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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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    $\begingroup$ 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. $\endgroup$
    – Hans
    May 31, 2019 at 8:10
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    $\begingroup$ Possible duplicate of Oberth effect for Earth vehicles $\endgroup$
    – Hans
    May 31, 2019 at 8:19
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    $\begingroup$ 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. $\endgroup$
    – Hans
    May 31, 2019 at 8:24
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    $\begingroup$ 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" $\endgroup$
    – Jack
    May 31, 2019 at 10:54
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    $\begingroup$ @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 ;) $\endgroup$
    – Jack
    May 31, 2019 at 11:44

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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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  • $\begingroup$ I think this answer is spot-on. $\endgroup$
    – uhoh
    Jun 1, 2019 at 1:45
  • $\begingroup$ So I've accepted it for now. I'm happy to consider a different answer though $\endgroup$
    – uhoh
    Jun 2, 2019 at 14:59
  • $\begingroup$ All these down votes, but no helpful comments, not even unhelpful ones, and no other answers proposed. $\endgroup$
    – uhoh
    Jun 3, 2019 at 16:40
  • $\begingroup$ it's probably because you answered a question before it was deemed well-received. I do like this explanation though, it's not all that... expansive on what he said either so that could be the negatives. $\endgroup$
    – Magic Octopus Urn
    Jun 6, 2019 at 17:07
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    $\begingroup$ Just an fyi I honestly, genuinely, like all of these questions even if theyre extremely specific/not well recieved. I saw a video I wouldntve otherwise here. All of your questions are thought provoking. $\endgroup$
    – Magic Octopus Urn
    Jun 9, 2019 at 1:08

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