Radial Motion of Two Mutually Attracting Particles
NAVAL ACADEMY ANNAPOLIS MD DEPT OF PHYSICS
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A pair of masses or opposite-sign charges released from rest will move directly toward each other under the action of the inverse-distance- squared 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, Keplers third law, and the familiar quadratic dependence of distance on time for a mass falling near Earths 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 Earths surface the time required for an asteroid of known starting position and speed to cross Earths orbit if it is bearing toward the Sun and the collision time of two oppositely charged particles starting from rest.
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- Numerical Mathematics