Motion under gravitation is according to the New View described by the following set of equations in terms of the gravitational potential and immaterial free fall trajectories ;
- , (mass conservation)
- , (Newton’s 2nd Law)
where the mass density $\rho (x,t)$ does not appear, but is instead tied to by the relation by differentiation as instant local action in space. Notice that the immaterial trajectories cover space even where expressing absence of matter. The differential equations 1-3 are complemented by initial conditions and and .
To avoid local gravitational collapse from the tendency of gravitational motion to concentrate matter, a pressure force with a pressure is needed to balance the gravitational force locally. With such a pressure force present the basic case to consider is a two-body problem as the motion of two bodies 1 and 2 as solid spheres of mass and under gravitation. The corresponding gravitational potential can be expressed as a smoothed version of the potential of the corresponding point masses (in normalized form):
where is the position of the center of body 1 at time and that of body 2. The net gravitational force acting on body 1 will then be given by
where is a unit vector in the direction , because the the force from will be balanced by a local pressure. Likewise the net gravitational force acting on body 2 is given by
We thus recover Newton’s law of gravitation, which is no surprise of course, but the important aspect is that the full gravitational potential is the sum of the gravitational potentials and , both changing with time, and that the self-gravitational force with acting on body 1 is balanced by a local pressure and thus effectively is canceled. This means that the trajectory is determined by Newton’s 2nd law with .
The whole mystery of motion under gravitation is now expressed in the equation , which is no mystery since it expresses mass conservation.