A Gravitational Optimization Problem

initial direction (radians)

0

time limit

20

configuration of masses

grid

circle

line

final time: 1.0544

Consider a collection of fixed particles of mass 1 at prescribed positions (shown as black locators). Another particle of mass 1 starts at

(0,0)

with velocity 1 in a direction θ (counterclockwise from the

x

axis). It then travels according to Newton's laws, subject to an inverse-square force of magnitude

-2

r

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.