I realize the response to this question is fairly involved but here goes. I need to have an alien spacecraft either in orbit around Uranus's moon Puck or somewhere in Puck's orbit around the planet if there is a stable point in the orbit that would work. Which option would be best for a decades long sojourn in that orbit using a minimal amount of power to maintain its position? Thanks.
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2$\begingroup$ Perhaps you could engage the expertise of the community better if you were to include mass, orbital radius, some details about the systems involved, rather than asking a blank question and requiring us to do all the work. Yes we can look it up, I get the feeling that you haven't. What research have you done? $\endgroup$– Angry MuppetApr 17, 2019 at 16:23
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$\begingroup$ FYI: Hill sphere calculator $\endgroup$– AlexanderApr 17, 2019 at 16:48
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3 Answers
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/somewhere in Puck's orbit around the planet/
Park it on Puck.
That is somewhere in Puck's orbit. You do not need to worry about it drifting off. On the surface of the moon it is unlikely to be discovered but floating around loose a space probe or strong telescope might spot it. You can cover it with a tarp or whatever they use on Puck for long term storage of space vehicles.
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$\begingroup$ Worth noting that surface gravity on Puck is about 0.03 m/s^2 .... less than 0.3% of what it is on Earth. Escape velocity on Puck is 68 m/s. It's not too hard to get off the surface if you want to. $\endgroup$ Apr 17, 2019 at 17:36
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Calculate the Hill Sphere of Puck
The Hill Sphere is the area around a celestial body where the gravitational attraction of that body dominates the attraction of other, smaller objects. The radius of the Hill sphere ($r_{H}$) of a body of mass $m$, orbiting a larger body of mass $M$ is calculated by
$$ r_H \approx a(1-e)\sqrt[3]{\frac{m}{3M}}.$$
For the case of Puck ($m = 3\times10^{18} \text{ kg}$) orbiting Uranus ($M = 9\times10^{25}\text{ kg}$) at a semi-major axis of $a = 9\times10^7\text{ m}$ with eccentricity $e=0.00012$; we see that $r_H \approx 200 \text{ km}$.
Puck has no atmosphere and is only some 80 km in radius; so, relative to the size of the planet, that isn't that close to it. The closer to the planet, the more stable the orbit will be on geological time scales. I would predict, however, that an object in orbit of Puck would not remain stable for millions of years. There are plenty of other moons of Uranus, and much bigger ones; certain alignments seem likely to pull the object of interest out of the orbit of Puck into the orbit of Uranus.
Ultimately, an object is more stable in an orbit of Uranus than it is of Puck; but, math says that you can expect an object to be somewhat stable in a close orbit of that small moon, certainly on a time scale of decades.
answered Apr 17, 2019 at 17:04
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$\begingroup$ Be very careful about your assumptions of long term stability. Mass concentrations can peturb your orbit enough to crash you in a surprisingly short time. Higher orbits are safer. $\endgroup$ Apr 17, 2019 at 20:23
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I like the answer by Willk regarding landing. If you want it to stay in space, with minimal power, consider the Lagrange Points of the Uranus/Puck system, notably L4 and L5.
On the long term Uranus is a little crowded, but for decades they should work nicely.
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$\begingroup$ The L4 and L5 points might be fine even over quite a long time... the Saturnian system has four trojan moons which seem unlikely to have all arrived in the very recent past. $\endgroup$ Apr 17, 2019 at 20:33