There was an ISS set built on the real ISS, but it needed to be disassembled after two hours due to the fire hazard. Unfortunately, that version can't be built on the ground: "It's a solid model but I believe it can't bear its own weight under gravity,"
> Made up of hundreds of bricks, the model was launched in partially-preassembled "chunks" to help make up for the difficulties working with very small pieces in microgravity. The space station could not be launched fully-assembled, because like the real orbiting outpost, it could only be built in space.
> The LEGO station's time fully assembled was short lived however. Due to the flammability hazards, the toy bricks could only be exposed to the open cabin air for two hours.
No. The orbital plane must intersect the (bary)center of Earth.
If you took that model and placed it to the right of ISS, with matching altitude and velocity vectors, then half the orbital period later, you'd find it somewhere to the left of the station.
If you want to keep two things close together in orbit for a while without active stationkeeping, your best bet is placing one ahead or behind of the other. Though in real life, they'll eventually drift their separate ways too, due to lots of small influences like solar pressure, residual air drag, gravitational pull of other bodies in the system, etc.
Wouldn't there be considerable slipstream from the trace atmosphere? Aft, slightly higher than the stations center of mass there should be a point were the slower angular speed of the minimally higher orbit would cancel out with the slipstream effect, until the next stationkeeping burn. I wonder how much it would start spinning from the uneven application of trace atmosphere in that time.
Might make a fun public experiment, try getting "the internet" to voice their predictions, kind of like everybody was commenting on the color of the dress. In any case I fully expect a kit to eventually make it up there but I doubt that it will see any EVA.
A 2x4(x1) lego brick (3001) weighs around 2.32 grams. Inflate it to 3 x 864 pieces and a good estimate is 2kg but based on the visible elements I'm betting more like 1kg.
Like, those 2x2 tiles (3068) are 0.5g each, those 8x3 flags (35252) for some of the PV panels are 2.75g each etc.