I don’t understand why Jupiter only eclipses Callisto in three year periods separated by three years. I get that the reason Callisto doesn’t always have eclipses is because of the combo of Jupiter’s slight tilt and the distance between Jupiter and Callisto, resulting in Callisto sometimes being completely out of Jupiter’s shadow. But why does this happen in 3 year intervals? I would assume eclipses would occur at certain points of the year, every year. I guess I don’t understand the full geometry of this.
They do happen at certain points of every Jovian year.
Jupiter's orbital period is approximately 12 Earth Years. the relative angle between the plane of Callisto's orbit and the plane of Jupiter's orbit is small. Jupiter is large, and Callisto, relatively close in proportion.
So for roughly three earth years, Callisto is, at a a pair of regions of its orbit, close enough to the line between Jupiter and the Sun that eclipses can happen.
Then for roughly three earth years, it passes above or below the eclipsable region when it nears Jupiter, from the Sun's point of view.
Then for three earth years, eclipses are possible again.
Then for three earth years, it's below or above the eclipsable region again.
Then it's a new Jovian year, and the cycle restarts.