http://wapedia.mobi/en/History_of_ce...ripetal_forces

Gottfried Leibniz as part of his "solar vortex theory" conceived of centrifugal force as a real outward force which is induced by the circulation of the body upon which the force acts. An inverse cube law centrifugal force appears in an equation representing planetary orbits, including non-circular ones, as Leibniz described in his 1689 Tentamen de motuum coelestium causis. [4] Leibniz's equation is still used today to solve planetary orbital problems, although his solar vortex theory is no longer used as its basis. [5]

Leibniz produced an equation for planetary orbits in which the centrifugal force appeared as an outward inverse cube law force in the radial direction: [6]

notice the inverse cube law for centrifugal force is wrong:

imagine an ellipse of minimun raidus one and maximus radius 2 with the sun in a focus

imagine center of arc when the planets is closest is the sun, but the center of arc when thet planet is farther is the oposite focus to the sun

therefore if you calculate centrifugal force of a curve with a wrong center youll have a wrong centrifugal force

therefore cubic rule for centrifugal force is wrong

how much is this wrong rule used today to claculate orbits?

i know he did it wrong cause i did myself the same mistake but realized later of it

centripetal force with this method happens to divide by four as you double the radius

so centrifugal force supposing true conservation of angular momentum in an ellipse(taking into account the right center of the curve) obbeys not an inverse cube law but an inverse square law