Angular COM Axis Regression (ACAR)

This paper introduces Angular COM Axis Regression (ACAR), a simple method for predicting the rotational behavior of the center-of-mass (COM) axis in gravitational $n$-body systems using only the angular positions of orbiting bodies. The approach bypasses traditional numerical integration by leveraging a simple linear regression model, achieving near-perfect accuracy across various configurations — including planetary systems, binary stars, and hierarchical systems. ACAR offers a lightweight, interpretable alternative for understanding and approximating gravitational dynamics.