In physics the benefits of using the center of mass to model a mass distribution can be seen by considering the resultant of the gravity forces on a continuous body. Consider a body Q of volume V with density ρ (r) at each point r in the volume. In a parallel gravity field the force f at each point r is given by, f ( r ) = − − d m g k ^ ^ = − − ρ ρ ( r ) d V g k ^ ^ , where dm is the mass at the point r, g is the acceleration of gravity, and k ^ ^ is a unit vector defining the vertical direction.