Radial Motion of Two Mutually Attracting Particles
Abstract
A pair of masses or oppositesign charges released from rest will move directly toward each other under the action of the inversedistancesquared force of attraction between them. An exact expression for the separation distance as a function of time can only be found by numerically inverting the solution of a differential equation. A simpler, approximate formula can be obtained by combining dimensional analysis, Kepler's third law, and the familiar quadratic dependence of distance on time for a mass falling near Earth's surface. These exact and approximate results are applied to several interesting examples: the flight time and maximum altitude attained by an object fired straight upward from Earth's surface; the time required for an asteroid of known starting position and speed to cross Earth's orbit if it is bearing toward the Sun; and the collision time of two oppositely charged particles starting from rest.
 Publication:

The Physics Teacher
 Pub Date:
 November 2009
 DOI:
 10.1119/1.3246467
 Bibcode:
 2009PhTea..47..502M
 Keywords:

 du.mm.y1