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This document summarizes the solution to finding the force law and properties of a central force field that allows a particle to move in a logarithmic spiral orbit given by r = keαθ. The force law is derived to be fr = -l2/(μr3)(α2 + 1). The total energy of the system is found to be E = l2α2/2μr2 + l2/(2μr2) - l2/(2μr2)(α2 + 1) = 0, representing a bound system. An equation is also derived relating the time derivative of θ to constants l, μ, k, and α, which can be integrated to determine the value of

Author

Micah Parsons

Language

EN