Bsrhrki

Given a system similar to the Earth/Moon/Sun system, how would one go about making solar eclipses rarer than they are here on earth, but keep new moons similar to how they currently are (or at least similar)?

At first I thought that increasing the lunar tilt from 5 degrees to, say, 10 degrees would help, but there would still always be two "nodes" indicating where solar eclipses could happen on the planet. Even at a 90 degree angle, twice a year, the planet would see solar eclipses. at 10 degrees, new moons would still be relatively as frequent, though at 90 degrees, I don't think there would ever be a new moon.

Is there a way to make total solar eclipses happen infrequently, while keeping new moons frequent? And if so, what variable(s) need to change to make that happen?

Keep sun and moon sizes, make the orbit of the Earth around the sun more excentric and with a smaller mean distance.

The new moon is unnafected, but full solar eclipses will only happen if the eclipse happens together with the Earth's apoapsis, or close to it. And that will only happen during a few specific days of the year. Any solar eclipse far from the apoapsis will be partial.

That also implies shorter years and a whole different set of conditions on the planet that might not be compatible with life as we know it, though.

Just shrink the moon by 6%, and there will never be another total solar eclipse, but new moons will still happen as normal. The moon will be too small to fully cover the sun, so there will be partial and annular eclipses, but no total ones. If you still want the occasional total eclipse, make the moon slightly bigger again, so that eclipses are total if and only if it happens to be at the closest point to the Earth in its orbit at the time of the eclipse. We’d still get the same number of eclipses at the same time, but hardly any of them would be total.

Since both the moon and the Earth are in elliptical orbits, the apparent angular sizes of the moon and sun vary. Specifically, the moon varies between 29' 26" and 33' 30" while the sun varies between 31' 36" and 32' 42". You want the moon’s maximum to be just larger than the sun’s minimum, so that there are very occasional total eclipses if we happen to get an eclipse when the moon is at its closest and the sun is at its furthest. So to reduce the moon’s maximum angular size to 31’ 40” you need to make it 5.5% smaller without changing its orbit.

At 90 degree inclination, you could still get new moons near the nodes where the inclination of the moon's orbit with respect to the line from the planet to the sun is low.

The presence of nodes in the planet's orbit where the inclined orbital path of the moon intersects a line pointing towards the sun, however, is not itself problematic, because it is not itself sufficient to cause eclipses. And that's a good thing for you, because it's a simple geometric fact that you can't avoid them. In order to get an eclipse, the moon also has to actually pass through that intersection point during the brief period when it exists every half-year. As such, a very simple solution to avoid ever having an eclipse presents itself: just tweak the moon's orbital period so that it forms a simple integer ratio with the year, such that the moon is always in the same phase on the same date every year--and then just declare that the phases are such that you never have things line up for an eclipse.