Skip to main content
Erschienen in: Archive of Applied Mechanics 12/2021

04.09.2021 | Original

Analysis of nominal halo orbits in the Sun–Earth system

verfasst von: Elbaz I. Abouelmagd, Ashok Kumar Pal, Juan Luis García Guirao

Erschienen in: Archive of Applied Mechanics | Ausgabe 12/2021

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

In this paper, the effect of radiation pressure force on formation of the nominal halo orbit around the collinear point \(L_1\) is estimated in the framework of Sun–Earth system. Using Lindstedt–Poincaré technique, the periodic solutions up to third-order approximation are computed. Further, the Fourier series solutions of nominal halo orbit are also evaluated. With considering the radiation pressure force effect, the proposed analysis in this work can be used to design a trajectory for spacecraft moving in more realistic system.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Anhänge
Nur mit Berechtigung zugänglich
Literatur
1.
Zurück zum Zitat Abouelmagd, E.I., Mostafa, A., Guirao, J.L.: A first order automated lie transform. Int. J. Bifurcation Chaos 25(14), 1540026 (2015)MathSciNetCrossRef Abouelmagd, E.I., Mostafa, A., Guirao, J.L.: A first order automated lie transform. Int. J. Bifurcation Chaos 25(14), 1540026 (2015)MathSciNetCrossRef
2.
Zurück zum Zitat Pathak, N., Abouelmagd, E.I., Thomas, V.: On higher order resonant periodic orbits in the photo-gravitational planar restricted three-body problem with oblateness. J. Astronaut. Sci. 66(4), 475–505 (2019)CrossRef Pathak, N., Abouelmagd, E.I., Thomas, V.: On higher order resonant periodic orbits in the photo-gravitational planar restricted three-body problem with oblateness. J. Astronaut. Sci. 66(4), 475–505 (2019)CrossRef
3.
Zurück zum Zitat Abouelmagd, E.I., Guirao, J.L.G., Llibre, J.: Periodic orbits for the perturbed planar circular restricted 3-body problem. Dis. Contin. Dyn. Syst. Ser. B 24, 1007–1020 (2019)MathSciNetMATH Abouelmagd, E.I., Guirao, J.L.G., Llibre, J.: Periodic orbits for the perturbed planar circular restricted 3-body problem. Dis. Contin. Dyn. Syst. Ser. B 24, 1007–1020 (2019)MathSciNetMATH
4.
Zurück zum Zitat Abd El-Bar, S., Abd El-Salam, F., Al-Burkani, A.: Computation of the perturbed locations of l1 for all sun–planet rtbp systems with oblate primaries. Results Phys. 15, 0102659 (2019)CrossRef Abd El-Bar, S., Abd El-Salam, F., Al-Burkani, A.: Computation of the perturbed locations of l1 for all sun–planet rtbp systems with oblate primaries. Results Phys. 15, 0102659 (2019)CrossRef
5.
Zurück zum Zitat Zotos, E.E., Chen, W., Abouelmagd, E.I., Han, H.: Basins of convergence of equilibrium points in the restricted three-body problem with modified gravitational potential. Chaos Solitons Fractals 134, 109704 (2020)MathSciNetCrossRef Zotos, E.E., Chen, W., Abouelmagd, E.I., Han, H.: Basins of convergence of equilibrium points in the restricted three-body problem with modified gravitational potential. Chaos Solitons Fractals 134, 109704 (2020)MathSciNetCrossRef
6.
Zurück zum Zitat Alshaery, A., Abouelmagd, E.I.: Analysis of the spatial quantized three-body problem. Results Phys. 103067, (2020) Alshaery, A., Abouelmagd, E.I.: Analysis of the spatial quantized three-body problem. Results Phys. 103067, (2020)
7.
Zurück zum Zitat Pal, A.K., Abouelmagd, E.I., Kishor, R.: Effect of Moon perturbation on the energy curves and equilibrium points in the Sun–Earth–Moon system. New Astronomy 84, 101505 (2021)CrossRef Pal, A.K., Abouelmagd, E.I., Kishor, R.: Effect of Moon perturbation on the energy curves and equilibrium points in the Sun–Earth–Moon system. New Astronomy 84, 101505 (2021)CrossRef
8.
