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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.
At the top of the diagram, a satellite in a clockwise circular orbit (yellow spot) launches objects of negligible mass: (1 - blue) towards Earth, (2 - red) away from Earth, (3 - grey) in the direction of travel, and (4 - black) backwards in the direction of travel. Dashed ellipses are orbits relative to Earth.
English: Schematic illustrating Newton's theorem of revolving orbits. Meant to be coupled with Image:Newton revolving orbit 3rd subharmonic e0.6 240frames smaller.gif. The smaller angle θ here is 20 degrees, whereas the larger angle kθ equals 60 degrees; hence, k equals 3.
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.
Printable version; In other projects ... Newton's theorem may refer to: Newton's theorem (quadrilateral) ... Newton's theorem about ovals; Newton's theorem of ...
Theorem 2 considers a body moving uniformly in a circular orbit, and shows that for any given time-segment, the centripetal force (directed towards the center of the circle, treated here as a center of attraction) is proportional to the square of the arc-length traversed, and inversely proportional to the radius.
General relativity is a more exact theory than Newton's laws for calculating orbits, and it is sometimes necessary to use it for greater accuracy or in high-gravity situations (e.g. orbits near the Sun).