It’s an arbitrary convention. We could have equally well chosen a convention in which a left hand rule was valid. (Really a whole bunch of such conventions)
In the Newtonian 2-point model gravity is a purely radial force and so conserves angular momentum, which means that velocity remains in one plane. If the bodies are extended objects, then you can get things like spin-orbit coupling which can lead to orbits not being perfectly planar if the rotation axes aren’t aligned with the initial angular momentum axis. If there are multiple bodies then trajectories can be and usually will be at least somewhat non-planar, though energy losses without corresponding angular momentum losses can drive a system toward a more planar state. Zero dimensions would only be possible if both the net force and initial velocity were zero, which can’t happen if gravity is the only applicable force and there are two distinct points. In general relativity gravity isn’t really a force and isn’t always radial, and orbits need not always be planar and usually aren’t closed curves anyway. Though again, many systems will tend to approach a more planar state.
Whichever coordinate system we choose, the charge will keep flowing in the same “arbitrary” direction, relative to the magnetic field. This is the conundrum we seek to explain; why does it not go the other way? What is so special about this way?
If I’m a negligibly small body, gravitating toward a ~stationary larger body, capture in a ~stable orbit subtracts exactly one dimension from my available “linear velocity”, in the sense that, maybe the other two components are fixed [over a certain period] now, but exactly one component must go to zero.
Ptolemaically, this looks like the ~stationary larger body, dragging the rest of spacetime with it in a 2-D fixed velocity [that is, fixed over the orbit’s period] around me—with exactly one dimension, the one we see as ~Polaris vs ~anti-Polaris, fixed in place, relative to the me/larger-body system. That is, the universe begins rotating around me cylindrically. The major diameter and minor diameter of the cylinder are dependent on the linear velocity I entered at [ adding in my mass and the mass of the heavy body, you get the period ] - but, assuming the larger body is stationary, nothing else about my fate in the capturing orbit appears dependent on anything else about my previous history—the rest is ~erased—even though generally-relative spacetime doesn’t seem to preclude more, or fewer, dependencies surviving. My question is, why is this? Why don’t more, or fewer, dependencies on my past momenta [“angular” or otherwise] survive?
It’s an arbitrary convention. We could have equally well chosen a convention in which a left hand rule was valid. (Really a whole bunch of such conventions)
In the Newtonian 2-point model gravity is a purely radial force and so conserves angular momentum, which means that velocity remains in one plane. If the bodies are extended objects, then you can get things like spin-orbit coupling which can lead to orbits not being perfectly planar if the rotation axes aren’t aligned with the initial angular momentum axis.
If there are multiple bodies then trajectories can be and usually will be at least somewhat non-planar, though energy losses without corresponding angular momentum losses can drive a system toward a more planar state.
Zero dimensions would only be possible if both the net force and initial velocity were zero, which can’t happen if gravity is the only applicable force and there are two distinct points.
In general relativity gravity isn’t really a force and isn’t always radial, and orbits need not always be planar and usually aren’t closed curves anyway. Though again, many systems will tend to approach a more planar state.
Whichever coordinate system we choose, the charge will keep flowing in the same “arbitrary” direction, relative to the magnetic field. This is the conundrum we seek to explain; why does it not go the other way? What is so special about this way?
If I’m a negligibly small body, gravitating toward a ~stationary larger body, capture in a ~stable orbit subtracts exactly one dimension from my available “linear velocity”, in the sense that, maybe the other two components are fixed [over a certain period] now, but exactly one component must go to zero.
Ptolemaically, this looks like the ~stationary larger body, dragging the rest of spacetime with it in a 2-D fixed velocity [that is, fixed over the orbit’s period] around me—with exactly one dimension, the one we see as ~Polaris vs ~anti-Polaris, fixed in place, relative to the me/larger-body system. That is, the universe begins rotating around me cylindrically. The major diameter and minor diameter of the cylinder are dependent on the linear velocity I entered at [ adding in my mass and the mass of the heavy body, you get the period ] - but, assuming the larger body is stationary, nothing else about my fate in the capturing orbit appears dependent on anything else about my previous history—the rest is ~erased—even though generally-relative spacetime doesn’t seem to preclude more, or fewer, dependencies surviving. My question is, why is this? Why don’t more, or fewer, dependencies on my past momenta [“angular” or otherwise] survive?