This two-fold definition may be expressed mathematically as follows. The center of force O can be chosen as the origin of a coordinate system. The vector r joining O to the present position of the particle is known as the position vector. Therefore, a central force must have the mathematical form F = F ( r ) r ^ ^ where r is the vector magnitude | r | (the distance to the center of force) and r̂ = r /r is the corresponding unit vector. According to Newton's second law of motion, the central force F generates a parallel acceleration a scaled by the mass m of the particle F = F ( r ) r ^ ^ = m a = m r ¨ ¨