When you don’t know something, there are two ways to go. Figure out what you don’t know, usually some reading handles this pretty well. Or, make up something to fill in your gaps in knowledge. This idea of a “straight line” across spacetime, is an example of the second one. As for “gravity-corrected”, my understanding is, to do something like land a rover on Mars, you do need to consider relativity, so, you’re on the right track there.