Modified Newtonian Dynamics

[airbauer33]

Homework Statement

For very low rates of acceleration, Newton's 2nd law has to be modified where F<vector>=m*f(a/a0)*a<vector>. For "small" values of a<vector>, f(a/a0) = a/a0.
Determine the component equations of motion for the case of f(a/a0) = a/a0 in polar coordinates (don't try to solve the radial equation!). Show that the angular momentum is conserved.

Homework Equations

F<vector> = m*f(a/a0)*r<double dot>

The Attempt at a Solution

Since we are dealing with orbits, I am assuming the the two forces are the gravitational and centripetal forces (or are they the same thing). I also can determine r<double dot> in polar coordinates.

 

[Dick]

Angular momentum is m*r(t)xv(t). (x is cross product). What's the derivative of angular momentum? What properties of the force and the cross product can help you prove this derivative is zero?