This equation attempts to show the relationship between gravitational mass and inertial mass.
It is a combination of the formula for relative acceleration (gravitational) and reduced mass (inertial):
If the equivalence principle holds true, then the ratio between gravitational mass and inertial mass is one to one. So it can be canceled out, revealing the familiar law of gravitation.
However, leaving the equation in it's expanded form can be very illustrative. For example, the relationship between gravitational mass and inertial mass in the universality of free fall can be demonstrated simply by showing the equation for the acceleration of the free falling body:
In the above equation it is easy to see why the free falling body will fall at the same rate regardless of it's own mass. Any change in the gravitational mass in the left fraction is balanced by the same change in inertial mass in the right fraction.
Another interesting aspect of this equation is that the proportional equivalence of gravitational mass and inertial mass is not a requirement.
Have you seen anything like this before?
What is your opinion?