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Newton's theorem of revolving orbits was his first attempt to understand apsidal precession quantitatively. According to this theorem, the addition of a particular type of central force—the inverse-cube force—can produce a rotating orbit; the angular speed is multiplied by a factor k , whereas the radial motion is left unchanged.
Newton derived an early theorem which attempted to explain apsidal precession. This theorem is historically notable, but it was never widely used and it proposed forces which have been found not to exist, making the theorem invalid. This theorem of revolving orbits remained largely unknown and undeveloped for over three centuries until 1995. [14]
In classical mechanics, the central-force problem is to determine the motion of a particle in a single central potential field.A central force is a force (possibly negative) that points from the particle directly towards a fixed point in space, the center, and whose magnitude only depends on the distance of the object to the center.
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In astrodynamics, the vis-viva equation is one of the equations that model the motion of orbiting bodies.It is the direct result of the principle of conservation of mechanical energy which applies when the only force acting on an object is its own weight which is the gravitational force determined by the product of the mass of the object and the strength of the surrounding gravitational field.
The inverse-cube force is chosen to change the 2nd (blue), 3rd (green) and 6th (red) harmonics of the base ellipse (shown in black). The eccentricity is 0.8, as in Newton revolving orbits 1 inv2 inv3.png and Newton revolving orbits 1 0.95.png.
Nearly a century later, Isaac Newton had formulated his three laws of motion. In particular, Newton's second law states that a force F applied to a mass m produces an acceleration a given by the equation F=ma. Newton then posed the question: what must the force be that produces the elliptical orbits seen by Kepler?
Composed in 1669, [4] during the mid-part of that year probably, [5] from ideas Newton had acquired during the period 1665–1666. [4] Newton wrote And whatever the common Analysis performs by Means of Equations of a finite number of Terms (provided that can be done) this new method can always perform the same by means of infinite Equations.