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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, or 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. ==Perturbation of spacecraft orbits== 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-centred 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 modelled 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. All celestial bodies of the Solar System follow in first approximation a Kepler orbit around a central body. For a satellite (artificial or natural) this central body is a planet. But both due to gravitational forces caused by the Sun and other celestial bodies and due to the flattening of its planet (caused by its rotation which makes the planet slightly oblate and therefore the result of the Shell theorem not fully applicable) the satellite will follow an orbit around the Earth that deviates more than the Kepler orbits observed for the planets. The precise modelling of the motion of the Moon has been a difficult task. The best and most accurate modelling for the lunar orbit before the availability of digital computers was obtained with the complicated Delaunay and Brown's lunar theories. For man-made spacecraft orbiting the Earth at comparatively low altitudes the deviations from a Kepler orbit are much larger than for the Moon. The approximation of the gravitational force of the Earth to be that of a homogeneous sphere gets worse the closer one gets to the Earth surface and the majority of the artificial Earth satellites are in orbits that are only a few hundred kilometres over the Earth surface. Furthermore they are (as opposed to the Moon) significantly affected by the solar radiation pressure because of their large cross-section to mass ratio; this applies in particular to 3-axis stabilized spacecraft with large solar arrays. In addition they are significantly affected by rarefied air below 800–1000 km. The air drag at high altitudes is also dependent on solar activity. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Orbital perturbation analysis (spacecraft)」の詳細全文を読む スポンサード リンク
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