# Modified Newtonian Dynamics

1. Nov 5, 2007

### airbauer33

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

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

3. 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.

Last edited: Nov 5, 2007
2. Nov 5, 2007

### 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?