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"
Mass–energy equivalence equivalence of mass and energy". In addition, Einstein used the formula , with being the energy of a system of mass points, to describe the energy and mass increase of that system when the velocity of the differently moving mass points is increased. In June 1907, Max Planck rewrote Einstein's mass–energy relationship as , where is the pressure and the volume to express the relation between mass, its "latent energy", and thermodynamic energy within the body. Subsequently, in October 1907, this was rewritten as and given a quantum interpretation by Johannes Stark, who assumed its validity and correctness ("Gültigkeit"). In