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Eclipses
So I was trying to figure out, from first principles, how and when eclipses happen. The Moon's orbital plane and the Earth's orbital plane don't exactly agree, and an eclipse can happen only when the Moon is in (or close enough to) the Earth's orbital plane -- not too high, not too low. It can also happen only when the Moon is on (or close enough to) the line between the Earth and the Sun. Combining these facts, an eclipse (lunar or solar) can only happen when the line determined by the intersection of these two planes matches (reasonably closely) the line between the Earth and the Sun. Which should happen twice a year, so those are the only times of year that an eclipse should be possible.
And yet in recent years there have been solar eclipses in both August and May, three months (90°) apart. How is this possible? I thought "perhaps the angle between the Moon's and Earth's orbital planes is small enough that 'close enough' happens frequently." So I Googled "what's the angle between the Earth's orbit and the Moon's orbit?" and got 5.145°. Since the Moon and the Sun are each only half a degree wide as seen from the Earth, that should mean that at its highest (northernmost) point, the Moon is ten times too high to be involved in an eclipse, and since it's a roughly sinusoidal curve that spends less time near its mean than near its extremes, "close enough" probably doesn't happen frequently.
But the page that gave me the 5.145° figure was at eclipse.gfsc.nasa.gov, which goes into lots of detail about the Moon's orbit. In particular, one of my assumptions fails: the Moon's orbital plane isn't quite fixed relative to the sidereal background. The time from one ascending crossing of the ecliptic to the next (the "draconic month") averages 27.211 days, while the sidereal month averages 27.322 days, so the Moon's orbital plane precesses by 360° every 18.6 years. So the times of year that eclipses are possible, based on my reasoning above, should also follow a cycle of 18.6 years.
Furthermore, actual draconic months vary by several hours above and below the aforementioned 27.211 days, correlating with the direction of the sun: the longest draconic months are when the line of intersection of the two orbital planes matches the Earth-Sun line (i.e. when eclipses are possible), and the shortest draconic months are when those two lines are perpendicular. Further furthermore, the amplitude of this variation follows a multi-year cycle that the Web page points out but doesn't explain (or I've missed the explanation).
In addition to the sidereal month (from alignment with the background of "fixed" stars to the next such alignment) and the draconic month (from ascending node to ascending node), the page also discusses the synodic month (from new moon to new moon) and the anomalistic month (from perigee to perigee). All of these are relevant to calculating eclipses. No two of these months are quite the same length, and each of them (perhaps except the sidereal?) varies significantly from one month to the next, with different patterns of variations. Wow.
And yet in recent years there have been solar eclipses in both August and May, three months (90°) apart. How is this possible? I thought "perhaps the angle between the Moon's and Earth's orbital planes is small enough that 'close enough' happens frequently." So I Googled "what's the angle between the Earth's orbit and the Moon's orbit?" and got 5.145°. Since the Moon and the Sun are each only half a degree wide as seen from the Earth, that should mean that at its highest (northernmost) point, the Moon is ten times too high to be involved in an eclipse, and since it's a roughly sinusoidal curve that spends less time near its mean than near its extremes, "close enough" probably doesn't happen frequently.
But the page that gave me the 5.145° figure was at eclipse.gfsc.nasa.gov, which goes into lots of detail about the Moon's orbit. In particular, one of my assumptions fails: the Moon's orbital plane isn't quite fixed relative to the sidereal background. The time from one ascending crossing of the ecliptic to the next (the "draconic month") averages 27.211 days, while the sidereal month averages 27.322 days, so the Moon's orbital plane precesses by 360° every 18.6 years. So the times of year that eclipses are possible, based on my reasoning above, should also follow a cycle of 18.6 years.
Furthermore, actual draconic months vary by several hours above and below the aforementioned 27.211 days, correlating with the direction of the sun: the longest draconic months are when the line of intersection of the two orbital planes matches the Earth-Sun line (i.e. when eclipses are possible), and the shortest draconic months are when those two lines are perpendicular. Further furthermore, the amplitude of this variation follows a multi-year cycle that the Web page points out but doesn't explain (or I've missed the explanation).
In addition to the sidereal month (from alignment with the background of "fixed" stars to the next such alignment) and the draconic month (from ascending node to ascending node), the page also discusses the synodic month (from new moon to new moon) and the anomalistic month (from perigee to perigee). All of these are relevant to calculating eclipses. No two of these months are quite the same length, and each of them (perhaps except the sidereal?) varies significantly from one month to the next, with different patterns of variations. Wow.