Lie series solution of the bicircular problem

Abouelmagd, Elbaz I.; Mia, Rajib; Perdiou, A. E.

doi:10.1016/j.rinp.2021.104848

Cited by 7 publications

(2 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this model, the lunar orbit is still assumed as a circle, and the barycenter of the Earth+Moon is assumed to be on a circular orbit around the Sun (Simó et al 1995). This model has been extensively used in studies of orbital motions in the Earth-Moon system (Abouelmagd et al 2021;Jorba & Nicolás 2021;Singh et al 2021). The problem with the BCP model is that it is incoherent.…”

Section: Introductionmentioning

confidence: 99%

The Main Problem of Lunar Orbit Revisited

Hou

2023

View full text Add to dashboard Cite

A novel algorithm based on the Lindstedt–Poincaré method is proposed to construct an analytical solution of the lunar orbit. Based on the analytical solution, a numerical fitting algorithm is proposed to improve the coefficients of the analytical solution so that its accuracy can reach the level of a few kilometers within 20 yr. By fitting our solution to the long-term JPL ephemerides, we are able to recover the receding speed of the Moon from the Earth due to tidal effects. The proposed algorithm also provides a general way to treat the third-body perturbation in rectangular coordinates.

show abstract

Section: Introductionmentioning

confidence: 99%

The Main Problem of Lunar Orbit Revisited

Hou

2023

View full text Add to dashboard Cite

show abstract

“…There are many researchers who have studied the stability of solar system and exoplanetary systems. Many researchers (Abouelmagd et al, 2013;Pal and Kushvah, 2015;Singh et al, 2016;Mia and Kushvah, 2016b;Singh et al, 2018;Yadav et al, 2021;Abouelmagd et al, 2021;Gyegwe et al, 2022) aslo studied the stability of an infinitesimal particle like asteroid, satellite, dust grain etc., in the solar and exoplanetary systems. For example Petrovich (2015) studied the stability and fates of hierarchical tow planet systems with arbitrary eccentricities and mutual inclinations.…”

Section: Introductionmentioning

confidence: 99%

Analysis of the dynamics of the resonant planetary system HD 45364

Mia

Paul

2022

Preprint

Self Cite

View full text Add to dashboard Cite

The aim of this work is to analyse the orbital dynamics and stability of exoplanetary system in which two planets are in nearly 3:2 MMR. We have taken HD 45364 system for our study in which two planets are most likely in a 3:2 MMR. We have plotted two resonant angles and the relative apsidal longitudes and it is observed that they are librating around a constant value. From this observation our opinion is that there exist nearly 3:2 MMR between HD 45364b and HD 45364c. The perturbative solution is obtained for the time variation of the semi-major axes. The short and long term variations of semimajor axes are studied. For the validation of our analytical results we have compared our analytical solutions with the numerical solutions. The effect of planetary perturbations on eccentricity is studied with the help of secular resonance dynamics theory. The short and long term variations of eccentricities of HD 45364b and HD 45364c are shown graphically. Moreover, using the latest stability criteria, we have studied the dynamical stability of HD 45364 system.

show abstract

Halo orbits around $L_{1}$, $L_{2}$, and $L_{3}$ in the photogravitational Sun–Mars elliptical restricted three-body problem

Sheth

Thomas

2022

Astrophys Space Sci

View full text Add to dashboard Cite

Lie series solution of the bicircular problem

Cited by 7 publications

References 25 publications

The Main Problem of Lunar Orbit Revisited

The Main Problem of Lunar Orbit Revisited

Analysis of the dynamics of the resonant planetary system HD 45364

Halo orbits around $L_{1}$, $L_{2}$, and $L_{3}$ in the photogravitational Sun–Mars elliptical restricted three-body problem

Contact Info

Product

Resources

About