Well I am pretty sure playing KSP will give one a much deeper "feel" for orbital mechanics. The linked page contains all the math if you actually want to calculate the orbits optimally. I think i will stick with mechjeb. :)

Yeah, KSP is great for getting an intuitive feeling for what one would have to do to navigate space successfully – at least to the point where one would be able to identify grossly inefficient behavior immediately and be able to do something that’s somewhat effective at getting where you want to go (though probably not most effective). I think that’s pretty awesome, mostly because orbital mechanics is not something we think of being able to have an intuitive understanding of, at least if you don’t have the requisite math background (and maybe even then not).

With KSP, at least if you play it long enough, you really do gain a rough intuitive understanding, even if you do not ever calculate anything. But one should probably also mention that it is time-inefficient and, well, not exactly rigorous. (Both of those things don’t matter that much since it’s just a game.)

Obviously you can also break out the calculator and approach it that way (but I don’t think that’s necessary, except maybe when it comes to interplanetary stuff and getting the right angles). The game is luckily easy enough to brute force things and when you are stuck around KSP’s Mars equivalent with little fuel you can still always fiddle around with maneuver nodes forever to see if there is some way out – and then be forced to learn to be efficient that way.

Solving things analytically is overrated and only possible in rare circumstances. Everything I need to solve orbital mechanics is F = Gm1m2/r^2

Relevant xkcd:

https://xkcd.com/1356/