@Article{CarvalhoMora:2020:SeApUs,
               author = "Carvalho, Jean P. S. and Moraes, Rodolpho Vilhena de",
          affiliation = "{Universidade Federal do Rec{\^o}ncavo da Bahia (UFRBA)} and 
                         {Instituto Nacional de Pesquisas Espaciais (INPE)}",
                title = "A semi-analytical approach using the single and double averaged 
                         methods and the Lidov–Kozai mechanism",
              journal = "European Physical Journal Special Topics",
                 year = "2020",
               volume = "229",
               number = "8",
                pages = "1491--1500",
                month = "May",
             abstract = "An analysis of the orbital motion of artificial satellites around 
                         Mercury is presented taking into account its non-sphericity (J(2), 
                         J(3), C-22) and the perturbation of the third body. The disturbing 
                         potential due to the third body is developed in circular and 
                         inclined orbit. The double-averaged method should be used with 
                         caution in some situations where the averaging is applied at 
                         different timescales. In this work, a study is presented 
                         considering this observation for orbits around Mercury. When the 
                         mean anomaly of the Sun is eliminated, the idea is that all 
                         effects whose periods below 88 days are neglected. As the rotation 
                         of Mercury is about 58.6 days, this means that the perturbation 
                         due to the C-22 term must also be neglected. However, since the 
                         C-22 term is important and should be taken into account, then 
                         terms longer than 58.6 days should also be preserved. In other 
                         words, keeping the C-22 term with a period of 58.6 days means that 
                         the solar terms with the longest period (88 days) will be 
                         maintained here. The single-averaged method is applied to 
                         eliminate only the mean anomaly of the spacecraft. A comparison 
                         between the single and double averaged models is presented. We 
                         found that for the case of Mercury the two models are in 
                         agreement, but the single-averaged model is more realistic because 
                         it keeps more terms in the disturbing potential. Several types of 
                         resonances can be analyzed starting of the single-averaged 
                         potential. Considering our single-averaged disturbing potential, 
                         the terms due to Lidov-Kozai resonance were isolated to make a 
                         qualitative analysis considering the libration and circulation 
                         regions in the diagram, eccentricity versus argument of the 
                         pericenter.",
                  doi = "10.1140/epjst/e2020-900161-1",
                  url = "http://dx.doi.org/10.1140/epjst/e2020-900161-1",
                 issn = "1951-6355",
             language = "en",
           targetfile = "carvalho_semi.pdf",
        urlaccessdate = "25 abr. 2024"
}