SPACECRAFT PROPULSION - KTH

- 5 -This expresses that the spacecraft experiences acceleration in theopposite direction to v e, or that the external force acting on thespacecraft is by definition the force of thrust. That is, constantexhaust propellant velocity v v at nozzle outlet ( ev v is theerelative velocity between spacecraft and exhaust propellant) gives thebasic equation for force of thrust:F dmdt v mv e e N, (4)withdmdt mkg s for the propellant mass flow rate. (5)Strictly speaking, veand F are vectors. They are here taken to becollinear, so no vector notation is needed.Eq. (3) can be integrated to get the accumulated velocity incrementv of a spacecraft:Integrated:vvv0dv vmfemmv velnmodmmfo. (6)m s , (7)where m 0 is the initial mass of the spacecraft at the beginning and m fis the final mass of the spacecraft at the end of its mission.