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How long can the chain of satellites of satellites be?

The Lunar Reconnaissance Orbiter is a satellite of the moon, which is a satellite of Earth, which is a satellite of the sun, which orbits around the center of the Milky Way.

That's a chain of 5. How long does it go?

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  • $\begingroup$ a different way to get at this concenpt might be to ask "Given a range of masses with a max/min ratio of 10$^N$, what's the largest number of objects, each sufficiently smaller than the last, such that each could simultaneously orbit the next-larger one as a satellite?" though it's a bit awkward that way. $\endgroup$ – uhoh Dec 24 '19 at 9:57
  • $\begingroup$ I expect that there's no concrete answer/it would be very high. Realistically, there's a minimum mass something needs to have for something to be able to orbit it. Also, extremely high chains might be unstable due to peturbations from other satellites $\endgroup$ – Dragongeek Dec 24 '19 at 11:05
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    $\begingroup$ I think you need to look at the hill's sphere associated. It tells you until what radius is the gravitational forces effective on a close body. $\endgroup$ – Adham Dec 24 '19 at 12:26
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The Lunar Reconnaissance Orbiter is a satellite of the moon, which is a satellite of Earth, which is a satellite of the sun, which orbits around the center of the Milky Way.

The answer depends in part on what you mean by "orbit", and the timeframe for what it means for one body to orbit another. If you allow objects that orbit for a short period of time, the yes, it is possible for moons to have moons. But if you want those orbits to have lasted for a good fraction of the current lifetime of the solar system, moons cannot have moons.

You picked the Lunar Reconnaissance Orbiter. The LRO doesn't quite count as orbiting the Moon. It needs to use fuel on occasion to maintain its orbit. The vehicle's fuel will run out in about seven year, and after that, the spacecraft will likely collide with the Moon in short order. What this means is that while stars can have planets and planets can have moons, that's about the extent at the lower end of the scale. No moons in the solar system have been observed to have submoons orbiting them.

Some have argued that moons can have moons, but the assumptions they make are a bit too spherical (as in spherical cows). Calculations of the Hill sphere implicitly assume spherical bodies. As bodies get smaller they tend to deviate more and more from spherical. For example, our Moon has seven large mass concentrations (mascons) on the near side and exhibits a marked discrepancy between the near and far sides with regard to crustal thickness. Arguing from the perspective of the Hill sphere also ignores perturbations caused the central star, perturbations caused by the planet's equatorial bulge, and weird perturbations such as the Kozai mechanism.

What about larger than a galaxy? The Milky Way is gravitationally bound to the Local Group, which in turn is gravitationally bound to the Virgo Supercluster, which in turn might be gravitationally bound to the Laniakea Supercluster. However, it's rather tough to call the Milky Way interactions with the Local Group an "orbit", and it's even tougher to label the interactions with even larger structures as "orbits".

This means that the chain you have found is about the extent of such chains. One has to view things with eyes squinted very tightly to claim longer chains.

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The galaxy Milky Way may be in orbit around the center of a structure of many galaxies.

Each satellite should be much smaller than its center object. But the Moon is already too small, not all orbits around it are stable due to mascons of the Moon.

So the answer depends on how many larger structures are the central object for the Milky Way. We don't know if our visible universe is in orbit around a center.

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