Frozen orbits at high eccentricity and inclination: application to Mercury orbiter

Research output: Book/Report/JournalOther report

Abstract

We hereby study the stability of a massless probe orbiting around an oblate central body (planet or planetary satellite) perturbed by a third body, assumed to lie in the equatorial plane (Sun or Jupiter for example) using an Hamiltonian formalism. We are able to determine, in the parameters space, the location of the frozen orbits, namely orbits whose orbital elements remain constant on average, to characterize their stability/unstability and to compute the periods of the equilibria. The proposed theory is general enough, to be applied to a wide range of probes around planet or natural planetary satellites. The BepiColombo mission is used to motivate our analysis and to provide specific numerical data to check our analytical results. Finally, we also bring to the light that the coefficient $J_2$ is able to protect against the increasing of the eccentricity due to the Kozai-Lidov effect.
Original languageEnglish
Place of PublicationNamur
PublisherFUNDP, Faculté des Sciences. Département de Mathématique.
Publication statusPublished - 2010

Fingerprint

natural satellites
eccentricity
inclination
planets
orbits
orbital elements
probes
Jupiter (planet)
sun
formalism
coefficients

Keywords

  • Methods: analytical study
  • Stability
  • Long-term evolution
  • Kozai resonances
  • Frozen Orbit equilibria

Cite this

Delsate, N., Robutel, P., Lemaître, A., & Carletti, T. (2010). Frozen orbits at high eccentricity and inclination: application to Mercury orbiter. Namur: FUNDP, Faculté des Sciences. Département de Mathématique.
Delsate, Nicolas ; Robutel, P. ; Lemaître, Anne ; Carletti, Timoteo. / Frozen orbits at high eccentricity and inclination: application to Mercury orbiter. Namur : FUNDP, Faculté des Sciences. Département de Mathématique., 2010.
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abstract = "We hereby study the stability of a massless probe orbiting around an oblate central body (planet or planetary satellite) perturbed by a third body, assumed to lie in the equatorial plane (Sun or Jupiter for example) using an Hamiltonian formalism. We are able to determine, in the parameters space, the location of the frozen orbits, namely orbits whose orbital elements remain constant on average, to characterize their stability/unstability and to compute the periods of the equilibria. The proposed theory is general enough, to be applied to a wide range of probes around planet or natural planetary satellites. The BepiColombo mission is used to motivate our analysis and to provide specific numerical data to check our analytical results. Finally, we also bring to the light that the coefficient $J_2$ is able to protect against the increasing of the eccentricity due to the Kozai-Lidov effect.",
keywords = "Methods: analytical study, Stability, Long-term evolution, Kozai resonances, Frozen Orbit equilibria",
author = "Nicolas Delsate and P. Robutel and Anne Lema{\^i}tre and Timoteo Carletti",
note = "Publication code : FP SB010/2010/04 ; QA 0002.2/001/10/04",
year = "2010",
language = "English",
publisher = "FUNDP, Facult{\'e} des Sciences. D{\'e}partement de Math{\'e}matique.",

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Delsate, N, Robutel, P, Lemaître, A & Carletti, T 2010, Frozen orbits at high eccentricity and inclination: application to Mercury orbiter. FUNDP, Faculté des Sciences. Département de Mathématique., Namur.

Frozen orbits at high eccentricity and inclination: application to Mercury orbiter. / Delsate, Nicolas; Robutel, P.; Lemaître, Anne; Carletti, Timoteo.

Namur : FUNDP, Faculté des Sciences. Département de Mathématique., 2010.

Research output: Book/Report/JournalOther report

TY - BOOK

T1 - Frozen orbits at high eccentricity and inclination: application to Mercury orbiter

AU - Delsate, Nicolas

AU - Robutel, P.

AU - Lemaître, Anne

AU - Carletti, Timoteo

N1 - Publication code : FP SB010/2010/04 ; QA 0002.2/001/10/04

PY - 2010

Y1 - 2010

N2 - We hereby study the stability of a massless probe orbiting around an oblate central body (planet or planetary satellite) perturbed by a third body, assumed to lie in the equatorial plane (Sun or Jupiter for example) using an Hamiltonian formalism. We are able to determine, in the parameters space, the location of the frozen orbits, namely orbits whose orbital elements remain constant on average, to characterize their stability/unstability and to compute the periods of the equilibria. The proposed theory is general enough, to be applied to a wide range of probes around planet or natural planetary satellites. The BepiColombo mission is used to motivate our analysis and to provide specific numerical data to check our analytical results. Finally, we also bring to the light that the coefficient $J_2$ is able to protect against the increasing of the eccentricity due to the Kozai-Lidov effect.

AB - We hereby study the stability of a massless probe orbiting around an oblate central body (planet or planetary satellite) perturbed by a third body, assumed to lie in the equatorial plane (Sun or Jupiter for example) using an Hamiltonian formalism. We are able to determine, in the parameters space, the location of the frozen orbits, namely orbits whose orbital elements remain constant on average, to characterize their stability/unstability and to compute the periods of the equilibria. The proposed theory is general enough, to be applied to a wide range of probes around planet or natural planetary satellites. The BepiColombo mission is used to motivate our analysis and to provide specific numerical data to check our analytical results. Finally, we also bring to the light that the coefficient $J_2$ is able to protect against the increasing of the eccentricity due to the Kozai-Lidov effect.

KW - Methods: analytical study

KW - Stability

KW - Long-term evolution

KW - Kozai resonances

KW - Frozen Orbit equilibria

M3 - Other report

BT - Frozen orbits at high eccentricity and inclination: application to Mercury orbiter

PB - FUNDP, Faculté des Sciences. Département de Mathématique.

CY - Namur

ER -

Delsate N, Robutel P, Lemaître A, Carletti T. Frozen orbits at high eccentricity and inclination: application to Mercury orbiter. Namur: FUNDP, Faculté des Sciences. Département de Mathématique., 2010.