Leibniz was heavily influenced by the Cartesian tradition and classical mechanics predating Newton, where force and motion were conceptualized differently. While Newton framed orbital motion through his laws of motion and universal gravitation, Leibniz rejected the notion of “action at a distance” and sought explanations rooted in direct, mechanical interactions.

The term “accelerationless” refers to Leibniz’s rejection of the Newtonian understanding of centripetal acceleration as the cause of orbital motion. Instead, Leibniz viewed motion in orbits as governed by pre-established harmony or inherent principles of motion, not by external forces acting over a distance. He argued for a system in which orbits were sustained by a balance of internal dynamics, emphasizing conservation principles such as the conservation of vis viva (living force, related to kinetic energy) and momentum.

Leibniz believed in the conservation of vis viva, proportional to the square of the velocity (akin to kinetic energy). He considered the orbit of a body to result from the innate properties of motion, influenced by constraints like geometrical or dynamical relationships with other bodies, rather than an external force compelling it toward a center.

Leibniz was critical of Newton’s concept of gravity as an inherent, action-at-a-distance force. He sought to explain phenomena like orbital motion through mechanical and metaphysical principles without invoking a direct pulling force. For example, he speculated that a body’s orbital path might arise from the balance between its natural inertia and the constraints imposed by the ether or surrounding environment.

Leibniz’s philosophy also played a role in his physical theories. He argued for a universe governed by rational principles and pre-established harmony. This metaphysical framework led him to see motion and interaction as expressions of underlying laws designed by God, avoiding the need for “ad hoc” forces like Newton’s gravity.

Leibniz critiqued Newton for introducing forces that could not be physically or mechanically explained. He dismissed Newton’s idea of an invisible, universal force acting across empty space, as it conflicted with Leibniz’s mechanistic worldview. This philosophical difference also influenced his scientific interpretations.

Leibniz’s understanding of orbital motion can be seen as an attempt to reconcile observable phenomena with his philosophical commitments to a rational, mechanistic, and metaphysical framework. While he acknowledged the empirical success of Newton’s Principia, he remained skeptical of its conceptual foundation. Ultimately, Leibniz’s view failed to gain traction because it could not account for the precision and predictive power of Newtonian mechanics. However, his emphasis on conservation laws and dynamical constraints remains influential in later developments in physics.