Orbital perturbation analysis (spacecraft)

Orbital perturbation analysis is the activity of determining why a satellite's orbit differs from the mathematical ideal orbit. A satellite's orbit in an ideal two-body system describes a conic section, usually an ellipse. In reality, there are several factors that cause the conic section to continually change. These deviations from the ideal Kepler's orbit are called perturbations.

It has long been recognized that the Moon does not follow a perfect orbit, and many theories and models have been examined over the millennia to explain it. Isaac Newton determined the primary contributing factor to orbital perturbation of the moon was that the shape of the Earth is actually an oblate spheroid due to its spin, and he used the perturbations of the lunar orbit to estimate the oblateness of the Earth.

In Newton's Philosophiæ Naturalis Principia Mathematica, he demonstrated that the gravitational force between two mass points is inversely proportional to the square of the distance between the points, and he fully solved the corresponding "two-body problem" demonstrating that the radius vector between the two points would describe an ellipse. But no exact closed analytical form could be found for the three body problem. Instead, mathematical models called "orbital perturbation analysis" have been developed. With these techniques a quite accurate mathematical description of the trajectories of all the planets could be obtained. Newton recognized that the Moon's perturbations could not entirely be accounted for using just the solution to the three body problem, as the deviations from a pure Kepler orbit around the Earth are much larger than deviations of the orbits of the planets from their own Sun-centered Kepler orbits, caused by the gravitational attraction between the planets. With the availability of digital computers and the ease with which we can now compute orbits, this problem has partly disappeared, as the motion of all celestial bodies including planets, satellites, asteroids and comets can be modeled and predicted with almost perfect accuracy using the method of the numerical propagation of the trajectories. Nevertheless several analytical closed form expressions for the effect of such additional "perturbing forces" are still very useful.

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