Radial Motion of Two Mutually Attracting Particles

• Autores: Carl E. Mungan
• Localización: The Physics Teacher, ISSN 0031-921X, Vol. 47, Nº. 8, 2009, págs. 502-507
• Idioma: inglés
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• Resumen

  • 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, 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.