{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T00:31:59Z","timestamp":1760229119681,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2022,5,31]],"date-time":"2022-05-31T00:00:00Z","timestamp":1653955200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"RUDN University Strategic Academic Leadership Program"},{"name":"National Council for Scientific and Technological Development (CNPq)"},{"name":"Coordination of Superior Level Staff Improvement (CAPES)"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>To present a set of trajectories derived from the retrograde periodic orbits around the Lagrangian equilibrium point L1, this paper considers the Circular Restricted Three-body Problem with Earth-Moon masses (CR3BP), the Restricted Bicircular, and Full Four-Body Sun-Earth-Moon-spacecraft Problems (BCR4BP and FR4BP, respectively). These periodic orbits are predicted by the dynamics of the CR3BP. To generate the trajectories of this set, first, slightly different increments of velocity (\u2206Vs) from those needed to generate periodic orbits around L1 are applied to a spacecraft in circular low Earth orbits in the same direction of their motion when the Earth, the spacecraft, and the Moon are aligned in this order. Thus, translunar trajectories derived from the periodic orbits are obtained and they will lead the spacecraft to the vicinity of the Moon. Depending on the values of the |\u2206Vs|, which are also functions of the relative positioning between the Sun, the Earth, and the Moon, three types of trajectories of interest are found: Collision with the Moon, escape, and geocentric orbits with large semi-major axes. For a well-defined interval of the |\u2206Vs|, the trajectories accomplish swing-bys with the Moon and obtain energy to escape from the Earth\u2013Moon system and reach Near-Earth Asteroids (NEAs) between the orbits of Venus and Mars. This procedure reduces the costs of inserting spacecraft into transfer trajectories to a set of NEAs in terms of the required |\u2206V| by up to 5% when compared to Lambert\u2019s problem, for example. This work also presents analyses of examples of transfers to the NEAs 3361 Orpheus, 99942 Apophis, and 65803 Didymos, from 2025 on.<\/jats:p>","DOI":"10.3390\/sym14061132","type":"journal-article","created":{"date-parts":[[2022,5,31]],"date-time":"2022-05-31T09:24:29Z","timestamp":1653989069000},"page":"1132","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Trajectories Derived from Periodic Orbits around the Lagrangian Point L1 and Lunar Swing-Bys: Application in Transfers to Near-Earth Asteroids"],"prefix":"10.3390","volume":"14","author":[{"given":"Rebeca S.","family":"Ribeiro","sequence":"first","affiliation":[{"name":"Space Mechanics and Control Division (CMC), National Institute for Space Research, INPE, S\u00e3o Jos\u00e9 dos Campos 12227-010, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cristiano F.","family":"de Melo","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering (DEMEC), Federal University of Minas Gerais, UFMG, Belo Horizonte 31270-901, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ant\u00f4nio F. B. A.","family":"Prado","sequence":"additional","affiliation":[{"name":"Graduate Division (DIPGR) National Institute for Space Research, INPE, S\u00e3o Jos\u00e9 dos Campos 12227-010, Brazil"},{"name":"Academy of Engineering, Peoples\u2019 Friendship University of Russia (RUDN University), 6 Miklukho Maklaya, Moscow 117198, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,5,31]]},"reference":[{"key":"ref_1","unstructured":"Minor Planet Center (2022, March 30). \u201cLatest Published Data,\u201d 2022. Available online: https:\/\/www.minorplanetcenter.net\/mpc\/summary."},{"key":"ref_2","unstructured":"Asteroids, T.G. (1979). Orbital Classes, Collision Rates with Earth, and Origin, University of Arizona Press."},{"key":"ref_3","unstructured":"Broucke, R.A. (1968). Periodic orbits in the restricted three body problem with earth-moon masses. Tech. Rep."