Lack of Orientation of a Point Mass

[0pt618]

The point mass (aka particle) is a fictional but useful concept. However, I have yet been able to find a definition of what exactly a point mass is. It is commonly accepted that a point mass does not have an orientation, and thus only 3 coordinates to determine its position are required (as opposed to 6 coordinates required for a rigid body).

Why does a point mass have no orientation? I'd appreciate it if someone can cite a definition of a point mass (if available), and show how this follows from the definition. An intuitive explanation would also be welcome.

 

[Svein]

Why does a point mass have no orientation?

No mass has any orientation. Mass is a scalar.

 

[jbriggs444]

One way to approach the problem would be to consider the properties of a small sphere of mass m and of a pair of small spheres of mass m/2 each, connected by a rod of negligible mass. The gravitational field surrounding the sphere is perfectly uniform outside the sphere and decreases toward zero inside. The gravitational field surrounding the dumbbell-shaped object is not uniform. It is relatively stronger end-on and relatively weaker side-on. The field decreases toward zero near the center of mass.

But suppose that we make both objects smaller and smaller (keeping their mass constant). As they shrink, the gravitational field at a fixed distance from the dumbbell becomes more and more uniform. The region near the center of mass where gravity behaves differently becomes smaller and smaller for both objects. In the limit, one has a uniform gravitational field following an inverse square law everywhere except exactly at the center of mass and an undefined field exactly at the center of mass.

For purposes of gravitational attraction, a "point mass" is the same as a "mass whose size is small enough to be negligible".