If you attend a lecture on physics, then be sure to doubt the tired metaphor of a bowling ball distorting a membrane that is meant to illustrate Einstein's idea of gravity. The truth is that a stationary field of gravity does not curve space at all, since that sort of curvature only shows in "planes" that are more or less aligned with time. (I fail to recall which one of the lectures made this error.) Especially do not be confused by an appeal to gravity and centrifugal force in order to explain the very same. And understand that spacial curvature by itself affects all moving trajectories in a way that does not match the ordinary understanding of gravity.
A proper understanding of the principle of general covariance and all of its corollaries allows you to calculate this by way of scale diagrams - very simply compared to other coordinate-based methods. I think this is teachable, along with a major portion of classical physics, to motivated novices in three to five hours of dialog over diagrams drawn on a scratch pad.
I challenge you to diagram a perfect tachyon, infinitely fast, and verify that it is not deflected or slowed at all by stationary fields, nor does it deflect stationary objects. Show that perfect tachyons repel each other unless their path is perpendicular - pure spacial curvature. Show that time-like trajectories are decelerated by a perfect tachyon unless they are stationary or perpendicular to the purely spacial path of the tachyon. You can do this with no strain if you truly understand general covariance.
Michael J. Burns