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Is it possible for a man-made probe to orbit Pluto given its closeness to Charon? The gravitational field interaction of Pluto and Charon is likely to make simple orbit structure difficult for a man-made probe. Thanks for your insight.

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Avoiding hard math, which I'm not very good at, the simple answer is yes, provided there's enough distance. Pluto/Charon have 4 moons orbiting them a bit further away, all in relatively stable orbits. Source

Here's distances to scale. - same source.

Because the ratio of gravitational field strength to size is exponential (Power of 1.5), the apparent closeness of Pluto and Charon to the 4 small moons looks unusual, but it's perfectly acceptable for objects of that size.

Lagrange point stability requires a mass ratio of about 26 to 1. (.0385 to 1 per source). The Earth has satellites in unstable Lagrange points, so it's certainly doable, it's just not technically "stable".

The hardest part about getting a satellite to orbit Pluto is that Pluto's sufficiently small that any ship that approaches it would need to slow down significantly on it's own to get captured into a Pluto Orbit. That's why New Horizon was a flyby, not an orbit.

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Yes it is possible if you have the probe orbiting the Pluto-Charon system at one their Lagrange points.

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    $\begingroup$ I hate to say it, but this is incorrect. Charon is too close to Pluto's mass so there are no stable Lagrange points in that system. It might be possible with regular adjustments, but it wouldn't be a stable orbit. $\endgroup$ – userLTK Oct 21 '15 at 5:30

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