TY - JOUR

T1 - Higher-order composition of short- and long-period effects for satellite analytical ephemeris computation

AU - Lara, Martin

AU - Fantino, Elena

AU - Susanto, Hadi

AU - Flores, Roberto

N1 - Publisher Copyright:
© 2024 Elsevier B.V.

PY - 2024/10

Y1 - 2024/10

N2 - The construction of an analytic orbit theory in closed form of the eccentricity that takes into account the main effects of the Geopotential is notably simplified when splitting the removal of periodic effects in several stages. Conversely, this splitting of the closed-form analytical solution into several transformations reduces the evaluation efficiency for dense ephemeris output. However, the advantage is twofold when the different parts of the mean-to-osculating transformation are composed into a single transformation. To show that, Brouwer's solution is extended to the second order of the zonal harmonic of the second degree by the sequential elimination of short and long period terms. Then, the generating functions of the different transformations are composed into a single one, from which a single mean-to-osculating transformation is derived. The new, unique transformation notably speeds up the evaluation process, commonly improving evaluation efficiency by at least one third with respect to the customary decomposition of the analytical solution into three different parts.

AB - The construction of an analytic orbit theory in closed form of the eccentricity that takes into account the main effects of the Geopotential is notably simplified when splitting the removal of periodic effects in several stages. Conversely, this splitting of the closed-form analytical solution into several transformations reduces the evaluation efficiency for dense ephemeris output. However, the advantage is twofold when the different parts of the mean-to-osculating transformation are composed into a single transformation. To show that, Brouwer's solution is extended to the second order of the zonal harmonic of the second degree by the sequential elimination of short and long period terms. Then, the generating functions of the different transformations are composed into a single one, from which a single mean-to-osculating transformation is derived. The new, unique transformation notably speeds up the evaluation process, commonly improving evaluation efficiency by at least one third with respect to the customary decomposition of the analytical solution into three different parts.

KW - Artificial satellite theory

KW - Brouwer's solution

KW - Hamiltonian simplification

KW - Lie transforms

KW - Perturbations

UR - http://www.scopus.com/inward/record.url?scp=85197253524&partnerID=8YFLogxK

U2 - 10.1016/j.cnsns.2024.108023

DO - 10.1016/j.cnsns.2024.108023

M3 - Article

AN - SCOPUS:85197253524

SN - 1007-5704

VL - 137

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

M1 - 108023

ER -