Is it possible to calculate how long a moon takes to orbit a gas giant?

if it takes the moon 6 months to pass through the gas giants shadow? Assume it is distant enough to not be tidally locked. The gas giant is 112.5 AU from the star. The star is 55 solar masses. It is undetermined how long the gas giant takes to orbit the star and the size of the gas giant can be varied to best fit the conditions necessary for the moon, which is 80% earths mass, to spend 6 months transiting the gas giants shadow. preferably, the moon would be far enough away to not be tidally locked.

Hope that is clearer. If you need more info, please specify what info needs to be added. Thank you.

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Is it possible to calculate how long a moon takes to orbit a gas giant?

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