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Space Exploration

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    $\begingroup$ Related: thelastmanonearth.blogspot.com/2008/06/… $\endgroup$
    – Organic Marble
    Commented Jan 4, 2018 at 1:35
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    $\begingroup$ Depends on which way you're thrusting. Rocket exhaust goes backward relative to the rocket at ~3000-4500 m/s; for typical LEO/GEO insertions, that leaves the exhaust in an Earth-suborbital trajectory, so you should expect the bulk of it to reenter. Even Apollo's translunar injection adds ~3200 m/s to LEO velocity using an exhaust velocity of ~4100 m/s! Obviously unless you have an infinitely long nozzle (= absolute zero exhaust temperature) there will still be some loss from plume dispersion, though. $\endgroup$
    – Russell Borogove
    Commented Jan 4, 2018 at 2:10
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    $\begingroup$ Rocket exhaust has a high temperature, so some molecules will be at escape velocity. $\endgroup$
    – Hobbes
    Commented Jan 4, 2018 at 9:38
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    $\begingroup$ @Hobbes however expansion $\rightarrow$ cooling, until the point where the density is so low that there are no further collisions, at which point the endpoint temperature will be "remembered" by the distribution of final velocities of the individual molecules with respect to the average CM exhaust velocity. There will be a ~4k m/s component behind the nozzle with a ~1k m/s transverse component, but the characteristic $k_B T$ of the exponential tail will reflect the temperature of the "cooled-off" gas after expansion. $\endgroup$
    – uhoh
    Commented Jan 4, 2018 at 10:07
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    $\begingroup$ @Hobbes The expansion cools the exhaust gas mightily; SSME has a chamber temperature of ~3400K and an exhaust temperature of only ~685K (~412C) (according to some random dude on the internet who sounded plausible to me). $\endgroup$
    – Russell Borogove
    Commented Jan 4, 2018 at 16:05