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/j.asr.2007.03.020","article-title":"Alternative paths for insertion of probes into high inclination lunar orbits","volume":"40","author":"Macau","year":"2007","journal-title":"Adv. Space Res."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1007\/s10569-009-9193-6","article-title":"Strategies for plane change of Earth orbits using lunar gravity and derived trajectories of family G","volume":"103","author":"Macau","year":"2009","journal-title":"Celest. Mech. Dyn. Astron."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"303604","DOI":"10.1155\/2009\/303604","article-title":"Alternative Transfers to the NEOs 99942 Apophis, 1994 WR12, and 2007 UW1 via Derived Trajectories from Periodic Orbits of Family G","volume":"2009","author":"Macau","year":"2009","journal-title":"Math. Probl. Eng."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1007\/s10569-012-9426-y","article-title":"Three-body problem, its Lagrangian points and how to exploit them using an alternative transfer to L4 and L5","volume":"114","author":"Salazar","year":"2012","journal-title":"Celest. Mech. Dyn. Astron."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0019-1035(82)90096-3","article-title":"An analysis of the physical, chemical, optical, and historical impacts of the 1908 Tunguska meteor fall","volume":"50","author":"Turco","year":"1982","journal-title":"Icarus"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1146\/annurev.ea.11.050183.002333","article-title":"Asteroid and comet bombardment of the Earth","volume":"11","author":"Shoemaker","year":"1983","journal-title":"Annu. Rev. Earth Planet. Sci."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"878","DOI":"10.1126\/science.257.5072.878.a","article-title":"Huge impact tied to mass extinction","volume":"257","author":"Kerr","year":"1992","journal-title":"Science"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1069","DOI":"10.1126\/science.1242642","article-title":"Chelyabinsk airburst, damage assessment, meteorite recovery, and characterization","volume":"342","author":"Popova","year":"2013","journal-title":"Science"},{"key":"ref_12","unstructured":"The Guardian (2022, May 23). Scientists Reveal the Full Power of the Chelyabinsk Meteor Explosion. Available online: https:\/\/www.theguardian.com\/science\/2013\/nov\/06\/chelyabinsk-meteor-russia#:~:text=Travelling%20at%20a%20speed%20of,knock%20people%20off%20their%20feet."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"539","DOI":"10.1146\/annurev.earth.32.101802.120453","article-title":"Space weathering of asteroid surfaces","volume":"32","author":"Chapman","year":"2004","journal-title":"Annu. Rev. Earth Planet. Sci."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1016\/S0094-5765(02)00098-X","article-title":"The NEAR shoemaker mission to asteroid 433 eros","volume":"51","author":"Prockter","year":"2002","journal-title":"Acta Astronaut."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"639","DOI":"10.1016\/j.actaastro.2008.01.028","article-title":"Hayabusa\u2014Its technology and science accomplishment summary and Hayabusa-2","volume":"62","author":"Kawaguchi","year":"2008","journal-title":"Acta Astronaut."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1016\/j.actaastro.2020.02.035","article-title":"Hayabusa2 mission status: Landing, roving and cratering on asteroid Ryugu","volume":"171","author":"Tsuda","year":"2020","journal-title":"Acta Astronaut."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"925","DOI":"10.1007\/s11214-017-0405-1","article-title":"OSIRIS-REx: Sample Return from Asteroid (101955) Bennu","volume":"212","author":"Lauretta","year":"2017","journal-title":"Space Sci. Rev."},{"key":"ref_18","unstructured":"NASA (2022, April 19). NASA, SpaceX Launch DART: First Test Mission to Defend Planet Earth, Available online: https:\/\/www.nasa.gov\/press-release\/nasa-spacex-launch-dart-first-test-mission-to-defend-planet-earth."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2529","DOI":"10.1016\/j.asr.2016.03.031","article-title":"Science case for the Asteroid Impact Mission (AIM): A component of the Asteroid Impact & Deflection Assessment (AIDA) mission","volume":"57","author":"Michel","year":"2016","journal-title":"Adv. Space Res."