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You want to know the range of RA where the Moon's orbital plane crosses the celestial equator from south to north, so we need to find the line of intersection of those two planes. The vector corresponding to the line of intersection of two planes equals the cross product of the normals of the planes. We can find those normals using rotation matrices. The ...

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I'm leaving this old answer here because the OP found it useful. But please see my new answer. ;) The Moon's ascending node progresses with (mostly) retrograde motion around the ecliptic. It's customary to specify it in terms of its ecliptic longitude, but we can easily convert it to equatorial coordinates using the standard spherical trigonometry equations....

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The precession of the moon's orbital plane does not align it with the ecliptic plane. The angle between those two planes is approximately 5.14° (it varies by ~±0.15°, mostly due to perturbation by the Sun). Precession causes the orientation of the lunar plane to vary, but the angle between the two planes stays (almost) the same. It's very similar to the ...

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There are few things here I think might be worth to state: The tilt of Earth is of no importance here. As the comment says what is of importance how much the Moon orbit is inclined to the ecliptic. Now, one can say that if both Sun-orbit and Moon-orbit have the same inclination to Earth equator (namely 23.5 deg) it means the Moon and Sun orbits have no ...

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