Zurück zum Zitat Ershkov, S., Rachinskaya, A.: Semi-analytical solution for the trapped orbits of satellite near the planet in ER3BP. Archive Appl. Mech. 91(4), 1407–1422 (2021)CrossRef Ershkov, S., Rachinskaya, A.: Semi-analytical solution for the trapped orbits of satellite near the planet in ER3BP. Archive Appl. Mech. 91(4), 1407–1422 (2021)CrossRef
9.
Zurück zum Zitat Pathak, N., Elshaboury, S.: On the triangular points within frame of the restricted three-body problem when both primaries are triaxial rigid bodies. Appl. Math. Nonlinear Sci. 2(2), 495–508 (2017)MathSciNetCrossRef Pathak, N., Elshaboury, S.: On the triangular points within frame of the restricted three-body problem when both primaries are triaxial rigid bodies. Appl. Math. Nonlinear Sci. 2(2), 495–508 (2017)MathSciNetCrossRef
10.
Zurück zum Zitat Atash, A.A., Selim, F., Al-Khaled, K., Hassan, I., Abouelmagd, E.I.: Periodic orbit in the frame work of restricted three bodies under the asteroids belt effect. Appl. Math. Nonlinear Sci. 5(2), 157–176 (2020)MathSciNetCrossRef Atash, A.A., Selim, F., Al-Khaled, K., Hassan, I., Abouelmagd, E.I.: Periodic orbit in the frame work of restricted three bodies under the asteroids belt effect. Appl. Math. Nonlinear Sci. 5(2), 157–176 (2020)MathSciNetCrossRef
11.
Zurück zum Zitat Abouelmagd, E.I., Asiri, H., Sharaf, M.: The effect of oblateness in the perturbed restricted three-body problem. Meccanica 48(10), 2479–2490 (2013)MathSciNetCrossRef Abouelmagd, E.I., Asiri, H., Sharaf, M.: The effect of oblateness in the perturbed restricted three-body problem. Meccanica 48(10), 2479–2490 (2013)MathSciNetCrossRef
12.
Zurück zum Zitat Singh, J., Kalantonis, V., Gyegwe, J.M., Perdiou, A.: Periodic motions around the collinear equilibrium points of the r3bp where the primary is a triaxial rigid body and the secondary is an oblate spheroid. Astrophys. J. Supplement Ser. 227(2), 13 (2016)CrossRef Singh, J., Kalantonis, V., Gyegwe, J.M., Perdiou, A.: Periodic motions around the collinear equilibrium points of the r3bp where the primary is a triaxial rigid body and the secondary is an oblate spheroid. Astrophys. J. Supplement Ser. 227(2), 13 (2016)CrossRef
13.
Zurück zum Zitat Abouelmagd, E.I., Alzahrani, F., Guirao, J.L.G., Hobiny, A.: Periodic orbits around the collinear libration points. J. Nonlinear Sci. Appl. (JNSA) 9(4), 1716–1727 (2016)MathSciNetCrossRef Abouelmagd, E.I., Alzahrani, F., Guirao, J.L.G., Hobiny, A.: Periodic orbits around the collinear libration points. J. Nonlinear Sci. Appl. (JNSA) 9(4), 1716–1727 (2016)MathSciNetCrossRef
14.
Zurück zum Zitat Alzahrani, F., Abouelmagd, E.I., Guirao, J.L.G., Hobiny, A.: On the libration collinear points in the restricted three-body problem. Open Phys. 15(1), 58–67 (2017)CrossRef Alzahrani, F., Abouelmagd, E.I., Guirao, J.L.G., Hobiny, A.: On the libration collinear points in the restricted three-body problem. Open Phys. 15(1), 58–67 (2017)CrossRef
15.
Zurück zum Zitat Selim, H.H., Guirao, J.L., Abouelmagd, E.I.: Libration points in the restricted three-body problem: Euler angles, existence and stability. Dis. Continuous Dyn. Syst. 12(4 & 5), 703 (2018)MathSciNetMATH Selim, H.H., Guirao, J.L., Abouelmagd, E.I.: Libration points in the restricted three-body problem: Euler angles, existence and stability. Dis. Continuous Dyn. Syst. 12(4 & 5), 703 (2018)MathSciNetMATH
16.
Zurück zum Zitat Pathak, N., Thomas, V., Abouelmagd, E.I.: The perturbed photogravitational restricted three-body problem: Analysis of resonant periodic orbits. Dis. Continuous Dyn. Syst. 12(4 & 5), 849–875 (2019)MathSciNetMATH Pathak, N., Thomas, V., Abouelmagd, E.I.: The perturbed photogravitational restricted three-body problem: Analysis of resonant periodic orbits. Dis. Continuous Dyn. Syst. 12(4 & 5), 849–875 (2019)MathSciNetMATH
