How Long Does Moon E Take to Orbit Planet?

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Moon E orbits a planet with an orbital radius of 4r, while Moon D orbits at radius r and takes 20 days for one complete orbit. The discussion highlights the application of Kepler's laws, particularly the third law, which relates the orbital periods of moons to their distances from the planet. It is clarified that the orbital period of Moon E cannot simply be assumed to be 80 days based on the radius alone. The correct approach involves using the ratio of the cubes of the orbital radii to determine the orbital period. Ultimately, the consensus is that Moon E's orbital period is longer than Moon D's, but not simply four times longer.
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Homework Statement



Two moons orbit a planet in nearly circular orbits. Moon D has orbital radius r, and moon E has orbital radius 4r. Moon D takes 20 days to complete one orbit. How long does it take for moon E to complete one orbit


Homework Equations



None - I think


The Attempt at a Solution



I am hoping that this problem is not complicated. Since it takes 20 days for moon D with radius r, it would take 80 days for moon E with radius 4r?

Is my reasoning correct ??
 
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No, it isn't. What do Kepler's laws have to say about this problem?
 
Is it just 20 days the same as moon D?

A line drawn from the sun to any planet sweeps out equal areas in equal time intervals.

Does the size - radius matter then?
 
Ok the above doesn't make sense.

Then I don't know, really.
 
It's not just 20 days.

Keplers second law is only valid for the same planet or moon (and it's trivial for a circular orbit)
Try the third law.
 

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