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The topic osculating orbit is discussed in the following articles:
...with a being the semimajor axis of the cometary orbit. The original value of a refers to the orbit when the comet was still outside of the solar system, as opposed to the osculating orbit, which refers to the arc observed from Earth after it has been modified by the perturbations of the giant planets. Passages through the solar system produce a rather wide diffusion...
The best conic section representing the path of the comet at a given instant is known as the osculating orbit. It is tangent to the true path of the chosen instant, and the velocity at that point is the same as the true instantaneous velocity of the comet. Nowadays, high-speed computers make it possible to produce a final ephemeris (table of positions) that is not only based on the definitive...
...perturbations the orbit is approximately an ellipse. In fact, however, perturbations cause the six formerly constant parameters to vary slowly, and the instantaneous perturbed orbit is called an osculating ellipse; that is, the osculating ellipse is that elliptical orbit that would be assumed by the body if all the perturbing forces were suddenly turned off.
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