{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:53:10Z","timestamp":1760147590803,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,2,14]],"date-time":"2023-02-14T00:00:00Z","timestamp":1676332800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001807","name":"S\u00e3o Paulo Research Foundation","doi-asserted-by":"publisher","award":["2016\/24561-0","2018\/19959-0","309089\/2021-2","202235-2-000"],"award-info":[{"award-number":["2016\/24561-0","2018\/19959-0","309089\/2021-2","202235-2-000"]}],"id":[{"id":"10.13039\/501100001807","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003593","name":"National Council for Scientific and Technological Development","doi-asserted-by":"publisher","award":["2016\/24561-0","2018\/19959-0","309089\/2021-2","202235-2-000"],"award-info":[{"award-number":["2016\/24561-0","2018\/19959-0","309089\/2021-2","202235-2-000"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100018647","name":"RUDN University Scientific Projects Grant System","doi-asserted-by":"publisher","award":["2016\/24561-0","2018\/19959-0","309089\/2021-2","202235-2-000"],"award-info":[{"award-number":["2016\/24561-0","2018\/19959-0","309089\/2021-2","202235-2-000"]}],"id":[{"id":"10.13039\/501100018647","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The present research performs numerical studies to search for the best maneuvers, from the point of view of minimum time, to make adjustments in the semi-major axis, eccentricity and inclination of a spacecraft traveling around the Earth. For those maneuvers, low thrust propulsion is used under optimal and sub-optimal assumptions, to verify the main differences in terms of transfer time. In addition, solar sail dynamics is used. The spacecraft is assumed to have a propulsion with a fixed magnitude and that the control is based on choosing the direction of the propulsion. It is found that optimal control gives the minimum transfer time, while sub-optimal control restricted the control to follow a predescribed function, which is assumed to be a constant or linear function in time. Finally, solar sails present themselves as an option where fuel is a critical factor, given their much longer maneuver duration, but with a zero fuel consumption. The numerical-analytical modeling of optimization methods developed in this study can break any type of symmetry in the solutions. In turn, they can increase their energetic efficiency. The present research compares those results in detail, in particular looking at the transfer time in all cases studied.<\/jats:p>","DOI":"10.3390\/sym15020512","type":"journal-article","created":{"date-parts":[[2023,2,15]],"date-time":"2023-02-15T03:09:21Z","timestamp":1676430561000},"page":"512","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Optimum, Suboptimal and Solar Sailing Orbital Maneuvers for a Spacecraft Orbiting the Earth"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0755-579X","authenticated-orcid":false,"given":"Lucas Gouv\u00eaa","family":"Meireles","sequence":"first","affiliation":[{"name":"Postgraduate Division, National Institute for Space Research (INPE), Av. dos Astronautas, 1758, S\u00e3o Jos\u00e9 dos Campos 12227-900, SP, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vivian Martins","family":"Gomes","sequence":"additional","affiliation":[{"name":"Department of Mathematics, S\u00e3o Paulo State University (UNESP), Av. Ariberto Pereira da Cunha, 333, Guaratinguet\u00e1 12516-410, SP, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ant\u00f4nio Fernando Bertachini de Almeida","family":"Prado","sequence":"additional","affiliation":[{"name":"Postgraduate Division, National Institute for Space Research (INPE), Av. dos Astronautas, 1758, S\u00e3o Jos\u00e9 dos Campos 12227-900, SP, Brazil"},{"name":"Academy of Engineering, RUDN University, Miklukho-Maklaya Street 6, 117198 Moscow, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cristiano Fiorilo de","family":"Melo","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Federal University of Minas Gerais, Av. Ant\u00f4nio Carlos, 6627, Belo Horizonte 31270-901, MG, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"571","DOI":"10.1016\/j.actaastro.2011.04.018","article-title":"Long-distance, drag-free, low-thrust, LEO formation control for Earth gravity monitoring","volume":"69","author":"Canuto","year":"2011","journal-title":"Acta Astronaut."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1740","DOI":"10.1016\/j.asr.2011.02.022","article-title":"On-orbit verification of fuel-free attitude control system for spinning solar sail utilizing solar radiation pressure","volume":"48","author":"Funase","year":"2011","journal-title":"Adv. Space Res."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/j.actaastro.2012.03.032","article-title":"Achievement of IKAROS\u2014Japanese deep space solar sail demonstration mission","volume":"82","author":"Tsuda","year":"2013","journal-title":"Acta Astronaut."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"McNutt, L., Johnson, L., Kahn, P., Castillo-Rogez, J., and Frick, A. (2014, January 4\u20137). Near-Earth Asteroid (NEA) Scout. Proceedings of the AIAA Space Conference and Exposition, San Diego, CA, USA.","DOI":"10.2514\/6.2014-4435"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2878","DOI":"10.1016\/j.asr.2020.06.029","article-title":"The LightSail 2 solar sailing technology demonstration","volume":"67","author":"Spencer","year":"2021","journal-title":"Adv. Space Res."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Wilkie, W.K. (2021, January 11\u201321). 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