Solving Kepler's Equation for Comet Orbit Time Around Sun

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To solve for the orbital time of a comet that is ten times farther from the sun than Earth, Kepler's Third Law is applied, which states T^2/R^3 = K, where K is a constant. The value of K is given as 3.36 x 10^18. The comet's distance (R) can be expressed as ten times Earth's distance, allowing the equation to be set up with the known ratios. The solution yields an orbital period (T) of approximately 31.6 years. Understanding that Kepler's constant is the same for both the comet and Earth is crucial for the calculation.
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Homework Statement



A comet is 10 times farther from the sun than the Earth. Find the time it take to make its orbit around the sun.

Homework Equations


T^2/R^3 = K
K= 3.36X10^18


The Attempt at a Solution



I tried to create a ratio, but I honestly have no idea where to start. I'm not even sure I need to know kepler's constant for this problem. and the answer is T=31.6

I don't know what to put as R, and that leaves me with two variables, R and T.
I also don't know if Kepler's constant is the same for the comet and the earth.
 
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since k is equal for both objects, you can set each objects time^2/distance^3 ratio equal to each other. Then use that R_{comet}=10R_{earth}.
 

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