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Model for Jupiter satellites here is based on Jean Meeus: Astronomical Formulae for Calculators.
Earth's and Sun's declinations are planetocentric, i.e. with respect to Jupiter
When a satellite transits over Jupiter, Sun casts a shadow:
- towards East, if Earth-Jupiter-Sun angle is positive (i.e. Sun is on the right with respect to Earth's point of view, and Jupiter rises after sunset, like decrescent moon)
- towards West, if Earth-Jupiter-Sun angle is negative (i.e. Sun is on the left side with respect to Earth's point of view, and Jupiter rises before sunset, like crescent moon)
- in vertical line with the satellite, if Earth-Jupiter-Sun angle is near to 0° (i.e. Jupiter is in opposition, Earth's point of view, and Jupiter rises at sunset, like full moon)
- towards North, if Earth's declination is higher than Sun's declination (i.e. viewed from Jupiter, Earth is higher than the Sun, with respect to Jupiter's equator)
- towards South, if Earth's declination is lower than Sun's declination (i.e. viewed from Jupiter, Earth is lower than the Sun, with respect to Jupiter's equator)
- in horizontal line with the satellite, if Earth's and Sun's declination are the same
Sun casts Jupiter shadow (and satellites shadows too) the same way, with respect to their actual position.
Eclipses are not visible for us when Earth-Jupiter-Sun is near 0°, but when it reaches extreme values far from 0° (it never exceeds +-12°) they may occur even far from Jupiter, and a satellite may disappear in the shadow and then appear again, while not being hidden behind Jupiter!
We assume that the four satellites are situated exactly in the plane of Jupiter's equator.
(Actually, the four satellites can reach extreme latitudes of 0° 02', 0° 31', 0° 19° and 0° 44' respectively, with respect to the equatorial plane of the planet)
As a consequence, mutual occultations and mutual eclipses cannot be calculated with certainty.
Model for eclipses here assumes that shadows are almost of cylindrical shape, due to the very small ratio between the radius of Jupiter's satellites orbits and Jupiter's distance from the Sun.
Satellites' sizes are emphasized in graphical representation, while they're approximated with 1/30 of Jupiter's radius for calculations.
We can expect a mutual occultation if two satellites are in straight line with our point of you, and this can occur only when Earth's planetocentric declination is near to 0°.
We can expect a mutual eclipse if two satellites are in straight line with with the Sun, and this can occur only when Sun's planetocentric declination is near to 0°.
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