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I watched "Apollo 13" yesterday, and they had the "angle-of-attack" problem that had to be manually solved, to prevent the ship from "ricochet[ing] off the atmosphere like a rock skipping off a pond".

I found and read this, but couldn't manage the term to further learn about this "ricochet".

Is there a term that reflects this "ricochet"?

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The term related to the quote you have stated, that has come up in a number of documents is skip reentry, some examples of its use and context are from:

FAA article on vehicle reentry, where they make the analogy of skipping stones. But, it is from the Aerospace Web article Atmosphere & Spacecraft Re-entry, where they state

A more unusual re-entry option that merges features of both ballistic and gliding profiles is the skip entry trajectory.

Another article, from NASA about the Apollo and Soyuz missions Reentry Vehicles: Spheres vs. Blunt Bodies also use the term in the caption for the diagram (below):

enter image description here

A 1963 sketch illustrating a possible skip reentry trajectory of the Apollo spacecraft.

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    $\begingroup$ It's also possible that the skip is not followed by a reentry. But a very long, lonely flight somewhere else. Assuming the speed is high enough and the angle shallow enough that is. $\endgroup$
    – tpg2114
    Commented Dec 25, 2013 at 5:22
  • $\begingroup$ Yes, a complete 'bounce',the FAA article has some information and calculations for that. $\endgroup$
    – user29350
    Commented Dec 25, 2013 at 5:23

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