Solving for Moon B's Orbital Period: A Homework Challenge

AI Thread Summary
To solve for Moon B's orbital period, Kepler's Third Law is essential, which states that the square of the orbital period is proportional to the cube of the semi-major axis of its orbit. Given that Moon A has an orbital radius r and takes 50 days for one orbit, the relationship can be established as T_A^2 ∝ r^3. For Moon B, with an orbital radius of 5r, the equation becomes T_B^2 ∝ (5r)^3, leading to T_B^2 = 125T_A^2. By substituting T_A with 50 days, it can be calculated that Moon B takes approximately 250 days to complete one orbit. Understanding and applying Kepler's Third Law is crucial for solving this homework challenge.
Devin Longo
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Homework Statement



Two moons orbit a planet in nearly circular orbits. Moon A has orbital radius r, and moon B has orbital radius 5r. Moon A takes 50 days to complete one orbit. How long does it take moon B to complete and orbit?


Homework Equations



Kepler's Third Law



The Attempt at a Solution



I know we're supposed to attempt it, but I'm not even sure I'm heading in the right direction! Can anybody give me some insight?
 
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have you tried looking up kepler's 3rd law /
 
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