@Article{SanchezPradYoko:2014:QuOr,
               author = "Sanchez, Diogo Merguizo and Prado, Antonio Fernando Bertachini de 
                         Almeida and Yokoyama, T.",
          affiliation = "{Instituto Nacional de Pesquisas Espaciais (INPE)} and {Instituto 
                         Nacional de Pesquisas Espaciais (INPE)} and {Universidade Estadual 
                         Paulista (UNESP)}",
                title = "On the effects of each term of the geopotential perturbation along 
                         the time I: Quasi-circular orbits",
              journal = "Advances in Space Research",
                 year = "2014",
               volume = "54",
               number = "6",
                pages = "1008--1018",
             keywords = "Geodetic satellites, Harmonic analysis, Space flight, China-brazil 
                         earth resources satellites, Computational effort, Direct solar 
                         radiation, Geopotential perturbations, Geopotentials, Mean squared 
                         error, Orbital mechanics, Satellite orbit, Orbits.",
             abstract = "This paper provides a useful new method to determine minimum and 
                         maximum range of values for the degree and order of the 
                         geopotential coefficients required for simulations of orbits of 
                         satellites around the Earth. The method consists in a time 
                         integration of the perturbing acceleration coming from each 
                         harmonic of the geopotential during a time interval T. More 
                         precisely, this integral represents the total velocity 
                         contribution of a specific harmonic during the period T. 
                         Therefore, for a pre-fixed minimum contribution, for instance 
                         1×10-8 m/s during the period of time T, any harmonic whose 
                         contribution is below this value can, safely, be neglected. This 
                         fact includes some constraints in the degree and order of the 
                         terms which are present in the geopotential formula, saving 
                         computational efforts compared to the integration of the full 
                         model. The advantage of this method is the consideration of other 
                         perturbations in the dynamics (we consider the perturbations of 
                         the Sun, the Moon, and the direct solar radiation pressure with 
                         eclipses), since these forces affect the value of the perturbation 
                         of the geopotential, because these perturbations depend on the 
                         trajectory of the spacecraft, that is dependent on the dynamical 
                         model used. In this paper, we work with quasi-circular orbits and 
                         we present several simulations showing the bounds for the maximum 
                         degree and order (M) that should be used in the geopotential for 
                         different situations, e. g., for a satellite near 500 km of 
                         altitude (like the GRACE satellites at the beginning of their 
                         mission) we found 35dMd198 for T=1 day. We analyzed the individual 
                         contribution of the second order harmonic (J2) and we use its 
                         behavior as a parameter to determine the lower limit of the number 
                         of terms of the geopotential model. In order to test the accuracy 
                         of our truncated model, we calculate the mean squared error 
                         between this truncated model and the {"} full{"} model, using the 
                         CBERS (China-Brazil Earth Resources Satellite) satellite in this 
                         test. © 2014 COSPAR. Published by Elsevier Ltd. All rights 
                         reserved.",
                  doi = "10.1016/j.asr.2014.06.003",
                  url = "http://dx.doi.org/10.1016/j.asr.2014.06.003",
                 issn = "0273-1177 and 1879-1948",
                label = "scopus 2014-11 SanchezPradYoko:2014:QuOr",
             language = "en",
        urlaccessdate = "27 abr. 2024"
}