Calculating Orbital Periods Using Kepler's Third Law

[craig.16]

Homework Statement

Assuming that the orbits of the Earth, and of Jupiter, around the Sun are circular and given that Jupiter orbits with a radius 5.2 times that of the Earth, calculate the orbital period of Jupiter around the Sun.

Homework Equations

T²=(4(pi)²/(G*M))*r³

The Attempt at a Solution

R_e=6400km (approx)
R_j=(6400*10³)*5.2=3.33*10⁷m
M_s=1.99*10³⁰kg

T²=[(4(pi)²)/((6.67*10^-11)*(1.99*10³⁰))]*(3.33*10⁷)³
=10963.03446
T=104.7=105 (approx)
The answer is meant to be roughly 12 so where exactly did I go wrong. I have done multiple checks to ensure there is no calculation error but I tried using this equation for the orbital period of the Earth and I got 8 roughly. So where is this factor of 8 coming from?

 

[phyzguy]

You're using the radii of Earth and Jupiter, not their orbital radii. You don't need to use G and Msun. If T^2/R^3 is a constant and R increases by 5.2X, what happens to T?

 

[craig.16]

Thanks for making that clear to me.