# Time to reach a required delta-v - rocket propulsion

## Description

Spacecraft propulsion is any method used to accelerate spacecraft and artificial satellites. Space propulsion or in-space propulsion exclusively deals with propulsion systems used in the vacuum of space and should not be confused with launch vehicles. Several methods, both pragmatic and hypothetical, have been developed each having its own drawbacks and advantages.

In the ideal case m1 is useful payload and m0 − m1 is reaction mass (this corresponds to empty tanks having no mass, etc.). The energy required can simply be computed as shown here

For a given objective such as moving from one orbit to another, the required Δv may depend greatly on the rate at which the engine can produce Δv and maneuvers may even be impossible if that rate is too low. For example, a launch to Low Earth orbit (LEO) normally requires a Δv of ca. 9.5 km/s (mostly for the speed to be acquired), but if the engine could produce Δv at a rate of only slightly more than g, it would be a slow launch requiring altogether a very large Δv (think of hovering without making any progress in speed or altitude, it would cost a Δv of 9.8 m/s each second). If the possible rate is only g or less, the maneuver can not be carried out at all with this engine.

in the case of a large ve the possible acceleration is inversely proportional to it, hence the time to reach a required delta-v is proportional to ve with 100% efficiency. For Δv ≪ v e the time is as shown here. Related formulas## Variables

t | time to reach a required delta-v (s) |

m | Rocket mass (kg) |

v_{e} | exhaust velocity relative to the rocket (m/s) |

Δ_{v} | Rocket's final velocity (m/s) |

P | Power (watt) |