> you'll absorb the most power at exactly the time you don't want to be changing your momentum
Thanks for doing the math. But I'm still confused, I thought you do want to accelerate when near the sun, as that makes the far end of the orbit go further? Again, no math behind, just how it worked in KSP :)
Whoops, you're quite right. I was thinking that you wanted to add momentum when you were moving the slowest, but that's for when you want to get into a circular orbit (which is the opposite of what you're talking about).
The simplest way (imo) to think about the Oberth effect is "you want to maximize the amount of time you're falling inwards (i.e. speeding up) and minimize the amount of time shooting outwards (i.e. slowing down.)"
It doesn't just work with orbits and rockets and propellants, it works just as well with an oscillating weight on a spring that you flick with your fingers.
Thanks for doing the math. But I'm still confused, I thought you do want to accelerate when near the sun, as that makes the far end of the orbit go further? Again, no math behind, just how it worked in KSP :)