# A Gravitational Optimization Problem

A Gravitational Optimization Problem

Consider a collection of fixed particles of mass 1 at prescribed positions (shown as black locators). Another particle of mass 1 starts at with velocity 1 in a direction θ (counterclockwise from the axis). It then travels according to Newton's laws, subject to an inverse-square force of magnitude from each of the fixed masses. What is the shortest time in which the moving particle can be made to reach a prescribed target (the red locator)? This Demonstration lets you vary the initial direction to thereby find an approximate value of the optimal angle and minimum time by trial and error.

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