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Is there a way to design an earth orbit so that it passes through the Moon's umbra with greater frequency than total solar eclipses occur on earth's surface?

What is the maximum frequency of eclipses that can result? I am not asking about the trivial case of a lunar orbit that obviously experiences the moon's full shadow every orbit.

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  • $\begingroup$ diagrams in this Space SE answer are for the Earth-Moon system ($\mu$=0.01215) I was going to say yes (these frequently have periods of very roughly half of the primary period) but those would be eclipses of the Earth, not the Sun. The whole mess is now orbited by the Sun (in the rotating frame shown). The paper is paywalled but there's a link to a copy at researchgate as well. There are several classes of orbits to choose from, have fun! $\endgroup$
    – uhoh
    Jan 22 at 1:16

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