Calculate the Orbital Radius of a Planet

[Slurpee12]

Homework Statement

Planet X of mass mx = 2.1 × 10²⁴ kg orbits S in uniform circular motion at a distance rx and with a period Px = 2.1 years (=66225600 s). The mass of the star S is MS = 2 × 10³¹ kg and its radius is RS = 3.2 × 10⁸m.

Homework Equations

T=2pi * sqrt(r³/(GM)

The Attempt at a Solution

I used the above equation to derive: r=(3(√(T²GM)/4pi²) (where 3sqrt is cube root)
I then plugged in 66225600 for T, 6.67 × 10^-11 for G, 2 × 10³¹ for M.
I solved for r, and I got 2.43 × 10¹², but this isn't the correct answer. I'm not sure where/what I've done wrong

 

[gneill]

Hi Slurpee12, Welcome to Physics Forums!

Your derivation looks okay. Must be a calculator/finger issue Maybe break down the calculation into smaller parts and show your intermediate values and we can check them.

If you want to show your math in a more slick fashion you could try learning a bit of LaTeX syntax. You can embed it in your posts and it will be rendered automatically when viewed. If you look to the far left of the page on the level of the POST REPLY button you'll see a LaTeX link that will take you to a reference page. Using LaTeX syntax your formula would become:
$$r = \sqrt[3]{\frac{T^2 GM}{4 \pi^2}}$$
One thing I will mention is that the length of a year is actually a tad longer than 365 days. It's closer to 365.25 days. That's why we have leap years Presumably the number of seconds that was shown for 2.1 years was a given value for the problem, so you have to keep it that way.