oberth effect

[Red Iron Crown]

I've read nearly all this forum and have seen a lot of really complicated and unpractical examples so here is my own actually useful example:

When you have mining and refueling station at Minmus orbit and want to continue for example to Jool. Than it is better to at first lower you periapsis to 71km near Kerbin and at this point start to thrust for Jool.

Why? Because while you need to spend some dV around 200m/s to lower your Pe then you get much faster at Pe(in order to get to Jool) and it means that gravity of Kerbin has shorter time to slow you down than it had for accelerating you when you've been going towards Pe and because difference in time is quite large you not only get back yours 200m/s but even more.

And that is Oberth Effect which explains why longer road(by distance) is actually shorter in terms of dV. Another Similar situation can be met when going from Layethe back to Kerbin

You're on the right track in observing that completing the burn at periapsis, when speed is greatest, results in less dV expenditure to complete the transfer. But your reasoning for why that is happening is not correct. It has nothing to do with Kerbin having less time to slow you down, it has everything to do with each m/s added to your speed adding more kinetic energy to your orbit than if you had done the burn at lower speed.