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The Moon is inclined to the ecliptic 5.15 degrees, and the equator of the Earth tilts 23.44 degrees. Since the Moon's ascending node to the ecliptic rotates, the Moon's inclination to the Earth's equator varies between 18.3 ( = 23.44 - 5.15) to 28.6 ( = 23.44 + 5.15) degrees.

My question is:

"Does only our moon have this property, or are there some other moons of other planets with a similar property?"

From Wikipedia it seems many moons of other planets have a fixed inclination to the equator of their planet, so our Moon seems a special case. But is our moon's inclination property the only case?

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Our moon is special.

Other planets have relatively much smaller moons. The other rocky planets either have very small moons (Phobos and Deimos are probably captured asteroids) or no moons at all.

The giant planets have a central system of moons that orbit prograde around their equator, and a wider system of satellites that orbit in many different orbits, and are not aligned to the planet or to each other.

Our Moon is the only moon that orbits roughly in the plane of the ecliptic, and the only one which shows the particular orbital dynamics in which the inclination varies as the ascending node rotates.

This suggests that the formation of the moon was special, not part of normal planetary formation. The suggestion is that the moon was formed in a giant impact.

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