_A^3$ and $T_G^2= kR_G^3$

so just divide them and you'll get the formula

 

[mormreed]

I think I found the answer after some searching, which I did try before which brought me here, but I think it is $$(T_A/T_B)^2=(R_A/R_B)^3$$