17.
Zurück zum Zitat Farquhar, R.W.: Halo-orbit and lunar-swingby missions of the 1990s. Acta Astronautica 24, 227–234 (1991)CrossRef Farquhar, R.W.: Halo-orbit and lunar-swingby missions of the 1990s. Acta Astronautica 24, 227–234 (1991)CrossRef
18.
Zurück zum Zitat Wu, T., Pan, X., Xu, M., Qu, Q., Xia, Q., Liu, S.: Parallelly generating halo orbit and its transfer trajectory in the full ephemeris model. Astrophys. Space Sci. 364(1), 7 (2019)MathSciNetCrossRef Wu, T., Pan, X., Xu, M., Qu, Q., Xia, Q., Liu, S.: Parallelly generating halo orbit and its transfer trajectory in the full ephemeris model. Astrophys. Space Sci. 364(1), 7 (2019)MathSciNetCrossRef
19.
Zurück zum Zitat Shirobokov, M.: Libration point orbits and manifolds: Design and station-keeping. Keldysh Institute Preprints 90, 1–31 (2014) Shirobokov, M.: Libration point orbits and manifolds: Design and station-keeping. Keldysh Institute Preprints 90, 1–31 (2014)
21.
Zurück zum Zitat Simó, C., Gómez, G., Llibre, J., Martinez, R., Rodriguez, J.: On the optimal station keeping control of halo orbits. Acta Astronautica 15(6–7), 391–397 (1987)CrossRef Simó, C., Gómez, G., Llibre, J., Martinez, R., Rodriguez, J.: On the optimal station keeping control of halo orbits. Acta Astronautica 15(6–7), 391–397 (1987)CrossRef
22.
Zurück zum Zitat Simó, C.: Dynamical systems methods for space missions on a vicinity of collinear libration points. In: Hamiltonian Systems with Three or More Degrees of Freedom, Springer, pp. 223–241 (1999) Simó, C.: Dynamical systems methods for space missions on a vicinity of collinear libration points. In: Hamiltonian Systems with Three or More Degrees of Freedom, Springer, pp. 223–241 (1999)
23.
Zurück zum Zitat Zhang, Y., Zeng, X., Liu, X.: Study on periodic orbits around the dipole segment model for dumbbell-shaped asteroids. Sci. China Technol. Sci. 61(6), 819–829 (2018)CrossRef Zhang, Y., Zeng, X., Liu, X.: Study on periodic orbits around the dipole segment model for dumbbell-shaped asteroids. Sci. China Technol. Sci. 61(6), 819–829 (2018)CrossRef
24.
Zurück zum Zitat Hou, X., Xin, X., Feng, J.: Genealogy and stability of periodic orbit families around uniformly rotating asteroids. Commun. Nonlinear Sci. Numer. Simulat. 56, 93–114 (2018)MathSciNetCrossRef Hou, X., Xin, X., Feng, J.: Genealogy and stability of periodic orbit families around uniformly rotating asteroids. Commun. Nonlinear Sci. Numer. Simulat. 56, 93–114 (2018)MathSciNetCrossRef
25.
Zurück zum Zitat Shirobokov, M., Trofimov, S., Ovchinnikov, M.: Survey of station-keeping techniques for libration point orbits. J. Guidance Control Dyn. 40(5), 1085–1105 (2017)CrossRef Shirobokov, M., Trofimov, S., Ovchinnikov, M.: Survey of station-keeping techniques for libration point orbits. J. Guidance Control Dyn. 40(5), 1085–1105 (2017)CrossRef
26.
Zurück zum Zitat Zhang, Y., Zeng, X., Zhang, F.: Spacecraft hovering flight in a binary asteroid system by using fuzzy logic control. IEEE Trans. Aerosp. Electron. Syst. 55(6), 3246–3258 (2019)CrossRef Zhang, Y., Zeng, X., Zhang, F.: Spacecraft hovering flight in a binary asteroid system by using fuzzy logic control. IEEE Trans. Aerosp. Electron. Syst. 55(6), 3246–3258 (2019)CrossRef
27.
Zurück zum Zitat Shirobokov, M., Trofimov, S., Ovchinnikov, M.: On the design of a space telescope orbit around the sun–venus \(l_2\) point. Adv. Space Res. 65, 1591–1606 (2020)CrossRef Shirobokov, M., Trofimov, S., Ovchinnikov, M.: On the design of a space telescope orbit around the sun–venus \(l_2\) point. Adv. Space Res. 65, 1591–1606 (2020)CrossRef
28.
