# How do you calculate shift in argument of periapsis for a not instantaneous burn assuming you're starting in circular orbit?

Most times we assume that burns are instantaneous, in this case if you burn (without a radial component) at the periapsis or apoapsis there is no shift in argument.

Let's say the engine is weak and it takes a long time to change orbit, the spacecraft would not have an instantaneous burn, in that case the argument of periapsis will shift but how do you calculate how much it shifts?

• It's a good question. 1. Of course one can always calculate the results of any complex propulsive maneuver numerically. but I think that you are asking for a set of equations? 2. "in this case(if you burn at the periapsis or apoapsis) there is no shift in argument" Is that always true, or only true for thrust in certain directions? – uhoh Jan 12 at 0:29
• I assume that you have no radial component of thrust. Sorry, Should've clarified. – alan Jan 12 at 0:52
• thanks, I've added that back into the question, feel free to edit further. – uhoh Jan 12 at 1:04