How to calculate centripetal acceleration in non-circular systems?

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Centripetal acceleration in non-circular systems, such as ellipses or parabolas, can be calculated using the formula a_c = v^2/r, where v is the tangential velocity and r is the radius of curvature at a specific point. For non-circular paths, the radius of curvature varies, so it’s essential to determine the instantaneous radius at the point of interest. The centripetal force required can also be derived from the motion equations specific to the shape of the trajectory. Understanding the geometry of the path is crucial for accurate calculations. This approach allows for the analysis of centripetal acceleration in complex motion scenarios.
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How can you calculate centripetal acceleration in a non circular system(I.E. if wanted to calculate the centripetal acceleration in an eclipse, or a parabola how could I do that?)
 
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