# Ground point

A mass point or point mass is the highest possible idealization of a real body in physics : One imagines that its mass is concentrated in its center of gravity . That simplifies the description of its movement.

The subject that deals with the movement of mass points is called point mechanics . The body is seen as a mathematical point that has a non-zero mass, perhaps also an electrical charge. Properties that have to do with its non-punctiformity (its extension), such as dimensions, volume, shape and deformability, are neglected. In particular, a mass point has no degrees of freedom of rotation . It can still have its own angular momentum.

To approximate an extended body by a mass point is appropriate in many cases, even if it is rotating. For example, thrown objects, but also entire celestial bodies, often follow the path of a mass point very precisely. Effects that go back to the expansion of the body, such as self-rotation with precession and nutation or deformations , can be better treated with the methods of rigid body or continuum mechanics . Their mathematics, however, is much more complicated, not least because the rigid body has six degrees of freedom and the deformable body an infinite number of degrees of freedom.

The movement of a mass point is described in Newtonian mechanics by Newton's law of motion :

${\ displaystyle {\ vec {F}} = m \; {\ vec {a}}}$

With

• ${\ displaystyle {\ vec {F}}}$= Force vector
• ${\ displaystyle m}$ = Mass
• ${\ displaystyle {\ vec {a}}}$ = Acceleration vector.

In classical mechanics, the variables place and momentum determine the state of a mass point: At any time it is at a certain place and has a certain momentum (mass times speed). With a given force acting on it, the change in the state of motion is determined by Newton's law of motion mentioned above. ${\ displaystyle t}$ ${\ displaystyle {\ vec {p}} = m {\ vec {v}}}$