Okay! Earlier today I was thinking about potential energy and how it is related to an orbiting object, O, around a centre, C, from which force emanates if the object O is traveling at radius r from this centre, we conclude that the force given by the change in direction must be equal to the force pulling O towards the field's centre. Great, thanks Captain Obvious. So, I was thinking that the force created by the change in direction of O about C is proportional to the change in the derivative of the function of the orbit. Since the equation of a circle is (r2 - x2)1/2 it's derivative is equal to x/(r2 - x2)1/2, which derives to produce r2/(r2 - x2)3/2 Which is odd considering it's intuitive to think that whatever change in change in direction around C would be constant. Imagine swinging a bottle around your body, it doesn't pull with more force halfway through the swing. I thought that perhaps this was due to it being a function of the x axis, so I tried it with parametric equations and got y=sint x=cost dy/dt/dx/dt = cost/-sint = -1/tant = -cot(t) using -cot(t) as the new function for the derivative (y) y=-cot(t), I get -csc(t)/-sin(t), which still isn't constant. I really don't understand how the second derivative of the direction of a particle around a circle can't be constant. Can anyone clear this up for me?