Gravitational fields whose brachistochrones and isochrones are identical curves

Chander, Ramesh (1977) Gravitational fields whose brachistochrones and isochrones are identical curves American Journal of Physics, 45 (9). pp. 848-850. ISSN 0002-9505

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Official URL: http://scitation.aip.org/content/aapt/journal/ajp/...

Related URL: http://dx.doi.org/10.1119/1.11060

Abstract

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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