The article presents a methodology for studying the two body problem and the law of universal gravitation through a kinematic analysis of elliptical motion. The proposed approach complements the traditional dynamical derivation of Kepler’s laws with an inverse analysis: from the geometry of the trajectory to the structure of acceleration and its reconciliation with dynamical laws. This methodology enables students to gain a deeper understanding of the interrelation between kinematics and dynamics, develop mathematical thinking, and overcome conceptual difficulties in learning celestial mechanics. Typical student difficulties (the problem of mass, the illusion of contradiction between Newton’s laws) and ways to overcome them are discussed. In addition to the first version, the article now contains an explicit algorithm for computing masses of bodies from observational data, using only kinematics and the experimental value of the gravitational constant G, without invoking the law of universal gravitation as a dynamical postulate. The proposed approach can be used in courses on theoretical mechanics, celestial mechanics, and general physics. The analytical results are additionally verified by numerical modelling on a mechanical ellipsograph, which confirms that the constancy of areal velocity is achieved only under a specific Keplerian law of angular velocity variation, not under arbitrary motion along an ellipse.