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Constraining exploration of outer bodies to flybys (such as New Horizons) seems unfortunate in terms of the amount of science that can be done per mission. Using a slower planetary approach has obvious disadvantages and transfering momentum to the body (or a moon) might be impractical, especially for bodies where aerobraking is not an option.

(Richochet braking seems likely to be even less practical. Even if a trajectory could be planned to bounce off two moons and the main body and the bouncing could be adequately controlled, the amount of padding required would seem almost certain to be more massive than the fuel and rocket engine for a more conventional insertion. While some of the padding mass might be dual purpose (e.g., small balloons might burst to absorb impact energy spreading microprobes, dyes, or reactive chemicals across the surface), it is hard to imagine such justify much of the mass cost.)

Obviously in very abstract theory a probe's momentum could be transferred from one component to another such that one part of the probe might be inserted into orbit while the other part is flung even faster into deeper space (which could be an attractive side effect). However, I cannot think of any mechanism that seems like it might be even close to practical (compared to alternatives that add expensive fuel/rocket engine mass).

A rail gun might be able to shoot one probe away from another and be useful for shooting objects at the body from orbit, but the amount of momentum transfer would seem to be far too small for a practical mass cost.

Likewise using a variation on gravitational slingshotting (inspired by how a binary star system can have one star fall into a black hole while the other is accelerated away) seems unlikely to be practical. (A modest-length tether might serve a dual purpose as an antenna, justifying some of its mass, but the necessary length and strength required for momentum transfer. Even if there were components at the midpoint of the tether that could be benefit from controlled distance from the primary probes — both the one flung off and the one inserted into orbit — it seems unlikely that any benefits of controlled distance would sufficiently justify the required mass.)

(Tethering to a component, which could still do a lot of science, that impacts the body, or a moon, could compensate for the issue of relatively weak gravity but aside from requiring even greater precision in approach the required strength of the tether seems certain to require too much mass even for a spring-like tether that breaks off at the orbiting component.)

Is there any practical way to use momentum transfer to allow fast approach (for lower arrival delay) and orbital insertion with reasonable mass costs?

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Obviously in very abstract theory a probe's momentum could be transferred from one component to another such that one part of the probe might be inserted into orbit while the other part is flung even faster into deeper space...

There's nothing abstract or theoretical about it; orbital insertion is invariably done by a probe transferring momentum to part of its mass, throwing it faster ahead to slow the rest of the probe into orbit. That's all a chemical rocket engine or an electromagnetic thruster does.

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