How long would this eclipse last?

For a moon orbiting a gas giant which is in turn orbiting a star, I want to know how long the eclipse would last for an observer standing on the moon when the planet passes between the moon and the star.

The actual values I intend to use in the end are likely to vary from these, somewhat, but I like simplicity so here's the parameters for this simplified version:

The star = our Sun.

The planet = Jupiter radius, orbits the star at a distance of 1 AU (Earth's distance from the Sun) giving it an orbital year equivalent to an Earth year (or close enough to be a negligible difference, for simplicity)

The moon = orbits the planet at a distance of 4 million KM, which should give it an orbital time around the planet of about 42 days. It is not tidally locked and rotates on its axis at a rate that will make the same point on the surface face the star exactly once every 24 hours (again, for simplicity)

For simplicity (seeing the trend here?), assume all orbits and equators of all 3 bodies share a plane, and are circular, no eccentric or inclined orbits or tilted axes, etc., and the observer is standing on a point on the equator of the moon. Assume the eclipse "starts" when the star is directly over head (noon) of the observer, and the observer says in the same location until the eclipse ends.

Please let me know if I left out any necessary variables, I probably have them available and just forgot to include them or didn't realize they were necessary.

How long before the observer sees the star/sun again? (rounded or approximate answers would work, but the more precise the better, and an explanation of how the numbers were determined is also appreciated)

posted over 5 years ago

Dalila‭

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