Here is a visual: the Enterprise drops out of warp and seamlessly takes up a standard orbit around an M-class planet. The Enterprise got to the planet from some other planet using its warp-drive, a feature which apparently allowed it to exceed the speed of light in normal space. Regardless of any problems inherent in a theoretical faster-than-light drive, in this scenario it is likely that the Enterprise violated the laws of physics by not conserving angular momentum. There was no kind of maneuvering present to avoid such consequences.
The problem exists for all speculated types of faster-than-light travel, including hyper-drives, slipstream-drives, and inter-dimensional-drives.
The conservation of angular momentum is indicated by the cross-products:
R1 x P1 = R2 x P2, where R is a vector (or tensor) radius, and P is a vector (or tensor) linear momentum.
However, the situation is not so simple as the equation implies, since in real-world situations these vectors have to be treated as tensors (matrices instead of vectors,) not ordinary cross-products, unless the starship has a starting position in interstellar space away from all major bodies of mass. Remember, all spatial trajectories are actually orbits:
· We assume that that travel is within a single galaxy, so the first component of angular momentum would be that of a star in orbit around the center of a galaxy.
· The second component would be the orbit of a planet around the star. The orbit could be inclined to the stellar plane and possibly even retrograde.
· The third component would be the spin of a planet, which could have any orientation relative to its orbital plane.
· The fourth component would be the angular momentum of the starship itself, in orbit around the planet.
It should be noted that the planetary plane of individual stars in a galaxy is not related to stars’ orbital planes in the galaxy. Planetary systems can have any random orientation with respect to the galactic plane.
In science fiction, writers routinely ignore the problems of physics and essentially just plot a course from one star to another star. However, the details associated with the conservation of angular momentum are not trivial, since all the actual maneuvering to achieve the desired orbit could consume enormous amounts of energy.
Writers also ignore the following collateral problems:
· Habitable planets might have natural moons, which would have to be factored in.
· Such planets might have small satellites and space stations.
· Such planets might also have significant traffic generated by other starships coming and going.
· Depending on the mechanics of a particular drive system, there could be accuracy problems that increase with distance traveled, which could make it dangerous to drop into normal space too close to the destination planet.
The Star Trek universe features stable (and unstable) wormholes that allow starships to pass through intact, thus making wormholes shortcut pathways through space. It is not clear whether any kind of wormhole would actually allow this, and it is also not clear whether such a wormhole would help conserve angular momentum.
The Stargate universe defines its wormholes differently. Starships and travelers cannot simple pass through intact, but must be disassembled into energy first, and reassembled at the destination stargate. This is more in keeping with the speculation that wormholes could only contain information in chaotic states, and that, despite the chaos caused by turbulence, sufficient information is present to reconstruct any disassembled matter to its original state.
For this kind of a wormhole, the conservation of angular momentum would be just another component of the chaos, so travelers could arrive at a destination stargate with no ill effects. However, stargates must be delivered to planets by starships which travel through hyperspace, so there is still a problem of unresolved conservation of angular momentum.
Dr. Who’s TARDIS seems to be a special case. It dematerializes from ordinary space without turning it and its occupants into energy. Yet, it can rematerialize anywhere in space and time, usually making precise landings on some exotic location. This would have to involve unimaginably accurate calculations. Still, I fail to see how the conservation of angular momentum is ever applied.
Time machines, in general, have problems with spatial references, besides the usual problems with paradoxes. Due to all the combined motion through space of celestial bodies, a given location can have a markedly different spatial reference in past or future times.