Describing a Vector Field–Newton’s Law of Gravitation

A gravitational field is defined by the vector field \[ {\bbox[5px, border:1px solid black, #F9F7ED]{\bbox[#FAF8ED,5pt]{{ \mathbf{F}=\mathbf{F}(x,y,z)=-\dfrac{{\boldsymbol G}m{\boldsymbol M}}{x^{2}+y^{2}+z^{2}}\mathbf{u} }}}} \]

where \(m\) and \(M\) are the masses of two objects, one located at the origin \((0,0,0)\) and the other at the point \((x,y,z)\); \(G\) is the gravitational constant; and \(\mathbf{u}\) is a unit vector in the direction from \((0,0,0)\) to \((x,y,z)\). Here, \(\mathbf{F}\) is the force of attraction between the two objects. The force vectors \(\mathbf{F}\) are directed from the object at \((x,y,z)\) toward the object at \((0,0,0)\). Figure 7 illustrates a gravitational field.