Has any moon achieved "retrograde equatorial orbit"? There are many moons which have low (almost negligible) inclination and can be considered to rotate at the planet's equatorial plane. For instance, Galilean moons have almost negligible inclination (&lt; 1$^\circ$) and so they are considered to have a &quot;prograde equatorial orbit&quot;.
OTOH, &quot;Retrograde equatorial orbit&quot; is that orbit which has an inclination of exactly 180° (or near 180°). Has any moon achieved such kind of orbit? I have found some Saturnian moons (or moonlets) which have inclination around 177° and didn't found anything beyond that. Why is it hard to achieve a &quot;Retrograde equatorial orbit&quot;?

Tangentially related questions: Can a moon rotate perpendicular to planet's plane? [90° inclination] (Theoretically yes, practically hard to achieve; See Kozai Mechanism)

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Also related:  Are all satellites of all planets in the same plane?
This is directly related to another question: Why are asteroids with zero orbital inclination rare?
If captured, irregular moons are randomly oriented in space then there is very little chance of them having either inclination angles near zero or near $180^\circ$. This is because, if they are uniformly distributed in space, the fraction of orbits within a given inclination range $i_1 &lt; i &lt; i_2$ is given by
$$ f = \frac{\int^{i_2}_{i_1} \sin i\ di}{\int_{0}^{180^\circ} \sin i\ di}$$
$$f = \frac{1}{2}\left(\cos i_1 - \cos i_2\right)$$
Thus for $i_1 =177^\circ$ and $i_2=180^\circ$, $f= 0.00068$ (i.e. about 0.07%).
Given that there are only $\sim 100$ irregular satellites, it is not that surprising that none are found with $i&gt;177^\circ$.
Note there are physical reasons why the regular satellites have low inclinations - they are not uniformly distributed and therefore they can have very low inclinations.