An important concept that is presented in the discussion of Newton's law of universal gravitation is that the gravitational effect external to a spherically symmetric mass distribution is the same as if all of the mass of the distribution were concentrated at the center.1,2 By integrating over ring elements of a spherical shell, we show that the gravitational force on a point mass outside the shell is the same as that of a particle with the same mass as the shell at its center. This derivation works for objects with spherical symmetry while depending on the fact that the gravitational force between two point masses varies inversely as the square of their separation.3 If these conditions are not met, then the problem becomes more difficult. In this paper, we remove the condition of spherical symmetry and examine the gravitational force between two uniform cubes.
Permission has been granted by The Physics Teacher to supply this article [http://dx.doi.org/10.1119/1.4905815] for educational and research purposes. More info can be found at http://aapt.scitation.org/journal/pte. © 2015 American Association of Physics Teachers.
J. Sanny and D. Smith, The Physics Teacher 53, 111 (2015); doi: 10.1119/1.4905815