# 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.

• Welcome to worldbuilding, your question is utterly underspecified: what do you mean with dark side? how far is the planet from the central star? How long is its orbital period? Please take the tour and visit the help center to better understand our culture. – L.Dutch Jul 31 at 12:44
• No, unless you provide more information. – L.Dutch Jul 31 at 13:05
• I don't think the math can work on this. A gas giant moon only spends a fairly small part of its time in the shadow of the giant. The closer it is, the higher that percentage is going to be. Io is the innermost of Jupiter's large moons and even then only spends 2 hours out of its 42 hour orbit in the shadow. That's less than 4%. By that math your theoretical moon would need to have an orbital period of 10 years to spend 6 months in the shadow, which I don't think is possible since that's how long Jupiter itself takes to get around the sun. – Morris The Cat Jul 31 at 14:27
• I'm not an expert on orbital dynamics, but I'm pretty sure that at that kind of distance, it's just not possible for your moon to remain in orbit around the gas giant instead of around the star itself. – Morris The Cat Jul 31 at 14:54

Trying to size the planet and the moon in a way that the transition through the planet's shadow takes around 6 months appears difficult.

When placing the moon very close, it will orbit fast and pass the shadow quickly.

When placing the moon very far out, the orbit is not realistically very stable, but its orbital velocity is slow so the shadow transition will be longer. But only if the plane of rotation is really parallel to the orbital plane of the planet itself.

Assuming a planet similar to Jupiter, it has a diameter of roughly 140000 kilometers. Ignoring the curvature for simplicity, transitioning through the shadow of this size in 6 month would give you a orbital velocity of 9 meters per second.

Even the extremely remote Jupiter moon 'Megaclite', with an orbital period of 790 days, has an orbital velocity of more than 2000 meters/second.

I think you will not find numbers anywhere near normal numbers that make you a shadow transition of 6 months...

If a part of the moon shall be dark for a long time, you could go for a moon with synchronous rotation on a somewhat far orbit.