The apparent motion of the sky due to the earth's rotation is upwards to the right parallel to the celestial equator. The line near the moon's path is the ecliptic, the apparent path of the sun in the sky. Astronomers use a fancy term for this angle. It's called the obliquity of the ecliptic, because that's what it looks like in the sky, assuming you could see these lines, which of course you can't. The words eclipse and ecliptic are related.
Eclipses can only occur when the moon is near the ecliptic.
The sun of course must cooperate by being either at the same spot, for solar eclipses, or at the opposite point in the sky, for lunar eclipses. The line running perpendicular to the celestial equator is the zero hour line of right ascension. The celestial counterpart of the zero longitude line on the earth that runs through the old Greenwich Observatory outside London. The point where the zero hour line, the ecliptic, and the celestial equator meet is the vernal equinox point, where the sun was on the first day of spring. When the sun is near the autumnal equinox, the full moon, being opposite the sun, will be near the opposite equinox point.