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Multistage rockets have the benefits of trimming dead weight and using different engines for different heights. But do they have some momentum gain benefits too?

For instance, during their detachment, does the first stage add more momentum to the second stage as per the conservation of momentum?

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    $\begingroup$ I'm not sure I understand your question, are you asking if the act of separation somehow imparts momentum to another section? That would be against the laws of physics. $\endgroup$ – GdD May 7 at 12:32
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    $\begingroup$ @GdD Stage separation by design is typically slightly propulsive. The goal is not however to add significant momentum to the part of the vehicle that still matters. It is to ensure that the part of the vehicle that still matters doesn't collide with the part of the vehicle that no longer matters. That should be an answer, so I'm making it one. $\endgroup$ – David Hammen May 7 at 14:03
  • $\begingroup$ I agree with what you say, I'm not sure that's the question though @DavidHammen. $\endgroup$ – GdD May 7 at 14:15
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Stage separation by design is typically slightly propulsive. The goal however is not to add a significant amount of momentum to the part of the vehicle that still matters. It is instead to ensure that the part of the vehicle that still matters doesn't collide with the part of the vehicle that no longer matters. Stage separation is a risky event. Several launches have failed due to collisions between recently separated segments.

Avoiding these risky stage separation events is one of the reasons why single stage to orbit (SSTO) has long been a very desirable goal. SSTO would be a highly disruptive technology. It might however be an unachievable goal, at least using current or near future technologies. Multiple decades of research have gone into this concept with no success (not even a promise of success) to date.

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    $\begingroup$ Staging was seen as complicated and risky early on, but it's become very routine and reliable. And while it requires a high performance vehicle, SSTO itself isn't technically that difficult to achieve. The problem has been doing it with an economical payload, SSTO inherently having a lower payload fraction due to carrying more vehicle mass to orbit, and requiring a more expensive, more mass-optimized vehicle for the same reason. I have a hard time seeing SSTO disrupting anything, especially now with reusable boosters flying. $\endgroup$ – Christopher James Huff May 7 at 16:48
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    $\begingroup$ At least one Falcon 1 failed due to staging issues. That wasn't that long ago. $\endgroup$ – Organic Marble May 8 at 3:13

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