In 1974, a well-known research problem in Statistical Mechanics entitled "To determine and define the probability function P.sub.2 of a particle hitting a predesignated area, given all its parameters of generation and ejection." was openly solicited for its solution from research and development organizations in U.S.A. One of many proposed solutions of the problem, initiated at that time, is by means of the TRAJECTORY SOLID ANGLE(TSA). TSA is defined as the integral of the dot product of the unit tangent of the particle's trajectory to the vectorial area divided by the square of the position vector connecting between the point of ejection and that of the surface to be hit. The invention provides:(1) The precise and the unique solution of a previously unsolved P.sub.2 problem:(2) Impacts to the governmental NRC safety standards and DOD weaponary systems and many activities in the Department of Energy;(3) Impacts to update the contents of text books of physics and mathematics of all levels; (4) Impacts to the scientific instrumentations with applications in high technologies. The importance of TRAJECTORY SOLID ANGLE can be quoted from a letter by the late Institute Professor P. M. Morse of MIT who reviewed the DOE proposal P7900450 (reference No. 7) in 1979 and addressed to the inventor." If the TRAJECTORY SOLID ANGLE is correct it will provide a revolutionary concept in physics. . . ".