What is the definition of centripetal acceleration?
This is a somewhat complicated problem that I dealt with in our Intermediate Mechanics class in college. For these ‘orbits’ which are typically elliptical, the term “centripetal force” is replaced by a “central force”. The central force has several requirements in order to be considered a central force. First of all, a central force must be conservative, i.e. the force is the negative gradient of the potential function (for orbits, this would be the gravitational potential energy function throughout space). This then implies that the total mechanical energy (1/2mv^2+V(r)) is a constant. A central force will obey Kepler’s second law, namely that equal areas are swept in equal time intervals. Finally, a consequence of being a conservative force is that the curl (del X F(r)) is identically zero. The first link below will point you to the Polar Orbital Equation that describes orbital motion. You should be versed in representing the conics in polar form, as well as specific relative angular
