An interesting thing that caught my attention before is how the space shuttle was oriented when it was in orbit (feels kinda sad to say "was" instead of "is"...). Maybe I'm not remembering right, or maybe the source was wrong, but I recall an astronaut mentioning that the tail end of the shuttle was pointed towards Earth, because in this posture, the shuttle was more stable from rotations under gravity's influence. He then mentioned something about a gravitational torque, which clearly must've been a Newtonian term. That... Seems very odd, but regardless of my inability to remember the details, it does have me wondering about what happens to, say, the space shuttle when it's orbiting. Now, in the context of GR, orbits are the result of geodesics - lines that are locally "straight," in that the derivative of a transposed vector is always zero along a geodesic. That would seem to imply, at least in the point-approximation case, that if the shuttle's nose was aligned with the velocity vector (with the Earth's center as the center of the coordinate system, of course), then it would stay aligned with the velocity vector through the entire orbit. Likewise if the tail, right wingtip, or any other arbitrary point was lined up with the velocity vector, it would stay that way through the entire orbit (the sidereal rotation period of the craft would be equal to the sidereal rotation period of its orbit). But perhaps that's a naive over-simplification? The back of my mind says that the fact that an orbit slightly closer to the Earth has a slightly smaller circumference means that there might be some rotational effect, since whichever end of the craft is closer to the Earth is travelling a smaller path. I really can't think of how this would alter the results of a point-approximation, though. Placing this in relativity instead of classic because of the appeal to geodesics. Theoretically, Newtonian should give the same result(?), but the only argument I can think of is the geodesic one.