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
Binary mass function hole), the mass function becomes formula_33 and since formula_34 for formula_35, the mass function gives a lower limit on the mass of the unseen object 2. In general, for any formula_20 or formula_3, formula_38 In an orbit with eccentricity formula_39, the mass function is given by formula_40 If the accretor in an X-ray binary has a minimum mass that significantly exceeds the Tolman–Oppenheimer–Volkoff limit (the maximum possible mass for a neutron star), it is expected to be a black hole. This is the case in Cygnus X-1, for example, where the radial velocity of the companion star has been measured.