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Centripetal force

Centripetal “force” was invented by Newton in analogy to Huygens’ centrifugal force that appears in sling motion. Newton needed a center seeking force so he just changed the direction of Huygens’ tendency that seeks to go away from the center.
This “force” is really the \(R/T^2\) term in Kepler’s Rule written like this \[\frac{R}{T^2}=\frac{1}{R^2}\]
Newton calls \(R/T^2\) term “force” or the mysterious and occult Newtonian force that causes this acceleration \(R/T^2\).
Newton calls the other term of Kepler’s Rule, \(1/R^2\) the measure of how this so-called force \(\frac{R}{T^2}\) varies in time.