For a collection of point masses, the position vector for the center of mass is written as the summation of the product of each mass and its position vector divided by the total mass of all the particles. For extended objects with a uniform mass distribution, the point mass is replaced with the differential mass element and the summation with an integral to obtain the center of mass coordinates. Consider a free-falling extended object along the y-axis under uniform acceleration due to gravity. The total potential energy of this object is the sum of the potential energy due to each mass element. Substituting the expression for the center of mass gives the total potential energy as the product of the total mass, the acceleration due to gravity, and the y-coordinate of the center of mass. This implies that the gravitational potential energy of any extended object can be estimated by considering the object's entire mass to be concentrated at its center of mass.