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This idea is simple, you send a Von Neuman Starship to a nebula that is collapsing into a planetary system, and you have the Von Neuman probes feed off of the coalescing material to multiply themselves, and then they arrange for matter to collapse into 6 equidistant positions at Trojan points in a single orbit within the life belt of the forming star. The Von Neuman probes would try to redirect matter so that about 1 Earth mass collects at each of the Trojan points in the orbit, that would be a roughly circular orbit with each forming planet seperated from the one ahead and behind by 60 degrees, the gravitational interplay between each of these planets and the star would keep the planets in their proper position and from colliding with each other. Then you wait for the planets to cool and you begin terraforming them.
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A more precise but technical definition is that the Lagrangian points are the stationary solutions of the circular restricted three-body problem. For example, given two massive bodies in circular orbits around their common center of mass, there are five positions in space where a third body, of comparatively negligible mass, could be placed which would then maintain its position relative to the two massive bodies.
If the planets at trojan points were not of comparatively negligible mass, but on a par with the other planets, would the system still be stable?
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I think so, I believe it is called a Rosette World. The trick is to accurately measure the mass and distribution of the dust cloud and then make a whole bunch of Von Neuman machines, have them all clump together at the six postions in that orbit and act as gravitational seeds to pull in more matter on top of themselves, with perhaps some shepard Von Neumans guiding the larger rocks and making sure that all six planets build up with equal masses while at the same time preventing too much mass from accumulating there. Probably they could set up a total of 18 worlds in three Rosette configurations of six each, the inner one would be tropical, the middle temperate and the outer ones cold but still within the life zone.
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If the planets at trojan points were not of comparatively negligible mass, but on a par with the other planets, would the system still be stable?
I think so, I believe it is called a Rosette World.
It is not stable. If the mass of the body at the Trojan point is more than 4% of the smaller of the two primaries it is unstable to outside permutations. The Rosette world is stable in a system with no other bodies but is unstable in the long term if there are any permutations to the orbit.
Warm regards, Rick.
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