In response to a question on STO’s sub-reddit, I started wondering about the mass of the dyson spheres in Star Trek Online. I love doing these paper-and-pencil what-ifs, and the sphere is one of my favorite zones in STO for look and feel. Here was my response to the original poster’s question about how the Solanae sphere jumping a few light years out from Iconia would affect the Iconia system …
There are too many unknowns to come up with a good guess at the sphere shell’s mass, but I assume it’s a fraction of its central star’s mass and wouldn’t contribute much beyond normal stellar-scale gravitational pull. So it’s no different than any other normal star a few light years away, having minimal gravitational impact.
An interesting consequence of the sphere jumping is having a clear way measure the speed of gravitational wave propagation. Barring some kind of Trekverse subspace effect, that’s theoretically at the speed of light, so it will take Iconia two years to feel even that tiny gravitational shift after the sphere jumped to two light years away.
If the sphere were constructed from the star’s original planets and we use our solar system as a base, then it’s no more than roughly 1/750th the mass of its star (based on planetary mass but not including asteroids and Oort cloud.) However, we do have some observations about the sphere to consider. And now, some math-based guessing …
Watching the Enterprise fly through the Jenolan sphere’s airlock in Relics, it looks like the sphere is several kilometers thick since the airlock’s inner and outer doors appear to be flush with the inner and outer surfaces. The gash in the Solonae sphere’s Wasteland zone looks much deeper, at least tens of kilometers thick. In either case, it’s thickness is much smaller than its radius, so we can approximate the shell’s volume as 4 * pi * r2 * t, where r radius (1.5E11 m, i.e., 1 AU) >> t thickness (1E4 to 1E5 m, i.e., 10 – 100 km).
That means it’s between 2.3E26 and 2.3E27 cubic meters (m3). The gash looks starship-like inside, and starships–like witches–float, e.g., Nandi at Risa. It may not be solid but may use superdense matter like neutronium for it shell, so let’s wildly guess at effective densities between water (1000 kg/m3) and iron (8000 kg/m3). To get a range, let’s use a lighter, thinner shell (1/2 as dense as water, i.e. like like a naval ship’s displacement) versus a thicker solid iron shell to get 1.2E28 kg to 1.8E31 kg.
For scale, the sun’s mass is roughly 2E30 kg which means our range is 1/100 to 10 times the mass of a Sol-type star. So, I could see the sphere’s mass being roughly the same magnitude as its star given a superdense impenetrable shell much like the doomsday device and vast energies from capturing the stellar output for force fields, integrity fields, artificial gravity, and active stabilization. It’s still measurable in normal stellar masses and not, say, galactic core black hole masses. Two solar masses over two light years is still not out of the ordinary gravitationally, but it points to the possibility that the sphere was constructed not from the mass of a solitary star’s planets but from one of the stars in a binary system.
Furthermore, if the shell were constructed only from the planetary mass around a Sol-type star, then its effective density is pretty low to absurdly low. With our solar system’s total planetary mass of roughly 3E27 kg and that volume between 2.3E26 and 2.3E27 m^3, the shell’s density would be 1.1 to 11 kg/m^3 or about 1/100 to 1/1000 the density of water. For reference, styrofoam is 40 kg/m^3 or about 1/25 the density of water. While anything is possible, the Solanae dyson sphere *shell* being 4 to 40 times less dense than sytrofoam is more than my brain can handle.
I wish they’d used a ringworld instead of a dyson sphere so my Kzinti–er, Ferasan–Captain would feel more at home exploring it.