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Today (March 20, 2015) is seeing a rare combination of the spring equinox, a total solar eclipse, and a supermoon. I am wondering if there is anything special astronomically about all three of these happening at the same time, like is the equinox a particularly more or less likely time for solar eclipses to happen (my guess is that it has no impact eclipses).

The supermoon/total solar eclipse combination doesn't seem surprising to me, since if the opposite were to happen (moon far away and solar eclipse) we would end up with an annular eclipse instead of a total eclipse.

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    $\begingroup$ Since the equinox and the orbit of the moon have no connection, then I would believe that having a solar eclipse on the day of the equinox would have the same probability as having a solar eclipse on your birthday. $\endgroup$ – LDC3 Mar 21 '15 at 0:42
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There wouldn't be a direct correlation between the equinox and the moon's orbit, so there really isn't any special - it's just a coincidence.

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