author = "Tresaco, Eva and Carvalho, Jean Paulo S. and Prado, Antonio 
                         Fernando Bertachini de Almeida and Elipe, Antonio and Moraes, 
                         Rodolpho Vilhena de",
          affiliation = "{Centro Universitario de la Defensa} and {Universidade Federal do 
                         Rec{\^o}ncavo da Bahia} and {Instituto Nacional de Pesquisas 
                         Espaciais (INPE)} and {Centro Universitario de la Defensa} and 
                         {Universidade Federal de S{\~a}o Paulo (UNIFESP)}",
                title = "Averaged model to study long-term dynamics of a probe about 
              journal = "Celestial Mechanics and Dynamical Astronomy",
                 year = "2018",
               volume = "130",
               number = "2",
                pages = "e9",
                month = "Feb.",
             keywords = "Frozen orbits, Orbital dynamics, Averaged models.",
             abstract = "This paper provides a method for finding initial conditions of 
                         frozen orbits for a probe around Mercury. Frozen orbits are those 
                         whose orbital elements remain constant on average. Thus, at the 
                         same point in each orbit, the satellite always passes at the same 
                         altitude. This is very interesting for scientific missions that 
                         require close inspection of any celestial body. The orbital 
                         dynamics of an artificial satellite about Mercury is governed by 
                         the potential attraction of the main body. Besides the Keplerian 
                         attraction, we consider the inhomogeneities of the potential of 
                         the central body. We include secondary terms of Mercury gravity 
                         field from J2 up to J6, and the tesseral harmonics C 22 that is 
                         of the same magnitude than zonal J2. In the case of science 
                         missions about Mercury, it is also important to consider 
                         third-body perturbation (Sun). Circular restricted three body 
                         problem can not be applied to MercurySun system due to its 
                         non-negligible orbital eccentricity. Besides the harmonics 
                         coefficients of Mercurys gravitational potential, and the Sun 
                         gravitational perturbation, our average model also includes Solar 
                         acceleration pressure. This simplified model captures the majority 
                         of the dynamics of low and high orbits about Mercury. In order to 
                         capture the dominant characteristics of the dynamics, short-period 
                         terms of the system are removed applying a double-averaging 
                         technique. This algorithm is a two-fold process which firstly 
                         averages over the period of the satellite, and secondly averages 
                         with respect to the period of the third body. This simplified 
                         Hamiltonian model is introduced in the Lagrange Planetary 
                         equations. Thus, frozen orbits are characterized by a surface 
                         depending on three variables: the orbital semimajor axis, 
                         eccentricity and inclination. We find frozen orbits for an average 
                         altitude of 400 and 1000 km, which are the predicted values for 
                         the BepiColombo mission. Finally, the paper delves into the 
                         orbital stability of frozen orbits and the temporal evolution of 
                         the eccentricity of these orbits.",
                  doi = "10.1007/s10569-017-9801-9",
                  url = "http://dx.doi.org/10.1007/s10569-017-9801-9",
                 issn = "0923-2958",
             language = "en",
        urlaccessdate = "27 nov. 2020"