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That's not at all true, the tsiolkovsky rocket equation relates to delta-v (change in speed) and mass fraction, NOT altitude.



Delta-v is not change in speed here:

Delta-v, as used in spacecraft flight dynamics is a measure of the impulse that is needed to perform a maneuver such as launch from, or landing on a planet or moon, or in-space orbital maneuver. It is a scalar that has the units of speed. >>As used in this context, it is not the same as the physical change in velocity of the vehicle<<.[1]

[1]: https://en.wikipedia.org/wiki/Delta-v


To clarify: is the distinction between delta-v and change in re velocity that thrust could be applied in any direction, including in the braking direction, so a rocket applying a maneuver of given delta-v could end up with an increased or decreased (or zero) final speed?

If the above distinction is correct, then in general delta-v is not coupled to the physical change in the rocket's velocity. But in the case of a conventional rocket with a fixed thrust vector launching from Earth's surface (as in OP's comment), isn't it perfectly true that delta-v is equivalent to change in velocity (barring air resistance)?


It's also that you can go "backwards", e.g. slow down to land on another planet.


Yes, you're right, I was talking about the restricted case of straight up as the Karman line would likely be.




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