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The determination of preliminary orbit by Laplace method in the framework of generalized problem of two fixed centers

V. Kuznetsov

Известия ГАО в Пулкове, № 225: Труды Всероссийской астрометрической конференции «Пулково-2018», Санкт-Петербург, 261–266 (2018)

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Laplace's method for determination of preliminary orbit of the artificial satellite is investigated. This work is continuation of the researches begun by N.I. Perov. The classical method of determination of an orbit for the point attracting center is transferred to point-to-point model with complex–conjugated masses and an imaginary distance between them. Such approach is allowed to consider the perturbation until to the third harmonica of a geopotential in the movement of artificial satellite. For Laplace's method the use of an intermediate geopotential is brings to more difficult then kepler form of the equations. The form, which was proposed by N.V. Emelyanov for derivatives of potential function, allows reducing the system to equation of the 38th degree of rather topocentric distance to an object. For its decision, it is offered using the continuation method with the best parametrization. For that, the corresponding system of the differential equations was constructed.