Zurück zum Zitat Yadav, A., Kushvah, B., Dolas, U.: Station-keeping error analysis for halo orbits around Libration point \(L1\) using linear control logic. Astronomy Comput. 35, 100462 (2021)CrossRef Yadav, A., Kushvah, B., Dolas, U.: Station-keeping error analysis for halo orbits around Libration point \(L1\) using linear control logic. Astronomy Comput. 35, 100462 (2021)CrossRef
29.
Zurück zum Zitat Eapen, R.T., Sharma, R.K.: Study of halo orbits at the Sun-Mars \(L_1\) Lagrangian point in the photogravitational restricted three-body problem. Astrophys. Space Sci. 352(2), 437–441 (2014)CrossRef Eapen, R.T., Sharma, R.K.: Study of halo orbits at the Sun-Mars \(L_1\) Lagrangian point in the photogravitational restricted three-body problem. Astrophys. Space Sci. 352(2), 437–441 (2014)CrossRef
30.
Zurück zum Zitat Pal, A.K., Kushvah, B.S.: Geometry of halo and Lissajous orbits in the circular restricted three-body problem with drag forces. Monthly Notices Royal Astronom. Soc. 446(1), 959–972 (2015)CrossRef Pal, A.K., Kushvah, B.S.: Geometry of halo and Lissajous orbits in the circular restricted three-body problem with drag forces. Monthly Notices Royal Astronom. Soc. 446(1), 959–972 (2015)CrossRef
31.
Zurück zum Zitat Srivastava, V.K., Kumar, J., Kushvah, B.S.: The effects of oblateness and solar radiation pressure on halo orbits in the photogravitational Sun–Earth system. Acta Astronautica 129, 389–399 (2016)CrossRef Srivastava, V.K., Kumar, J., Kushvah, B.S.: The effects of oblateness and solar radiation pressure on halo orbits in the photogravitational Sun–Earth system. Acta Astronautica 129, 389–399 (2016)CrossRef
32.
Zurück zum Zitat Gómez, G., Jorba, A., Masdemont, J., Simó, C.: Study of the transfer from the earth to a halo orbit around the equilibrium pointl 1. Celestial Mech. Dyn. Astronomy 56(4), 541–562 (1993)CrossRef Gómez, G., Jorba, A., Masdemont, J., Simó, C.: Study of the transfer from the earth to a halo orbit around the equilibrium pointl 1. Celestial Mech. Dyn. Astronomy 56(4), 541–562 (1993)CrossRef
33.
Zurück zum Zitat Andreu, M.A., Simo, C.: Translunar halo orbits in the quasibicircular problem. In: The Dynamics of Small Bodies in the Solar System, Springer, pp. 309–314 (1999) Andreu, M.A., Simo, C.: Translunar halo orbits in the quasibicircular problem. In: The Dynamics of Small Bodies in the Solar System, Springer, pp. 309–314 (1999)
34.
Zurück zum Zitat Yingjing, Q., Xiaodong, Y., Wuxing, J., Zhang, W.: An improved numerical method for constructing halo/lissajous orbits in a full solar system model. Chin. J. Aeronaut. 31(6), 1362–1374 (2018)CrossRef Yingjing, Q., Xiaodong, Y., Wuxing, J., Zhang, W.: An improved numerical method for constructing halo/lissajous orbits in a full solar system model. Chin. J. Aeronaut. 31(6), 1362–1374 (2018)CrossRef
35.
Zurück zum Zitat Angelopoulos, V.: The artemis mission. In: The ARTEMIS mission. Springer, pp. 3–25 (2010) Angelopoulos, V.: The artemis mission. In: The ARTEMIS mission. Springer, pp. 3–25 (2010)
36.
Zurück zum Zitat Sweetser, T.H., Broschart, S.B., Angelopoulos, V., Whiffen, G.J., Folta, D.C., Chung, M.-K., Hatch, S.J., Woodard, M.A.: Artemis mission design. In: The ARTEMIS Mission, Springer, pp. 61–91 (2012) Sweetser, T.H., Broschart, S.B., Angelopoulos, V., Whiffen, G.J., Folta, D.C., Chung, M.-K., Hatch, S.J., Woodard, M.A.: Artemis mission design. In: The ARTEMIS Mission, Springer, pp. 61–91 (2012)
37.
Zurück zum Zitat Abraham, A.J., Spencer, D.B., Hart, T.J.: Early mission design of transfers to halo orbits via particle swarm optimization. J. Astronaut. Sci. 63(2), 81–102 (2016)CrossRef Abraham, A.J., Spencer, D.B., Hart, T.J.: Early mission design of transfers to halo orbits via particle swarm optimization. J. Astronaut. Sci. 63(2), 81–102 (2016)CrossRef
