Why does Callisto only have eclipses every 3 years?

Question

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.

Isn't this really about whether eclipses occur at certain points of the year, every year, or is there something else to it? If you're really Asking whether eclipses occur at certain points of every Earth year, what made you think that?
What happens when compare the cycles of moons and stars, sun(s) and planets with the gears in your car, or on a child's bike or an electric toothbrush?

Do they all go round at the same rate? — Robbie Goodwin, Sep 29 '22 at 19:11

score 15 · Accepted Answer · answered Sep 15 '22 at 20:13

15

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.

answered Sep 15 '22 at 20:13

notovny

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Thanks so much! That makes so much more sense now. – Elhammo Sep 15 '22 at 20:22
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Interestingly, these eclipses of Jupiters Moons happen every six years! When will the next series of mutual eclipses of Jupiter's moons begin? – uhoh Sep 16 '22 at 05:35
So... can we say the eclipses happen during Jovian fall and spring, but not during Jovian summer and winter? – Eric Duminil Sep 16 '22 at 10:24
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@EricDuminil Maybe? Callisto's inclination is under a fifth of a degree relative to Jupiter's equator, but exactly which direction the orbital pole points relative to Jupiter's pole is relevant. I'd suspect that the Callisto eclipse seasons would contain the Jovian equinoxes, but not be centered on them. – notovny Sep 16 '22 at 11:53

Why does Callisto only have eclipses every 3 years?

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