Inner third-body perturbations
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(2020) 132:31
ORIGINAL ARTICLE
Inner third-body perturbations Guy Marcus1
· Pini Gurfil1
Received: 8 December 2019 / Revised: 12 June 2020 / Accepted: 18 June 2020 © Springer Nature B.V. 2020
Abstract Third-body perturbations have been extensively studied in recent years. Almost all previous works, however, assumed that the perturbations are caused by a third body that orbits the primary on a radius larger than the semimajor axis of the perturbed object. This assumption is justified as long as the primary is not accompanied by a third body in close orbit. In this work, we present an analytic model for the dynamics of a perturbed object that orbits the primary on an orbit with a semimajor axis larger than the semimajor axis of the third body. Such a third body is referred to as an inner third body. An analysis of the long-term evolution of the orbital elements is presented, followed by simulation results, which demonstrate the validity of the model. A more generalized model is then developed, which includes a nonzero eccentricity for the orbit of the third body. An analogy between the J2 problem and the inner third-body perturbation is indicated as well. Keywords Perturbations · Inner third body · Double averaging
1 Introduction The development of semi-analytical orbital models dates back to the work of Brouwer (1959), who separated the influence of the J2 perturbation into short-period, long-period and secular variations. This perturbation is dominant in low orbits. For higher orbits, third-body perturbations must be taken into account. For example, in the high Earth orbit region, the lunisolar attraction becomes a dominant perturbation. One of the first models of third-body perturbations was developed by Kozai (1966), who published a comprehensive special report, which introduced the short-period solutions for the orbital elements. Kozai (1966) showed that in order to compute the position of a satellite with seven significant digits, even if the mean motion is as large as ten revolutions per day, lunisolar short-period perturbations should be taken into account. Later Kozai (1973) used the ecliptic reference system for the Moon and the equatorial system for the satellite and introduced a new method for the evaluation of lunisolar per-
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Guy Marcus [email protected] Pini Gurfil [email protected]
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Faculty of Aerospace Engineering, Technion – Israel Institute of Technology, Haifa, Israel 0123456789().: V,-vol
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turbations, wherein it was proposed to compute secular and long-period perturbations by numerical integration and short-period perturbations by analytical formulae. A simplified approximate model was introduced by Broucke (2003), who described the effect of the third-body perturbation on a satellite using double averaging over the mean anomaly of the satellite, as well as the mean anomaly of a distant third body. This yielded an analytic model for the evolution of the mean orbital elements during a long time period. Solórzano and Prado
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