Furthest Earthlings From Earth: Apollo 13 or Cow?

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The discussion centers on the physics of a hypothetical scenario where a cow jumps over the moon, comparing it to the Apollo 13 mission's slingshot trajectory. It highlights that the cow's smaller mass would necessitate a closer lunar pass to achieve the gravitational slingshot effect, which is crucial for gaining sufficient velocity for trans-Earth injection. The conversation touches on the principles of physics, noting that while mass affects gravitational interactions, the rate of fall for objects in a vacuum remains constant regardless of mass, as illustrated by the example of a feather and a brick. The analysis emphasizes the importance of trajectory and timing in achieving the desired orbital mechanics for both the cow and the Apollo 13 spacecraft.
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Now, we all know that Apollo 13's slingshot trajectory around the moon carried the august crew of that storied ship further from Earth than any other human beings have ever been.

However, the ancient nursery rhyme assures us that the cow jumped over the moon.

Looking into the physics of bovine space-travel trajectories, it appears to me that the smaller mass of the cow as opposed to the Apollo13 CSM-LM combo would require a closer pass over the lunar surface. Assuming that expulsion of intestinal gasses from the cow (properly timed) would impart sufficient thrust for her to achieve trans-Earth injection, the nearer pass over the lunar surface would be required to counteract her lesser mass relative to Apollo 13 for her to gain full benefit from the gravitational slingshot effect.

Am I right or what?
 
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The mass of the projectile makes no difference. A feather and a brick fall at the same rate.
 
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