New Ultradense Planet Found; Astronomers Baffled

[eppur_se_muova]

7. Density in this situation is calc'd same as for a solid sphere ...

that is, mass (measurements involving celestial mechanics treat this as a point mass) per unit volume, with the *empty* volume of the hollow sphere included. So any hollow object is going to have a low overall density. It might be made of very dense material, but there's no way to know that without more info than orbital characteristics. A space probe orbiting a hollow planet/Dyson sphere would spot something wrong right away (orbit too big for a given velocity); one orbiting a dense planet, likewise (orbit too small). But in either case it would be the overall density that would be most apparent, assuming at least approximately spherical symmetry.

A Dyson sphere would be mechanically supported (think a huge geodesic dome) so not dependent on photon pressure for support, unlike a statite.