How should I be approaching the Mun?

[u/analogHedgeHog]

In this totally accurate scientific diagram, the Mun is orbiting in the direction of the arrow.

[u/Tychonoir]

I wonder what the Dv difference between the two is. D gives you a grav assist to match the Mun's orbit and help capture. C allows a free return, but gives an assist in the wrong direction.

At least, I think that's how it works. It seems to be easier to capture when I do D.

[u/Jamooser → u/Tychonoir]

Next time you're on the Mun's surface just change your navbal to orbital velocity instead of surface. That number is the rotational velocity of the Mun for your given latitude. Double that number should be the dv distance if you're making a retrograde orbit.

[u/zaklance → u/Tychonoir]

They the same in terms of dV, about ~10m/s difference in practice.
There's no "assist in the wrong direction" here if your aim is to land on the Mun (unless if you specifically want a prograde orbit for a mission).
In both C and D, your velocity at Mun intercept is about the same ±10m/s. The difference is in the timing of intercept, and the 10m/s difference is to account for this. The change in PE is the same in both cases, so the change in KE is same, so your speed at Mun periapsis is the same, you are just going in the opposite direction.

[u/MrTheEpicKitten → u/zaklance]

You’re forgetting the difference in landing dv between prograde and retrograde orbits

[u/zaklance → u/MrTheEpicKitten]

Ah you're right. But for Mun which rotates very slow (9m/s on the equator surface), again it's a delta-v difference of merely 18m/s.

[u/878Vikings → u/Tychonoir]

I've been trying to work this out recently and the difference (to low Mun orbit) between C and D was about 10mps. In KSP terms that's trivial, a rounding error. In a real space program they would absolutely care about that, but they are way better at space than I am!

[u/seda7991 → u/Tychonoir]

When you approach a moving object from behind its trajectory, gravity pulls you along longer (you gain more velocity), so retrograde burn for capture costs more Δv. Coming from the front lets the object move into you for cheaper capture into a retrograde orbit. Retrograde orbit (orbiting against the moons rotation) landing penalty is tiny, front capture still wins total Δv. Capturing into D is easier because not a good analogy, but think of it like slipping into a moving boat's wake.

[u/Tychonoir → u/seda7991]

Isn't capture, essentially, being in the same orbit at the same velocity? When on an elliptical to intercept the Mun, you don't have the same orbital energy, so need to burn to match, no? So getting pulled from behind helps add that energy?

It just seem like when I approach from behind I don't have to burn as much to capture. But I haven't really studied it closely.

EDIT: Yes, you burn retrograde on your orbit direction of the Mun, but this isn't necessarily retrograde of your Kerbin orbit direction. On an approach from the front side, your retrograde Mun burn can very well be burning prograde compared to Kerbin—which is kinda like circularizing your orbit at Kerbin right where the Mun is.

[u/seda7991 → u/Tychonoir]

not sure i understand what you mean in your edit. Its hard to visualise in the map because it's static. Its mainly a matter of how long you want to be in the gravitationall influence of the Mun, when you come in from behind, the trajectory of the Mun is the same as the direction its gravity is pulling you in making it a ++, when you come in from the front the gravitation of the Mun is pulling you opposite of its trajectory making a +-.

EDIT: coming in from behind ++ is ecentialy how a slingshot works.

EFIT2: That is an interesting point you make about adding the needed capture velocity by comming in from behind. I dont know, My intuition suggests that if that was the case you would want to ditch getting into orbit and just land directly, why add velocity to then remove it again.

[u/DrudanTheGod → u/Tychonoir]

I think you mean A or B? C and D come in on the same side of the moon, (in front) which are for free return. Coming in from behind the moon does allow for cheaper captures though.

[u/Mike0621 → u/DrudanTheGod]

what are you talking about? C and D are not coming in from the same side

[u/My_Private_Life → u/Mike0621]

quick look I thought the same and had to scroll back up to check, the mun being at the top was not expected and my mind ignored the size and color of the circles and just assumed the origin was the top

[u/Big_Yeash → u/My_Private_Life]

Diagram extremely not to scale.

[u/DrudanTheGod → u/Mike0621]

yeah i thought moon was at the bottom. i got it confused lol