A new model for the shape of the magnetopause is presented using a closed-form analytic function known as a tractrix. This shape is derived from several physics-based underpinnings, eliminating the need for fitting ad-hoc functional forms that, while convenient, are not physically motivated. One feature of the magnetopause predicted by this model is that the magnetotail flares outward until it reaches a constant width, a feature that has significant observational evidence but is seldom represented in functional forms of the magnetopause shape. To optimize the parameters of this model, a dataset of over 13,000 magnetopause crossings from THEMIS/ARTEMIS, Cluster, Geotail, Interball, and several other spacecraft is utilized. Using a Bayesian approach combined with a Markov Chain Monte Carlo (MCMC) method to estimate the posterior probability distribution in parameter space, the maximum likelihood parameters for the model that optimize its performance on this dataset are determined. The modelâ\euro™s performance is compared to that of other popular models of the magnetopause with a focus on their relative performance, and is shown to outperform models that assume the tail flares outward to infinity at far distances. The optimized model more accurately predicts magnetopause position along the tail than other popular static analytic magnetopause models, while still being easy to implement for a variety of applications.