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We study the equipotential surfaces around of a two particle system in 3-dunder a pairwise good potential as the one of Van der Waals. The level sets arecompletely determined by the solutions of polynomials of at most fourth degreethat can be solved by standard algebraic methods. The distribution of realpositive roots determines the level sets and provides a complete description ofthe map for the equipotential zones. Our methods can be generalized to a familyof polynomials with degree multiple of 2, 3, or 4. Numerical simulations of 2-dand 3-d pictures depicting the true orbits and equipotential zones areprovided.

Fully Algebraic Description of the Static Level Sets for the System of Two Particles under a Van der Waals Potential