In any event, our problem did not begin with J.J. Thompson. Some 2000 years after the Ancient Greeks, Tycho Brahe's careful observations on the behavior of celestial bodies and Kepler's subsequent careful analysis of those observations, revealed that the symmetry was in time and space. The predictable solar and celestial time-space symmetry was subsequently co-opted by Isaac Newton, and used as the carrier for our tactile sense of attraction to the earth, quantified in terms of our locally isolated (surface planet) "inertial mass", and declared as the controlling cause of the order we observe in the celestial, least action consistent universe. This was heralded as Newton's great synthesis  and is so considered even today.
Isaac Newton defined centripetal force in terms of his second law to act at a distance by setting his first law planet surface object on an imaginary circular path of motion at a constant orbital speed. Newton allowed his moving (planet surface like object) to impact the internal side of the circle circumference at equidistant points to inscribe a regular polygon. He dropped a radius to the center of the circle from each vertex (B) of the polygon to describe any number of equal area triangles. "...but when the body is arrived at (B), suppose that a centripetal force acts at once with a great impulse". Taking the length of each triangle base to the limit (approaching zero) the force vector [ma, mv/t, or dp/dt] at the vertex (B) is by definition directed along the radius toward the center of the circle as [mv^2/r]. [**] Again, as with Ptolemy we have a perfect circle and perfect motion where the law of areas falls out as an artifact of the circle itself.
Newton generalized the equal areas in equal times artifact of the perfect circle to any curved path directed radially around a point. "Every body that moves in any curve line... described by a radius drawn to a point... and describes about that point areas proportional to the times is urged by a centripetal force... to that point"
Newton extended the property of his planet surface like orbiting object to all celestial bodies. "Every body that by a radius drawn to the center of another body.. and describes about that center areas proportional to the times, is urged by a force.."
Newton then ties the force directly to the force he feels and calls gravity... "For if a body by means of its gravity revolves in a circle concentric to the earth, this gravity is the centripetal force of that body." In short the force acted on any orbiting object as though that object is identical to Newton's first law planet surface object where the force [ma] would then be proportional to the areas and times.
We cannot overly generalize sensory quantities that operate solely within least action parameters, beyond the specific frame within which they directly apply. Where we quantify a force we feel, in terms of our inertial mass, as isolated on the planet surface and applicable to surface planet inertial mass objects within the planet field, we cannot generalize that notion of force, to serve as the cause of the least action consistent behavior of the celestial bodies that apparently generate the field. We can, as inertial objects, use it to predict our operational and navigational requirements through the field.