Surprisingly, some Dyson spheres and ringworlds can be stable

In the realm of science fiction, Dyson spheres and ringworlds have been staples for decades. But it is well known that the simplest designs are unstable against gravitational forces and would thus be torn apart. Now a scientist from Scotland, UK has shown that certain configurations of these objects near a two-mass system can be stable against such fractures. The work is published in the journal Monthly Notices of the Royal Astronomical Society.

“I read ‘Ringworld’ and ‘Ringworld Engineers’ as a student, so I’ve long been fascinated by engineering on astronomical scales,” said Colin McInnes of the Larry Niven Ringworld series of hard sci-fi novels. McInnes is a professor of engineering science and holder of the James Watt Chair at the University of Glasgow in Scotland.

Physicist Freeman Dyson first proposed what has come to be known as a Dyson sphere in a 1960 paper in Science. It is a shell structure that would completely surround a star, built from dissembled planetary material in a solar system while requiring a great deal of energy. (The starship Enterprise encountered a Dyson Sphere in the sixth season of “Star Trek: The Next Generation.”) The aim is to capture all of the star’s energy for use by an advanced civilization.

Dyson calculated that such a spherical shell could be built with all the material in the solar system—essentially the mass of Jupiter—at twice the distance of Earth from the sun. Depending on its density, the shell would be a few meters thick.

Dyson believed that “…barring accidents, Malthusian pressures will ultimately drive an intelligent species to adopt some such efficient exploration of its available resources.” Such a shell in the cosmos would be a visibly dark object to us; but it would heat up and emit infrared radiation into space.

But a solid Dyson sphere around a single star would, though rigid, be unstable against gravitational forces and break apart. Objects inside the shell would feel no net gravitational force from the shell—a result known as Newton’s Shell Theorem—and so the star would drift under any slight perturbation in the shell’s mass, any deviation from perfect spherical symmetry.

The shell would then feel asymmetric gravitational forces from the drifting star and experience stress forces that could well break it apart. Masses close to the shell but outside it would also create differing forces on the shell. As a consequence, sci-fi writers and astrophysicists have considered partial shell pieces or a patchwork surrounding a star as a realistic Dyson sphere.

Similarly, a rigid ring around a star or planet, as in Larry Niven’s “Ringworld” series of novels, is also unstable, as it would drift under any slight gravitational differences and collide with the star. So McInnes considered a restricted three-body problem where two equal masses orbit each other circularly with a uniform ring of infinitesimal mass rotating in their orbital plane. The ring could enclose both masses, just one or none.

Unlike the full three-body problem, which has no analytic solution, “it’s an interesting problem of orbital dynamics in itself,” McInnes said. “Understanding the stability of such structures connects to SETI [Search for Extraterrestrial Intelligence] research.” McInnes also investigated a shell-restricted three-body problem with the shell also of infinitesimal mass, again with the shell enclosing two masses, one or none.

For the restricted ring, McInnes found that there are seven equilibrium points in the orbital plane of the dual masses, on which, if the ring’s center were placed, it would stay and not experience stresses, akin to the three stable Lagrange points where a small mass can reside permanently for the two-body problem. (For example, the James Webb Space Telescope resides at a solar orbiting Lagrange point 1.5 Mkm past Earth on the sun-Earth line.) The ring’s center would need to avoid lying on two circles McInnes calls “collision sets,” where—if placed on any point there—it would be in contact with one of the two masses.

Of the equilibrium points where the center of the ring could lie, one has the ring enclosing both masses, two of the points enclose one mass, and four enclose neither of the masses. Of the four enclosing no rings, two lie on a line connecting the mass centers and two (“triangular points”) reside on a line orthogonal to this line that goes through the center between them; their precise location depends on the ring radius. Thus, five equilibria lie on the line connecting the masses, and two perpendicular to that line.

McInnes restricted this research to a planar ring (in the plane of the circularly orbiting masses) but says it can be shown that a vertical ring, normal to the plane, can also generate equilibria. For example, one such point is a vertical ring with its center at the midpoint between the two masses.

For a Dyson-like hollow sphere of infinitesimally small mass, the shell-restricted three-body problem reveals similar equilibria. A shell can be envisioned as a connected series of rings with the same radius around the same point, and Newton’s Shell Theorem can be invoked to simplify the problem—a mass outside the shell acts gravitationally with the shell as if the shell’s mass were all at its center. For a shell enclosing both masses, the shell is not influenced by either mass, and the center of the shell can be put at any point where the two masses are both enclosed by the shell.

However, this is an unstable equilibrium configuration, since the shell feels no forces from the masses and so is free to drift relative to the two masses and will eventually collide with them.

If the shell encloses neither mass, Newton’s Shell Theorem implies that the shell can be considered a point mass at its center, and the situation reduces to the classical restricted three-body problem. McInnes finds there are seven equilibrium points where the shell can be centered, but the only positionally stable configuration is when it encloses the smaller of the two star masses. (If the shell encloses one mass, it feels no gravitational force from that object, but acts as a point mass to the other; the mass inside the shell will orbit around the center of mass of the two stars.)

Here the collision sets are spheres, not rings, and indicate where a sphere’s center cannot be placed without contact with a mass. McInnes’s mathematics shows that “a Dyson sphere can therefore in principle be in a stable equilibrium configuration in a binary system if the secondary mass has a radius of order half that of the primary mass,” assuming the stars have the same density.

These results can aid the search for extraterrestrial intelligence, McInnes said, “If we can understand when such structures can be stable, then this could potentially help direct future SETI surveys.”

An important technosignature would be one bright star orbiting in tandem with an object showing a strong infrared excess. Shells around a sun-exoplanet pair or an exoplanet-exoplanet pair could also be possible. A nested set of Dyson spheres is also a feasible geometry.

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