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In his recent video Apollo 10's Lunar Module Snoopy Is Lost In Space - Could We Bring it Home? Scott Manley uses some fancy supplemental techniques in KSP to simulate and explain a possible mission to capture Snoopy (Apollo 10 Lunar Module) "...and returning him safely to the Earth."

But at about 09:38 Manley surprisingly finds himself at a bit of a loss for words. This explanation says little more than "it takes less Delta V because you square it and so it takes less Delta V":

Now when you’re doing capture from deep space, you want to get down close to the Earth, because that way you’re actually using Earth’s gravity to reduce the amount of Delta V you need to perform the capture.

If Earth wasn’t there, you’d actually need more Delta V to match the orbit, because you fall down into it you get this square law where you’re adding your velocity squared, and… listen, it’s just a simple thing to do. You drop down into the gravity well and then you perform your burn there and then it becomes… it means you need less Delta V to perform this.

Question: Can someone help Scott Manley out and explain more clearly what it is that he's trying to explain?

cued at 09:38

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  • Sounds like it taught him the orbital mechanics apart from the vocabulary just fine. – Russell Borogove May 31 '19 at 06:13
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    Scott Manley studied Astrophysics. He definitely knows what he is talking about, he just doesn’t want to give a lengthy explanation that most people would not understand and make them just annoyed. – Hans May 31 '19 at 08:10
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    Possible duplicate of Oberth effect for Earth vehicles – Hans May 31 '19 at 08:19
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    I do not mean to be overly defensive here, but according to His bio on the B612 foundation homepage ”Scott spent a decade in academia studying astrophysics and computational physics at the University of Glasgow and Armagh Observatory where he focused on small bodies in the solar system and specifically the probabilities of collision.”, so he most definitely knows what he is talking about. – Hans May 31 '19 at 08:24
  • I am pretty sure this is about the Oberth Effect. It however is notoriously difficult to explain and wrap head around. I think the two big answers on that linked question explain it pretty good. A at least don’t think I can explain it in such a way that anyone else can understand it. – Hans May 31 '19 at 08:30
  • I have. I think this situation is about a combination of gravity assists and the oberth effect (which is specifically about maneuvers at higher velocities and close to planets). I however don’t really have the rime right now to write a good answer for that. – Hans May 31 '19 at 08:34
  • Does voting to close a question prevent other people from answering it? The question is not officially closed yet. If the community decides it should be closed it will be closed. If not other people can still answer it. – Hans May 31 '19 at 08:42
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    I'm pretty sure he's talking about the Oberth effect - I've heard him describe it similarly before in previous videos with a few "squarings then addings" and "bangs for bucks" – Jack May 31 '19 at 10:54
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    @uhoh yeah I agree, I don't think that answers your question - I was just confirming that, in my experience, Manley often talks in a - shall we say - inexact way about somewhat complex concepts ;) – Jack May 31 '19 at 11:44
  • I think he's talking about the Oberth effect--which for practical purposes says you should do burns as deep in a gravity well as you can. (The exception being plane change burns, which should be done as far out as you can.) – Loren Pechtel Jun 03 '19 at 04:06
  • @LorenPechtel That's consistent with what I wrote in my strangely down-voted answer as well. – uhoh Jun 03 '19 at 05:40
  • @uhoh I was trying to put it in simple terms without the math. – Loren Pechtel Jun 03 '19 at 14:11

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Despite watching a few times it looks like I linked the use of the term "capture" at this point in the video with the use of the term "capture" at 08:20 in the video. But that's about the mechanical capture of Snoopy during a docking maneuver and this is about the gravitational capture of the combined pair in the Earth's gravitational field.

What Manley is trying to say is that:

If you want to transition from a gravitationally unbound to gravitationally bound status in the Earth's field, this is a manipulation of the energy of the spacecraft's orbit, which depends on position and $v^2$, and a $\Delta v$ impulse can have the largest effect on $v^2$ when

  1. the $\Delta \mathbf{v}$ vector is parallel or antiparallel with $\mathbf{v}$, and
  2. the speed $v$ is maximum.

And for some further mathematical insight into why this is true, and some intriguing graphical illustrations of this as well, one can read the several excellent answers to Oberth effect for Earth vehicles.

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