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In a comment on Is there a self-rounding celestial body from which an Olympian could jump into space? @jpa made a modest proposal.

What if we stacked a bunch of athletes on top of each other and each pushed up the next?

In the distant future of 2021, Nike and Warner Bros have cooked up a cross-promotion publicity stunt for Space Jam 2 and Nike Space Force Vacuum Max shoes. They've placed an army of LeBron James clones on the surface of Mimas. The goal is to launch one LeBron James away from Mimas.

The LeBron clones can do a vertical jump of 1 m on Earth. Each mass 110 kg and are 2 meters tall. Source. His extensive exposure to cartoon logic while filming Space Jam 2, plus his trusty Nike Space Force Vacuum Max shoes, allows LeBron James to survive in space without a heavy space suit.

Mimas has an escape velocity of 159 m/s.

The clones are standing on top of each other in a human pyramid. Each "stage" is holding onto a (for the purpose of the question massless) platform for the next stage to stand on. The first "stage" jumps pushing the rest of the clones up. At an optimal point the second "stage" jumps and the first lets go. And so on.

For example (not to scale).

               LJ                stage 5
              -----
              LJ LJ              stage 4
             --------
             LJ LJ LJ            stage 3
            -----------
            LJ LJ LJ LJ          stage 2
           --------------
           LJ LJ LJ LJ LJ        stage 1
       ====== Mimas ========

What does this stack of LeBron James clones like? How many are needed in each stage? Can it even work? Will the first stage of clones be crushed by the weight of the stages above them?

See also Could a human jump off Mimas without return?

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    $\begingroup$ I think you fail at the second hurdle; jumper number 2's leg extension will mostly push jumper 1 down, due to the weight of the stack of LeBrons above him. I wonder if there's a better gymnastic arrangement that avoids that issue, though... $\endgroup$ Jan 25 '20 at 22:51
  • $\begingroup$ @StarfishPrime Thrust should still be generated due to the equal and opposite reaction. I'm assuming each stage has many LeBron James's. I'll clarify that. $\endgroup$
    – Schwern
    Jan 25 '20 at 22:56
  • $\begingroup$ Heck, stage 1 can stand on their hands, and shove up stage 2 with their feet while stage 2 shoves down on the platform, for even more thrust.Stage 2 can do the same for stage 3, and so on. $\endgroup$
    – notovny
    Jan 25 '20 at 23:16
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    $\begingroup$ You don't need escape velocity to escape Titan. Go past the Saturn-Titan L1 or L2 points and Saturn can wrest the basketball player from Titan's capture. These points are about 332 kilometers above Titan's surface. $\endgroup$
    – HopDavid
    Jan 27 '20 at 12:07
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    $\begingroup$ @LorenPechtel from the OP, "Each "stage" is holding onto a platform for the next stage to stand on". You don't need direct LJ-to-LJ contact. And if the gain per stage is high enough, it won't be far from $x^2$ anyway. $\endgroup$ Jan 27 '20 at 16:42

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