How Long Does Moon E Take to Orbit Planet?

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SUMMARY

The discussion centers on determining the orbital period of Moon E, which orbits a planet at an orbital radius of 4r, while Moon D orbits at radius r and takes 20 days for one complete orbit. According to Kepler's Third Law, the square of the orbital period (T) of a moon is directly proportional to the cube of its orbital radius (r). Therefore, the calculation reveals that Moon E takes 80 days to complete one orbit, as T² is proportional to r³, confirming that Moon E's period is four times that of Moon D.

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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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