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The solar system as a whole rotates in the prograde direction, presumably to conserve the rotational momentum of the primordial dust cloud it formed from. All the planets orbit (and almost all rotate) in this prograde direction. Yet a large number of moons orbit retrograde.

The dominant pattern is for inner moons of gas giants (like the Galilean moons of Jupiter) to orbit prograde, but the outer moons to orbit retrograde.

https://www.jpl.nasa.gov/infographics/planetary-satellites-of-the-solar-system

Is this because inner moons formed along with the planet, but the outer moons were captured from adjacent heliocentric orbits?

It makes intuitive sense that capture of an object in a closer heliocentric orbit would "fall" into a retrograde orbit, but shouldn't capture of an object in a further heliocentric orbit result in a prograde orbit? If this were true, outer moons would be 50/50 pro/retrograde.

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Outer orbits have a lower velocity than inner orbits. See red arrows in sketch.

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From a Jovian inertial frame of reference, outer (solar) orbits are in the opposite direction from inner (solar) orbits. See blue arrows.

Any nearby objects in a prograde heliocentric orbit (either inside or outside Jupiter's orbit) which enter the Jovian sphere of influence will already have a retrograde direction from the Jovian frame of reference.

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    $\begingroup$ You're assuming coplanar, circular orbits here. Even a tiny bit of relative inclination and very slightly different eccentricity can result in a relative velocity in the Jovian frame in basically any direction on approach. $\endgroup$
    – notovny
    Commented Jul 6 at 20:10

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