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Stellar Laplace Resonances & Lagrange Points

Posted 9 years ago


I am attempting to create a science fiction setting for a story about the inevitable travails of a space-faring civilization. The issues they face, of course, would include complications that arise from special relativity, which precludes superluminal travel.

In order to have a space-faring civilization without ignoring Einstein's theories, I have come to the conclusion that the civilization should inhabit a single star system with a high stellar multiplicity. Yet, the only other case I have seen that uses this solution is Joss Whedon's Firefly (2002-2003), and after an exhaustive review of J. Chris Bourdier's official The Verse in Numbers I cannot find a modicum of realism in the mechanics of the White Sun system's stars (though I will eagerly join the celebration of his keen attention to planetary mechanics). As such, I am forced to consult you, the experts, on certain advanced concepts that may influence the final vision of the stellar system I am creating.

We know from the recent discoveries that it is possible for exoplanets to form in stellar systems like the one I am attempting to create. (KIC 4862625 being a fascinating discovery in a quadruple star system.) However, aside from the recently discovered 1SWASP J093010.78+533859.5 all stellar systems with high multiplicity have considerable separation between their constituent members/groups. My favourite system to-date, Sigma Orionis, still has distances of thousands of AUs separating its constituents. Based on my calculations, even if you accelerated at 1000G for 8 hours (to 0.95c) it would still take you 76 days to go from Sigma Orionis AB to Sigma Orionis C (3,900 AU). This may not seem like that long given that we have, in history, seen human colonialism extend over oceans that took months to traverse in wooden ships; but when you consider the relativistic effects, there is the added dimension that the crew of a space ship would only experience approximately 24 days of transit. Ideally, I would like the stellar system to be traversable in a reasonable time frame at a less extreme velocity, as I intend to emphasize the mental strain experienced by a ship's crew when they are forced to travel at relativistic speeds that lead to noticeable time dilation.

To resolve this I have a number of possible solutions, but I have no idea how to perform the necessary calculations to create a proof, nor the theoretical knowledge to determine whether or not these solutions are even within the bounds of physics. Please find the solutions below:

Solution 1: Laplace Resonances

The moons of Jupiter, Ganymede, Europa, and Io have orbital periods related by a ratio of small integers. It takes the same amount of time for Ganymede to make a single rotation around Jupiter as it does for Europa to make two rotations and Io to make four. This creates a stable gravitational effect that maintains close(r) orbits. Sean Raymond used this, as well as Lagrange Points (see below) in his Ultimate Solar System thought experiment, to fit more planets into the circumstellar habitable zone (CHZ), but I am wondering if the same effect can be used for stars? Does anyone know of any examples?

Solution 2: Lagrange Points

As I mentioned above, another possible solution (one that works on a planetary basis) is to have co-orbital celestial bodies. Lagrange points are locations in an orbit where the combined effect of two gravitational pulls (such as the Sun and a planet) on a third body (such as an asteroid) provides the exact centrifugal force necessary to keep the third body in orbit with them. The third body (such as an asteroid) cannot be much more than one-tenth the size of the main orbiting body (such as a planet), otherwise the third body's orbit can be destabilized. One theory about the formation of the moon involves such a scenario, when a hypothetical celestial body called Theia destabilized from its orbit in Earth's L4 or L5 lagrange and collided with our planet. As with solution 1, I have seen no examples of this in any data I've seen of stellar bodies. The closest example is a trinary system, which is something else entirely. I am wondering if anyone has insights into extant examples or theoretical models that allow for this configuration?

If I could get some feedback on these ideas, I would very much appreciate it. Additionally, if someone has a third solution I would be very interested to hear.

POSTED BY: Taylor Reisdorf
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