author = "Domingos, R. C. and Prado, Antonio Fernando Bertachini de Almeida 
                         and Vilhena de Moraes, R.",
          affiliation = "{Universidade Estadual Paulista (UNESP)} and {Instituto Nacional 
                         de Pesquisas Espaciais (INPE)} and {Universidade Federal de 
                         S{\~a}o Paulo (UNIFESP)}",
                title = "A study of the errors of the averaged models in the restricted 
                         three-body problem in a short time scale",
              journal = "Computational and Applied Mathematics",
                 year = "2015",
               volume = "34",
                pages = "507--520",
             keywords = "Astrodin{\^a}mica, Perturba{\c{c}}{\~a}o de Terceiro Corpo.",
             abstract = "The objective of the present research is to study the accuracy of 
                         the double- and single-averaged models that are usually considered 
                         to predict the motion of spacecrafts or celestial bodies that have 
                         their motion perturbed by a third-body. Those two models are 
                         compared with each other and then validated against the complete 
                         elliptic restricted threebody problem. Those models are developed 
                         to give a faster but general behaviour of the motion of the 
                         perturbed body in a medium or longer time scale. The researches 
                         performed here verify the accuracy of those methods for shorter 
                         time scales by showing the differences in terms of the values of 
                         the inclination and eccentricity of the perturbed body predicted 
                         by those models. Those differences are calculated both at every 
                         instant of time and as an integral over the time. The use of the 
                         integral along the time for the errors is a new form to study 
                         those differences and show a more complete comparison of the 
                         accuracy of those approximations, completing the instantaneous 
                         picture given by the usual approach of looking at the 
                         instantaneous measurement. If the value of the integral is divided 
                         by the time integration, the mean error is obtained. The results 
                         show that the single-averaged model is better in the short time 
                         scale and the difference among those models is smaller when 
                         predicting the eccentricity than the inclination. The effects of 
                         the time scale is verified by varying the study to values from 2 
                         days up to 50 revolutions of the Moon (1,366 days). Another 
                         important point found in the present paper is the range of the 
                         eccentricities of the perturbing body that accelerates the 
                  doi = "10.1007/s40314-014-0148-5",
                  url = "http://dx.doi.org/10.1007/s40314-014-0148-5",
                 issn = "2238-3603",
                label = "lattes: 7340081273816424 2 DomingosPradVilh:2014:StErAv",
             language = "en",
           targetfile = "domingos_study.pdf",
        urlaccessdate = "30 nov. 2020"