Orbit correction on elliptical orbits: Part 2 Eccentricity 0 < e < 1

Using the extended Hill’s equations for elliptical orbits a method of path correction for satellites is presented. In part 1 the simplified differential equations for small eccentricities were used. In those governing equations the time was the independent variable. In this part the basic equations guilty for any elliptical orbit with the true anomaly as independent variable are used. Now, this time dependent orbital element may be used as variable instead of the transfer time. For such a chosen true anomaly at encounter, the two instantaneous velocity changes for a two-impulse transfer are determined. Additional the restrictions by singularities for this parameter are outlined by formulas and it is shown how the optimal parameter of minimal Δv, which is located between two singularities, will be computed. The objective function depends on one variable only, i.e. the true anomaly. Therefore, the minimum may be numerically determined straightforward by using an optimization program or more sophisticated by applying the Newton method. The method of path correction used here may be also applied to related problems of orbit mechanics. © Der/die Autor(en), exklusiv lizenziert an Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2024. Springer Nature oder sein Lizenzgeber (z.B. eine Gesellschaft oder ein*e andere*r Vertragspartner*in) hält die ausschließlichen Nutzungsrechte an diesem Artikel kraft eines Verlagsvertrags mit dem/den Autor*in(nen) oder anderen Rechteinhaber*in(nen); die Selbstarchivierung der akzeptierten Manuskriptversion dieses Artikels durch Autor*in(nen) unterliegt ausschließlich den Bedingungen dieses Verlagsvertrags und dem geltenden Recht.