38.
Zurück zum Zitat Heiligers, J., McInnes, C.R., Biggs, J.D., Ceriotti, M.: Displaced geostationary orbits using hybrid low-thrust propulsion. Acta Astronautica 71, 51–67 (2012)CrossRef Heiligers, J., McInnes, C.R., Biggs, J.D., Ceriotti, M.: Displaced geostationary orbits using hybrid low-thrust propulsion. Acta Astronautica 71, 51–67 (2012)CrossRef
39.
Zurück zum Zitat Zeng, X., Gong, S., Li, J., Alfriend, K.T.: Solar sail body-fixed hovering over elongated asteroids. J. Guidance Control Dyn. 39(6), 1223–1231 (2016)CrossRef Zeng, X., Gong, S., Li, J., Alfriend, K.T.: Solar sail body-fixed hovering over elongated asteroids. J. Guidance Control Dyn. 39(6), 1223–1231 (2016)CrossRef
40.
Zurück zum Zitat Iñarrea, M., Lanchares, V., Palacián, J.F., Pascual, A.I., Salas, J.P., Yanguas, P.: The effect of j2 on equatorial and halo orbits around a magnetic planet. Chaos Solitons Fractals 42(1), 155–169 (2009)MathSciNetCrossRef Iñarrea, M., Lanchares, V., Palacián, J.F., Pascual, A.I., Salas, J.P., Yanguas, P.: The effect of j2 on equatorial and halo orbits around a magnetic planet. Chaos Solitons Fractals 42(1), 155–169 (2009)MathSciNetCrossRef
41.
Zurück zum Zitat Sheth, D., Thomas, V., Abouelmagd, E.I., Srivastava, V.K.: Fifth order solution of halo orbits via lindstedt–poincaré technique and differential correction method. New Astronomy 87, 101585 (2021)CrossRef Sheth, D., Thomas, V., Abouelmagd, E.I., Srivastava, V.K.: Fifth order solution of halo orbits via lindstedt–poincaré technique and differential correction method. New Astronomy 87, 101585 (2021)CrossRef
42.
Zurück zum Zitat Ceccaroni, M., Celletti, A., Pucacco, G.: Bifurcations thresholds of halo orbits. In: Astrodynamics Network AstroNet-II: The Final Conference, Vol. 44, Springer, p. 35 (2016) Ceccaroni, M., Celletti, A., Pucacco, G.: Bifurcations thresholds of halo orbits. In: Astrodynamics Network AstroNet-II: The Final Conference, Vol. 44, Springer, p. 35 (2016)
43.
Zurück zum Zitat Farquhar, R., Muhonen, D., Richardson, D.: Mission design for a halo orbiter of the earth. In: Astrodynamics Conference, p. 810 (1976) Farquhar, R., Muhonen, D., Richardson, D.: Mission design for a halo orbiter of the earth. In: Astrodynamics Conference, p. 810 (1976)
44.
Zurück zum Zitat Thurman, R., Worfolk, P.A.: The geometry of halo orbits in the circular restricted three-body problem, University of Minnesota: Geometry Center Research Report GCG95 (1996) Thurman, R., Worfolk, P.A.: The geometry of halo orbits in the circular restricted three-body problem, University of Minnesota: Geometry Center Research Report GCG95 (1996)
45.
Zurück zum Zitat Tiwary, R.D., Kushvah, B.S.: Computation of halo orbits in the photogravitational sun–earth system with oblateness. Astrophys. Space Sci. 357(1), 1–16 (2015)CrossRef Tiwary, R.D., Kushvah, B.S.: Computation of halo orbits in the photogravitational sun–earth system with oblateness. Astrophys. Space Sci. 357(1), 1–16 (2015)CrossRef
46.
Zurück zum Zitat Conte, S.D., De Boor, C.: Elementary numerical analysis: an algorithmic approach. SIAM (2017) Conte, S.D., De Boor, C.: Elementary numerical analysis: an algorithmic approach. SIAM (2017)
Metadaten
Titel
Analysis of nominal halo orbits in the Sun–Earth system
verfasst von
Elbaz I. Abouelmagd
Ashok Kumar Pal
Juan Luis García Guirao
Publikationsdatum
04.09.2021
Verlag
Springer Berlin Heidelberg
Erschienen in
Archive of Applied Mechanics / Ausgabe 12/2021
Print ISSN: 0939-1533
Elektronische ISSN: 1432-0681
DOI
https://doi.org/10.1007/s00419-021-02031-y

Weitere Artikel der Ausgabe 12/2021

Archive of Applied Mechanics 12/2021 Zur Ausgabe

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.