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KStars can only calculate lunar eclipses, afaict:

KStars eclipse calculator

XEphem is another excellent calculator, but I don't think it supports eclipse calculations, either.

Is there any free, open-source software that calculates/predicts solar eclipses?

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XEphem can kinda do this.

§ 4.4 Earth of the manual says to use the earth view:

If a solar eclipse is occurring on the Earth a small X will mark the location of central totality.

It can be done for any satellite of the earth (not just the Moon):

Earth View

🎩-tip pidloop, GitHub issues comment


Also, the solver can find minimum angular separation, using this formula for small angular separations (Meeus, Astronomical Algorithms p. 105, eqn. 16.2):

sqrt(pow(("Sun.RA"-"Moon.RA")*cos(("Sun.Dec"+"Moon.Dec")/2),2)+pow("Sun.Dec"-"Moon.Dec",2))

cf. this GitHub issues comment

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