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Does the payload capacity of an interplanetary launch rocket increase with decreasing fuel mass or with increasing escape velocity? I was thinking that the escape velocity has nothing to do with it and it is solely depends on the (decreasing) fuel mass?

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    $\begingroup$ Escape velocity has nothing to do with the rocket or its design; it's a function of the mass of a gravitating object, and the current distance from it. Did you perhaps mean effective exhaust velocity? $\endgroup$
    – notovny
    Commented Feb 13, 2023 at 1:15
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    $\begingroup$ The fuel onboard that was not burned in order to reach escape velocity during the launch is also considered a payload. And what portion of your payload consists of propellant vs other equipment is a separate question. $\endgroup$ Commented Feb 13, 2023 at 1:31

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Your thrust, depends on the reactive mass ejected x ejection speed. Your acceleration depends on your thrust and your mass.

Escape velocity is more or less a fixed speed cost for leaving the planet. The higher the escape velocity, the smaller your payload (given the same rocket) The more fuel you embark, the greater your payload (given the same rocket)

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