Variable-mass system the momentum of the system varies for Therefore, by Newton's second law Noting that u - v is the velocity of d"m" relative to "m", symbolized as v, this final equation can be arranged as In a system where mass is being ejected or ablated from a main body, the derivation is slightly different. At time "t", let a mass "m" travel at a velocity v, meaning the initial momentum of the system is Since the main body will be losing mass, d"m" will be negative, meaning that at a time "t" + d"t" the momentum of the system becomes
Propellant mass fraction important role in the rocket equation: Where formula_10 is the ratio of final mass to initial mass (i.e., one minus the mass fraction), formula_11 is the change in the vehicle's velocity as a result of the fuel burn and formula_12 is the effective exhaust velocity (see below). The term effective exhaust velocity is defined as: where "I" is the fuel's specific impulse in seconds and "g" is the "standard acceleration of gravity" (note that this is not the local acceleration of gravity). To make a powered landing from orbit on a celestial body without an atmosphere requires the same mass