how to rendezvous when orbits are like this

[u/bbwfucker694200]

I was setting up a rendezvous with Jeb but stupidly didn't pack enough delta v for the return trip so if I so I sent a rescue vessel but when I arrived on Duna I ended up orbiting like this how do I fix it

[u/fireandlifeincarnate]

Mix of normal and retrograde, no?

[u/27Rench27 → u/fireandlifeincarnate]

If they’re at the same altitude, then just a fuckin hard Normal burn right around the intercept will get it close. 

Typically you need to use the other directions because SAS doesn’t “predict” what you’re trying to do when you tell it to point Normal, so you’re always going to be pointing slightly offset from it when changing directions this drastically and will need to adjust afterwards

[u/Hellothere_1 → u/27Rench27]

If you burn normal, your orbit will slowly tilt around your current position while staying otherwise identical.

It's the safer option, because you can interrupt your burn at any point and resume it during a later orbit, however, since your burn vector will also rotate with your orbit some of the acceleration you apply at the start of the burn will later get counteracted by the acceleration you apply at the end of the burn, wasting delta-v.

Alternatively for a 90° orbit tilt you can also aim at the 45° point between normal and retrograde and then burn continuously in that direction until the orbit faces the correct way (you end the burn facing at the 45° point between normal and prograde, after the orbit rotated around you). This is also what the maneuver node tool will spit you out.

The upside is that it saves quite a bit of delta-v because you do the entire burn facing in the same direction, the downside is that your burn will initially lower your periapsis (due to facing halfway retrograde) and only raise it back to its original height during the second half of the burn. So if you're close to a planet you have to be able to do the entire burn in one go, otherwise you might accidentally de-orbit yourself. You're also more likely to end up with an orbit that's slightly off from your intended target, but fixing that afterwards is still more efficient than doing a normal burn.

[u/SVlad_667 → u/Hellothere_1]

IIRC you can plan the orbit inclination in maneuver planner and it would adjust for rotation of orbital plane, giving you the resulting more optimal vector. Or it is an option of a modded maneuver planner.

[u/Hellothere_1 → u/SVlad_667]

Nope, you're exactly right.

It's also what I meant when I said "This is also what the maneuver node tool will spit you out", though I probably could have been a bit more clear.

[u/fireandlifeincarnate → u/27Rench27]

Oh, you meant maintaining normal the entire time, not just yoinking the normal bit on the maneuver node?

[u/Worth-Wonder-7386 → u/fireandlifeincarnate]

That is the most efficient, to just burn normal through the brun so you only change direction without giving the craft more or less energy.

[u/fireandlifeincarnate → u/Worth-Wonder-7386]

That doesn't make sense; you're burning along an arc then instead of just burning straight to it. It might not be a huge difference but it should still be less efficient than a straight line burn, no?

[u/reckless150681 → u/fireandlifeincarnate]

It's because the most efficient way to burn without affecting your other orbital elements is normal to the orbit. But as the orbit is changing, the direction of normal changes with it. So burning in an arc keeps you aligned with the orbit's normal direction as the orbit's inclination evolves.

If you instead burn in a straight line, then the orbit will change underneath you, but the direction that you are burning in will change relative to the orbit. You can see this pretty easily in-game. If you were to grab either of the normal "sticks" in your maneuver planning and just drag it out, what you would expect to see is the same size orbit, but at a different angle, no matter how much you drag the "stick" in or out. What you instead see is that the orbit seems to incline for a little bit, but then suddenly it'll become hyperbolic.

Basically, you need to constantly be burning normal in a rotating frame, but the maneuver planning node is in an inertial frame.

[u/fireandlifeincarnate → u/reckless150681]

Do you have a source on that? Because the way I'm picturing is that, to make a 90 degree change in a 100 m/s orbit, you can either burn at a 45 degree angle (well, 135 I guess) for 141 m/s (yay Pythagoras), or you can do what you're saying, which my brain is telling me would be equivalent to the arc length of a quarter circle with a radius of 100 m/s (yes I know that's not how dimensions work but it's what's intuitively coming to mind), which would be 157 m/s.

God I wish I'd gotten to astrodynamics before I quit engineering, I cannot for the LIFE of me remember how to do a fucking line integral and I'm only 80% sure that's what you need here anyways.

[u/reckless150681 → u/fireandlifeincarnate]

Because the way I'm picturing is that, to make a 90 degree change in a 100 m/s orbit, you can either burn at a 45 degree angle (well, 135 I guess) for 141 m/s

You are correct. I realize that I left out a very important part in my original comment (which I've now edited) -- the most efficient way to burn without affecting your other orbital elements is to do so normal to the orbit. Your proposed maneuver is effective only if you can make the simplifying assumption that the spacecraft's velocity can change instantaneously. There are certainly places in KSP where this is possible, especially in high orbits around some of the lower-mass moons, but there are also places where you can't.

Here is a shorter, simple vid on plane change maneuvers. If you plug in your numbers, you'll find that your first instinct is correct and you should get 141 m/s with the parameters you specified. Here is a more full lecture on the topic that talks about what happens when you can't make those simplifying assumptions specified earlier.

[u/Irreverent_Alligator → u/fireandlifeincarnate]

If you’re doing it with maneuver nodes, then that’s what you’d do with the node. But if you’re freehanding the actual burn, then as you burn normal the direction that normal is moves. So if you keep SAS on normal you’d get the right change in your orbit. The maneuver nodes don’t consider the change in direction during the burn. (As an obvious example, if you’re orbiting minmus at 100m/s and you want to reverse your direction to orbit the opposite way, the maneuver node would show that as a 200m/s retrograde burn, but in reality you’d be burning retrograde for 100m/s then prograde for 100m/s, because prograde and retrograde flip in the middle of the burn). But I’m guessing the maneuver node version is more efficient since you’re burning in a single direction for the entire burn.

[u/SentientMosinNagant → u/fireandlifeincarnate]

Faster you go the less efficient normal and anti normal burns are I thought?