# Geometry of Dyson Clouds

From: Alex Future Bokov (alexboko@umich.edu)
Date: Sat Mar 17 2001 - 12:20:09 MST

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Let's say you want to populate an orbital distance R around a planet
as densely as possible with satellites, such that no two ever come
closer than distance N from each other. Let's assume non-decaying
orbits and that they are not constrained to any particular orbital
angle. What kind of arrangement would these orbits have?

Related question, maybe the same one-- what is the mathematical
relationship between the number of intersecting orbital planes (all at
distance R, but at different angles) and the number of satellites in
each orbit? In other words, if you just have one orbit, then you can
pack it with pi*2R/N satellites. If two such orbits intersect, then
obviously each has to contain fewer satellites (they need to 'take
turns' going through the two points of intersection) and so on for
each additional orbit added to the mix, but what is the actual
relationship?

I have a hunch that when there are many orbits, it's best to angle
them such that there are never more than two intersecting. I also have
a hunch that for each R there is an optimal number of orbits beyond
which any additional satellite capacity from more orbits would be
offset by the decrease in the number of satellites each of the orbits
would have to undergo in order to accomodate the new one. I don't know
how to evaluate these hunches, but if they are correct, then I can
sort of envision how a densely populated orbital distance would look--
sort of like a hollowed out ball of yarn, with relatively large gaps.

I'm not expecting somebody to actually have the right equation or
software simulator handy (though of course it would be great if
somebody did). Any helpful information at all would be appreciated:
references to books or papers, names of authors, the proper technical
terms for the question I'm asking, search terms to try, or even the
name of the subdiscipline/s of math/physics that study these
questions.

--Thanks, AFB

- --

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