Physics
Scientific paper
Jul 2009
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009ejph...30..785l&link_type=abstract
European Journal of Physics, Volume 30, Issue 4, pp. 785-792 (2009).
Physics
Scientific paper
To find the point between two massive spherical bodies at which their gravitational fields cancel is an apparently simple problem usually found in introductory physics textbooks. However, by noting that such a point does not exist when the distance between the spheres is small and one of the masses is much smaller than the other—e.g., between the Earth and a billiard ball near the ground—I develop here a simple analysis for establishing existence conditions for this point. Unexpectedly, I have found that the net gravitational field can be null also in certain points inside each sphere. The position of these 'inner' points can be determined by solving a cubic equation via the standard method, known as Cardan's solution. However, when the discriminant of this equation is negative one has the irreducible case, for which Cardan's solution 'fails', but a trigonometric method proposed recently yields exact closed-form expressions. Interestingly, it is shown that these 'inner points' do occur in the Earth-Moon system, in which they are determined just by solving irreducible cubic equations.
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