Comment Re: Incorrect options summary (Score 1) 59
Ok, I see where you are going wrong.
Under newtonian physics, a body remains at rest, or in motion at a constant speed in a straight line, except insofar as it is acted upon by a force.
The moment you thrust in a particular direction away from your direction of travel, that is the "acted upon by a force" - your direction changes.
The moment that thrust stops, the change in direction stops, and you revert to "in motion at a constant speed in a straight line".
Your thrust needs to be constant to fully change direction, until you have reached the new direction you want.
There wasn't enough fuel between Columbia and Soyuz to continually thrust enough to both end up going in the same direction.
Its the constant thrust that you are missing - newtonian physics dont help here because thats oriented around continuing in a straight line, whereas for this orbital change you need a curve, and that needs a constant force for the duration of the curve.