其中dm是在點r的質量，g 是重力加速度，以及k 是定義垂直方向的單位向量。 在这个体系中选择位置矢量为R的点为参考点，计算出點r所受的合力：
Some of the inhomogeneity in a gravitational field may be modeled by a variable but parallel field: g(r) = g(r)n, where n is some constant unit vector. Although a non-uniform gravitational field cannot be exactly parallel, this approximation can be valid if the body is sufficiently small. The center of gravity may then be defined as a certain weighted average of the locations of the particles composing the body. Whereas the center of mass averages over the mass of each particle, the center of gravity averages over the weight of each particle:
where is the (scalar) weight of the ith particle and W is the (scalar) total weight of all the particles. This equation always has a unique solution, and in the parallel-field approximation, it is compatible with the torque requirement.
A common illustration concerns the Moon in the field of the Earth. Using the weighted-average definition, the Moon has a center of gravity that is lower (closer to the Earth) than its center of mass, because its lower portion is more strongly influenced by the Earth's gravity.
If the external gravitational field is spherically symmetric, then it is equivalent to the field of a point mass M at the center of symmetry r. In this case, the center of gravity can be defined as the point at which the total force on the body is given by Newton's Law:
where G is the gravitational constant and m is the mass of the body. As long as the total force is nonzero, this equation has a unique solution, and it satisfies the torque requirement. A convenient feature of this definition is that if the body is itself spherically symmetric, then rcg lies at its center of mass. In general, as the distance between r and the body increases, the center of gravity approaches the center of mass.
Another way to view this definition is to consider the gravitational field of the body; then rcg is the apparent source of gravitational attraction for an observer located at r. For this reason, rcg is sometimes referred to as the center of gravity of M relative to the point r.