In this article, we introduce Newtonian spectral clustering, a method that employs Newtonian preprocessing to promote cluster perspicuity and trajectory analysis to gain valuable affinity information. A simple two-body potential is used to model the interaction under the influence of which the points move according to Newton's second law. This procedure produces a transformed data set with reduced cluster overlap, which favors the spectral clustering approach. This is so, because the affinity matrix can be enriched with information derived from the underlying interaction model. Special care is also given to estimate the Gaussian kernel parameter, since its role is important for the clustering procedure. The method is further extended appropriately to treat problems of high dimensionality. We have tested the proposed methodology on several benchmark data and compared its performance to that of rival techniques. The superiority of the new approach is readily deduced by inspecting the reported results.