Sun-Jupiter L1 is 1/3 of an AU from Jupiter. Could it be used to slow down or redirect a spacecraft approaching Jupiter? And the same for Sun-Jupiter L4 and L5 for a spacecraft on the way to e.g. Saturn?
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2$\begingroup$ A Lagrangian point does not have its own gravity. A restricted three-body problem can be exploited to give a "weak ballistic capture", reducing $\Delta V$ requirements somewhat. $\endgroup$– Deer HunterAug 5, 2015 at 9:41
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$\begingroup$ @DeerHunter Yes, AFAIK the reason one can orbit it has to do with the instability between Sun and Jupiter in this case. But is there no use of that instability for a fast flyby spacecraft? (A space telescope specialized on observing solar system planets is on NASA's wishlist. Maybe such a thing could be put at Sun-Jupiter L1 to study the Jupiter system fairly up close. But that's another topic.) $\endgroup$– LocalFluffAug 5, 2015 at 9:46
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$\begingroup$ @DeerHunter According to this accepted answer a spacecraft can move .06 AU from Sun-Earth L2 with "a nudge". With only .3 AU left to Jupiter, I thought that a similar effect out there might substantially benefit an orbital insertion. $\endgroup$– LocalFluffAug 5, 2015 at 9:56
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$\begingroup$ Like this (a trajectory of J002E3, aka Apollo 12 mission's Saturn V S-IVB third stage, from April 2002 to July 2003 as it was gravitationally captured into the Earth-Moon system from the heliocentric trajectory via SEL1 and then perturbed out of it again back into heliocentric regime). Yes, this actually happened "naturally" (no propulsion) and resulted in several Earth-Moon flybys of the object that was initially considered an Earth-crossing asteroid, until it was realized it's covered with titanium oxide paint. :) $\endgroup$– TildalWaveAug 5, 2015 at 13:30
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The Sun-Jupiter L1 and L2 (SJL1 and SJL2) are lot more interesting than the Sun-Earth L1 and L2 (SEL1 and SEL2). The Sun-Earth mass parameter is only 3.04e-6 while the Sun-Jupiter mass parameter is 9.54e-4. The Weak Stability Boundaries (WSBs) emanating from SJL1 and SJL2 are a lot more extensive than the WSBs from SEL1 and SEL2.
Comet Oterma enjoys some fame due to it's occasional transits through SJL1 and SJL2. Sometimes Oterma orbits beyond Jupiter's 5.2 A.U. orbit. Then it falls through SJL2 and leaves Jupiters' realm via the SJL1 neck. Here's a screen capture from a pdf by Koon, Lo, Marsden & Ross:
It's interesting that in a rotating frame, Oterma's inside orbit looks a lot like a Hilda Comet but rotated 60º. The Hildas have a 3:2 resonance but their aphelions take them to the L4, L5 and L3 regions far from Jupiter's influence. Oterma's third aphelion brings it to SJL1, close enough that Jupiter is a big influence.
To answer your question, is the SJL1 useful for fly-by probes? In my opinion, no. The arrival Vinf for an earth to Jupiter ellipse is around 5.6 km/s. Too high for ballistic capture. SJL1 orbits a little slower than Jupiter, but this delta V savings is minor compared to the substantial Oberth benefit Jupiter's deep gravity well can offer.