},{"key":"ref_20","first-page":"EPSC-DPS2019","article-title":"Observations of Didymos in support of DART and Hera","volume":"2019","author":"Scheirich","year":"2019","journal-title":"EPSC-DPS Jt. Meet."},{"key":"ref_21","first-page":"329","article-title":"Perturbation maneuvers","volume":"13","author":"Lawden","year":"1954","journal-title":"J. Br. Interplanet Soc."},{"key":"ref_22","first-page":"130","article-title":"A method for determining interplanetary free-fall reconnaissance trajectories","volume":"312","author":"Minovitch","year":"1961","journal-title":"JPL Tec. Memo."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Broucke, R. (1988). The celestial mechanics of gravity assist. Astrodyn. Conf., 69\u201378.","DOI":"10.2514\/6.1988-4220"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Dunham, D., and Davis, S. (1985). Optimization of a multiple lunar-swingby trajectory sequence. Astrodyn. Conf., 1978.","DOI":"10.2514\/6.1984-1978"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1590\/S1678-58782006000100012","article-title":"Orbital control of a satellite using the gravity of the moon","volume":"28","author":"Prado","year":"2006","journal-title":"J. Braz. Soc. Mech. Sci. Eng."},{"key":"ref_26","first-page":"4","article-title":"Detour to a Comet; Journey of the International Cometary Explorer","volume":"5","author":"Farquhar","year":"1985","journal-title":"Planet. Rep."},{"key":"ref_27","unstructured":"NASA Science (2021, September 22). ISEE-3\/ICE, Available online: https:\/\/solarsystem.nasa.gov\/missions\/isee-3-ice\/in-depth\/."},{"key":"ref_28","unstructured":"Kawaguchi, J. (1999). On the lunar and heliocentric gravity assist experienced in the planet-b (\u2018nozomi\u2019). Fourth Int. Symp. Space Flight Dyn. Iguassu Falls Braz., 8\u201312."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1016\/S0094-5765(02)00156-X","article-title":"Synthesis of an alternative flight trajectory for Mars explorer, Nozomi","volume":"52","author":"Kawaguchi","year":"2003","journal-title":"Acta Astronaut."},{"key":"ref_30","unstructured":"National Aeronautics and Space Administration (2021, September 22). \u201cNozomi,\u201d NASA Space Science Data Coordinated Archive, Available online: https:\/\/nssdc.gsfc.nasa.gov\/nmc\/spacecraft\/display.action?id=1998-041A."},{"key":"ref_31","first-page":"104","article-title":"STEREO trajectory and maneuver design","volume":"28","author":"Dunham","year":"2009","journal-title":"Johns Hopkins APL Tech. Dig."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"232","DOI":"10.1196\/annals.1370.021","article-title":"Trajectory analysis for the lunar flyby rescue of AsiaSat-3\/HGS-1","volume":"1065","author":"Ocampo","year":"2005","journal-title":"Ann. N. Y. Acad Sci."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Murray, C.D., and Dermott, S.F. (1999). Solar System Dynamics, Cambridge University Press.","DOI":"10.1017\/CBO9781139174817"},{"key":"ref_34","first-page":"1","article-title":"Connaissance actuelle des orbites dans le probleme des trois corps","volume":"100","author":"Stroemgren","year":"1933","journal-title":"Publ. Og Mindre Meddeler Fra Kbh. Obs."},{"key":"ref_35","unstructured":"Jet Propulsion Laboratory (JPL) (2022, May 15). Horizons System, Available online: https:\/\/ssd.jpl.nasa.gov\/horizons\/."},{"key":"ref_36","unstructured":"Jet Propulsion Laboratory (JPL) (2022, May 23). Horizons Web Application, Available online: https:\/\/ssd.jpl.nasa.gov\/horizons\/app.html#\/."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/6\/1132\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:22:33Z","timestamp":1760138553000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/6\/1132"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,31]]},"references-count":36,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2022,6]]}},"alternative-id":["sym14061132"],"URL":"https:\/\/doi.org\/10.3390\/sym14061132","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2022,5,31]]}}}