Among the radial gravitational fields the property that the brachistochrones and the isochrones of a field are identical curves is possessed by only those fields whose potentials vary directly as the squares of distances from the centers of the fields. The gravitational field obtaining inside a sphere of constant density is of this type. The relevant curve for such fields is the hypocycloid.
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© 1977 American Association of Physics Teachers.
1977
American Association of Physics Teachers
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