This is pure speculation, but my little kid brain always assumed they were asteroids left over from the (possibly apocryphal) earlier time when the Cygnus had been hit by asteroids. Reinhardt alludes to this early on as the event which made the original human crew abandon ship.
The red-orange sphere looks quite similar to the asteroids that appear later in the movie. It's got what look like clamps holding it in place, like it has a lot of mass. I have no idea why they would be studying one in this manner, but it's plausible.
The blue one on the other hand...There are no clamps, it's a hemisphere, rather than a full sphere. Maybe some kind of force field? Holographic projection? We know there is some kind of anti-gravity device on the Cygnus, but it's never really explained, so it could be a part of that?