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Easiest way is smart way. Go high for ~2500, switch direction for another 2500(?) at Ap, get back to circular with 2500 again at Pe. Use Jool+Tylo gravity underway for even more savings. Rather less than 10ooo m/s from LKO. It really depends on contract orbit as well of course. Retrograde at Moho level or retrograde at Eeloo level?
Those are very approximate numbers. The higher you go, the cheaper it will be and the more time take.
I'm confused XD
At higher altitudes above Sun, orbital speed is much lower. That's why reversing there will cost much less! Getting higher is rather cheap (compared to getting lower).
Google also Bi-elliptical transfers.
You sure do know Mun and Minmus by now.
To reverse Kerbin orbit on low orbit, you will need 2x2290m/s
To reverse Kerbin orbit at Mun level, you will need 2x542.5m/s
To reverse Kerbin orbit at Minmus level, you will need 2x274.1m/s
To get to Mun level, you need 860m/s
To get to Minmus level you need 930m/s
Even if you don't do aerobraking and have to do the same transfer burn=slow down burn returning back to LKO, simple math can show you
2x2290 > (2*542.5+2*860)
4580 > 2805
those are simplified numbers, as you won't reach full orbital velocity (542.5) in the first place "jumping" up. You would have to circulize for that first! So reverse at Mun and Minmus level jumping from LKO is actually even cheaper - 200+m/s more saved at Mun and a bit less at Minmus
See the difference? That's how orbital mechanics work. Orbital velocity isn't linear. The closer to the gravity well, the quicker it grows. The further you go, the less energy you need to go even further. See the difference between Mun and Minmus transfer burns (860 vs. 930)? Almost nothing. While their altitude above Kerbin differs 4 TIMES!
Now the same (again, simplified) math with Minmus
2x2290 > (2*274.1+2*930)
4580 > 2408.2
So 4580 > 2805 > 2408.2
Or 180° reverse is more expensive on LKO than it is at Mun and that one is more expensive than it would be at Minmus.
In case of Kerbin you can save ~800m/s more using aerobraking on return. In solar orbit that is not an option. Encountering Jool or Laythe while doing so - at the right spot, it may be again. In addition to the huge gravity assist you get there for free as well.
KSP is about hard space turned easy challenges. Knowledge and creativity. But it is also sandbox. Don't like, don't do.
You need the same energy to reach the same changes! Orbit is accumulated energy (during launch). To balance 10t you need another 10t. No way around it. Straight or square
There is no leverage on the same orbit. You go for it higher where speeds are slower like described above.
In reality (also KSP) there may be slight differences between retrograde and normal approach. Due to burn times needed. Both will introduce bad drifts as you can't have perfect impulse burn. Drifts in different planes. One correction may be easier than the other one, not sure.
I prefer retrograde, it is cleaner for staying equatorial and KSP engines are strong enough in most cases to not fall down or touch atmosphere/some surface (or you should be smart enough to avoid that risk). Also I would never do full retrograde on LKO. Just launch West.
Solar is different. You have to be even smarter there due to higher orbital speeds and you not launching from the Sun.
It’s like launching a satellite in the opposite direction of Kerbins rotation. You have to have the normal delta V for an orbit plus you have to add the speed of Kerbins rotation.
Now imagine the speed of the planet going around the Star. You want to go the opposite way that the planet is already moving then it is going to take a huge amount of energy. You have to add that speed to the delta V needed. A huge difference.
I hope I am making sense. If not just say so.
Edit: It’s like you are already traveling around the Star very fast in one direction just because you are on a planet. Now you want to turn around and go the exact opposite direction.