Definition
where
- T is the instantaneous thrust
- m is the instantaneous mass
In the absence of external forces:
where a is the acceleration. When thrust is applied in a constant direction this simplifies to:
which is simply the magnitude of the change in velocity. However, this relation does not hold in the general case: if, for instance, a constant, unidirectional acceleration is reversed after (t1 − t0)/2 then the velocity difference is t1 − t0 = 0, but delta-v is the same as for the non-reversed thrust.
For rockets the 'absence of external forces' usually is taken to mean the absence of atmospheric drag as well as the absence of aerostatic back pressure on the nozzle and hence the vacuum Isp is used for calculating the vehicle's delta-v capacity via the rocket equation, and the costs for the atmospheric losses are rolled into the delta-v budget when dealing with launches from a planetary surface.
Read more about this topic: Delta-v
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