{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:59:12Z","timestamp":1760151552346,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2022,3,19]],"date-time":"2022-03-19T00:00:00Z","timestamp":1647648000000},"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":["2018\/16442-6","2016\/24561-0","2016\/23542-1"],"award-info":[{"award-number":["2018\/16442-6","2016\/24561-0","2016\/23542-1"]}],"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":["300923\/2017-1","406841\/2016-0","301338\/2016-7","114190\/2018-6"],"award-info":[{"award-number":["300923\/2017-1","406841\/2016-0","301338\/2016-7","114190\/2018-6"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper presents a handful of the underlying properties of a spacecraft\u2019s transfer from a low Earth orbit (LEO) to the moon\u2019s orbit using an electric propulsion (low-thrust) system. The use of analytical and numerical-analytical modeling in complex natural and technical processes is a key factor in this issue of Symmetry, which has been thoroughly explored in this paper. First, an optimization problem was considered to find the locations and lengths of the thrust arcs that maximizes the final mass of the spacecraft for a number of transfer orbits, thereby limiting the scope of trajectories to the most fuel-efficient ones. In addition to this, the Van Allen belts were modelled according to the density of electrons and protons in each point of space, in order to measure the total radiation absorbed by the spacecraft through an integration of the density of particles over the corresponding time. The simulations were then able to predict the relationship between the fluence of the particles and several initial parameters, such as the initial orbit\u2019s eccentricity and the propulsion system\u2019s characteristics. Then, a multi-linear regression and an artificial neural network were fitted to the data through a regression that related the fluence of protons and electrons as a function of the following parameters: mission time, specific impulse, thrust, final mass (i.e., propellant consumption) and the initial height of the perigee, eccentricity and inclination. This analysis was proven to be powerful due to the expressive values from statistical tests, showing underlying positive correlations between thrust, mission time and final spacecraft mass with the fluence of particles, and negative correlations between specific impulse, initial orbit eccentricity, inclination and the height of the perigee with the fluence of particles. Finally, an analysis of a swing-by maneuver was also carried out, together with the radiation incidence, revealing hidden dependencies of the increments in energy and velocity with respect to the fuel consumption, radiation absorption, propulsion system and initial orbit parameters.<\/jats:p>","DOI":"10.3390\/sym14030617","type":"journal-article","created":{"date-parts":[[2022,3,20]],"date-time":"2022-03-20T21:37:17Z","timestamp":1647812237000},"page":"617","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Swing-By Applications and Estimation of the Van Allen Belts\u2019 Radiation Exposure for a Spacecraft in a Low Thrust Transfer to the Moon"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7047-1092","authenticated-orcid":false,"given":"Rodrigo N.","family":"Schmitt","sequence":"first","affiliation":[{"name":"National Institute for Space Research (INPE), Av. dos Astronautas\u2014Campus do CTA, Sao Jose dos Campos 12227-010, SP, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7966-3231","authenticated-orcid":false,"given":"Antonio F. B. A.","family":"Prado","sequence":"additional","affiliation":[{"name":"National Institute for Space Research (INPE), Av. dos Astronautas\u2014Campus do CTA, Sao Jose dos Campos 12227-010, SP, Brazil"},{"name":"Academy of Engineering, Peoples\u2019 Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Street, Moscow 117198, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexander","family":"Sukhanov","sequence":"additional","affiliation":[{"name":"Space Research Institute (IKI) of the Russian Academy of Sciences, Profsoyuznaya Street, 84\/32, Moscow 117997, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3421-4811","authenticated-orcid":false,"given":"Vivian M.","family":"Gomes","sequence":"additional","affiliation":[{"name":"S\u00e3o Paulo State University (UNESP), Av. Dr. Ariberto Pereira da Cunha, 333-Pedregulho, Guaratinguet\u00e1 12516-410, SP, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,3,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Topputo, F., and Zhang, C. (2014). Survey of direct transcription for low-thrust space trajectory optimization with applications. Abstract and Applied Analysis, Hindawi.","DOI":"10.1155\/2014\/851720"},{"key":"ref_2","unstructured":"Pontryagin, L.S. (1962). The Mathematical Theory of Optimal Processes, John Wiley & Sons Inc."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1134\/S0010952507050061","article-title":"Optimization of transfers under constraints on the thrust direction: I","volume":"45","author":"Sukhanov","year":"2007","journal-title":"Cosm. 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Available online: https:\/\/zenodo.org\/record\/5796896."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/3\/617\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:39:39Z","timestamp":1760135979000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/3\/617"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,3,19]]},"references-count":26,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2022,3]]}},"alternative-id":["sym14030617"],"URL":"https:\/\/doi.org\/10.3390\/sym14030617","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2022,3,19]]}}}