Mass in special relativity what causes these particles to be termed "massless." However, even massless particles have a relativistic mass, which varies with their observed energy in various frames of reference, The invariant mass is the ratio of four-momentum (the four-dimensional generalization of classical momentum) to four-velocity: and is also the ratio of four-acceleration to four-force when the rest mass is constant. The four-dimensional form of Newton's second law is: The relativistic expressions for "E" and "p" obey the relativistic energy–momentum relation: where the m is the rest mass, or the invariant mass for systems, and "E" is the total energy. The equation is
Mass ratio from Tsiolkovsky's rocket equation: where This equation can be rewritten in the following equivalent form: The fraction on the left-hand side of this equation is the rocket's mass ratio by definition. This equation indicates that a Δv of formula_4 times the exhaust velocity requires a mass ratio of formula_5. For instance, for a vehicle to achieve a formula_6 of 2.5 times its exhaust velocity would require a mass ratio of formula_7 (approximately 12.2). One could say that a "velocity ratio" of formula_4 requires a mass ratio of formula_5. Sutton defines the mass ratio inversely as: In this case, the values