A satellite is in a circular orbit around an airless spherical planet of radius R. An asteroid of equal mass falls radially towards the planet, starting at zero velocity from a very large distance. The satellite and the asteroid collide inelastically and stick together, moving in a new orbit that just misses the planet's surface. What was the radius of the satellite's original circular orbit?
(Submitted by Philip R. Blanco, Grossmont College, El Cajon, CA)
We received many solutions to our October Challenge, The Alpha Dogs. Many—actually, most of them—were incorrect, unfortunately. The most common error, especially among the student solvers, was to assume that the answer was just the vector sum of the dog velocities.
We are pleased to recognize the following contributors:
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Juan M. Aguirregabiria (University of the Basque Country, Spain)
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Don Easton (Lacombe, Alberta, Canada)
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Gerald E. Hite (TAMUG, Galveston, TX)
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José Ignacio Íñiguez...