Variable-mass system events. The following derivation is for a body that is gaining mass (accretion). A body of time-varying mass "m" moves at a velocity v at an initial time "t". In the same instant, a particle of mass dm moves with velocity u. The initial momentum can be written as Now at a time "t" + d"t", let both the main body and the particle accrete into a body of velocity v + dv. Thus the new momentum of the system can be written as Since d"m"dv is the product of two small values, it can be ignored, meaning during d"t"
Escape velocity kg or 1,000 kg; what differs is the amount of energy required. For an object of mass formula_9 the energy required to escape the Earth's gravitational field is "GMm / r", a function of the object's mass (where "r" is the radius of the Earth, "G" is the gravitational constant, and "M" is the mass of the Earth, ). A related quantity is the specific orbital energy which is essentially the sum of the kinetic and potential energy divided by the mass. An object has reached escape velocity when the specific orbital energy is greater or equal to zero. An