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After reading up on irregular moons in the solar system - moons that are thought to be captured, most seem to be in retrograde orbit around their parent body. That led me to wonder if retrograde orbits are easier to capture objects than prograde orbits - say prograde orbits are more likely to gravitationally slingshot the object away from the parent body before capture, whereas retrograde orbits would be more likely to capture before flinging the object away.

When viewing the capture from the perspective of the parent body, an object that is moving retrograde past the body appears to slow down as it interacts with the gravity well of the body, whereas an object moving prograde past the body appears to accelerate in the same frame of reference.

Is there any validity to this, or is that just a flaw in reasoning?

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  • $\begingroup$ Isn't it the case that we suspect a moon has been captured because it's orbit is retrograde? If it was prograde how would we distinguish it from the other moons? $\endgroup$ – John Rennie Apr 9 '14 at 16:42
  • $\begingroup$ Yes, therefore you might expect an observational bias if we were just looking at the moons, but it seemed like most of the small rocky irregular bodies around the gas giants were retrograde. Just curious if there was evidence for that. $\endgroup$ – Foo Barrigno Apr 9 '14 at 16:43
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Are retrograde capture orbits “easier” than prograde capture orbits?

The answer is not just yes, but a rather emphatic yes. This is why the irregular moons of Jupiter predominantly have retrograde orbits, and why all of the outer moons of Jupiter have retrograde orbits. This is also why NASA has been interested in capturing an asteroid and putting into a distant retrograde orbit about the Earth's Moon.

Unfortunately, there are no nice, closed formed solutions to explain why this is the case. This result comes from perturbation theory and simulations galore. Prograde orbits with a semi-major axis greater than about 1/3 the Hill sphere radius tend to be markedly unstable. Retrograde orbits can be stable to the Hill sphere radius, and can be relativity stable even beyond the Hill sphere radius.

A lot of work has been done in the last couple of decades in analyzing distant retrograde orbits. Search for "distant retrograde orbit" in scholar.google.com and you will get a large number of recent hits. This search shows the results from just this year (2014).

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There are several effect that could explain retrograde captures being easier than prograde.

As Nickolai noted, aside from atmospheric effects and non-uniform gravitational fields, there's not way for an orbiting object to know about the spin of the primary. However, in general, planet's do have non-uniform gravitational fields- they bulge due to rotation, and satellites raise tidal bulges which induce drag. A body approaching on a retrograde path will always experience tidal drag opposing it's motion, lowering its orbit around the planet. An object on a prograde path whose closest approach is higher than synchronous orbit will experience forward drag pushing it farther away- no possibility of capture. If it's closest approach is below synchronous orbit, it will experience capturing drag, but less than a retrograde body would.

Additionally, you have to consider that a planet capturing a new moon is itself in orbit around the sun, as is the body to be captured. If the planet has prograde rotation and the body to be captured is initially on a lower orbit, it will be moving faster than the capturing planet, and thus will have retrograde motion when it passes by on the sunward side. If the body to be captured is on a higher orbit, it will be moving slower but pass by on the opposite side- again resulting in retrograde motion relative to the planet. In order to make a prograde approach, the body to be captured must have a highly elliptical solar orbit, so as to move much slower than normal on the inside track or much faster on the outside track.

Finally, there's the effect of gravitational interactions with existing moons. Depending on the exact relative positions of existing moons, the passing body can be either sped up or slowed down regardless of whether it's prograde of retrograde. I have no idea what the probability distribution is for different course changes, but I would not be surprised if it turned out to be more likely that a body would be accelerated in the prograde direction, which means ejection for an initially-prograde body and capture for a retrograde one. Even if that is not the case, however, the other two effects should be quite sufficient to explain the increased ease of retrograde capture.

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I think there's a flaw in your reasoning. From a parent-body-fixed reference frame, an object coming in retrograde would actually appear to move faster than a prograde object. In any case, the only way a retrograde capture would be more likely is if the orbital path of the incoming object takes it through the parent body's atmosphere, in which case a retrograde object will experience more drag, which will slow it down more. That difference in drag may or may not allow for enough energy loss for capture - if it's moving fast enough it'll still shoot past the planet.

In general, other than atmospheric effects and non-uniform gravity fields, there's no way for an orbiting object to "know" which way its host body is spinning, or if its spinning at all.

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