Originally posted by twhitehead
I still don't understand what your triangular thrust was. Are you saying you head north west then turn south west, or are you talking about vertical triangles?
When you say 'vector of thrust' are you saying you must thrust in only one direction, and if so are we talking about one direction relative to the surface of the earth or relative to space?
Picture the Earth, in this case no atmosphere to muck things up. You are on the surface or on top of a mountain, and you draw a representation of a triangle where one leg is where you are standing and on the opposite side of the globe is another mountain which is leg #3. Leg #2 is pointing out into space and as close to equilateral as possible so if you drew a line directly down from leg #2 it would bisect Earth and go directly to the center of Earth if it was drawn long enough.
I hope that is clear.
Then you take off following the path of leg 1 and accelerate halfway through leg one at one g or whatever, maybe it takes 2 g's to overcome gravity, but halfway, you switch the engines around 180 degrees and thrust negative to slow you down to get to point 2, the point furthest from Earth, then you turn around 120 degrees so the engine is pointed back into space, accelerate at the same rate on leg #2 going back to Earth but aiming at the opposite end of the globe. So you accelerate at your 2 g's or so halfway through THAT leg the do the same maneuver reversing the thrust to slow down at the same g rate so when you get to the top of the mountain you land with zero velocity there.
Does that clear up the triangle path? I said on top of a mountain to get the triangles out far enough not to touch ground early. If for instance, you made the triangle more obtuse say with 40 degrees on the outbound legs you would be cutting through Earth before you got up in space. So I thought 60 degrees would be the minimum angle to undertake such a journey. It could be 65 degrees, don't know for sure.
For instance, if you were not sure and wanted to make totally sure, you could just go tangent to a line linking the apex of the triangle to Earth's center, parallel to that line up then instead of a triangular trip you would basically travel on three edges of a box where you go each leg half way, decelerate the rest of that leg, now do only a 90 degree turn now going perpendicular to the line of the previous triangle apex to Earth, do the same thing, then turn 90 degrees again for the last leg, do the same thing, halfway accelerate, halfway decelerate and end up in the same spot with zero velocity. Does that make sense?