author = "Formiga, Jorge K. S. and Santos, D. P. S. and Fiore, F. A. and 
                         Moraes, R. V. de and Prado, Antonio Fernando Bertachini de 
          affiliation = "{Universidade Estadual Paulista (UNESP)} and {Universidade 
                         Estadual Paulista (UNESP)} and {Universidade Estadual Paulista 
                         (UNESP)} and {Universidade Federal de S{\~a}o Paulo (UNIFESP)} 
                         and {Instituto Nacional de Pesquisas Espaciais (INPE)}",
                title = "Study of collision probability considering a non-uniform cloud of 
                         space debris",
              journal = "Computational and Applied Mathematics",
                 year = "2019",
               volume = "39",
               number = "1",
                pages = "e21",
             keywords = "close approach, orbital maneuver, space debris, space 
             abstract = "The present paper aims to study the cumulative collision 
                         probability of a target that crosses a cloud of particles that has 
                         the orbital parameters of each individual element modified by a 
                         close approach with the Earth. Clouds of this type are formed when 
                         natural or man-made bodies explode for some reason. After an 
                         explosion like that, the individual particles have different 
                         trajectories. The clouds are specified by a non-uniform 
                         distribution of semi-major axis and eccentricity of their 
                         particles which are assumed to pass close to the Earth, making a 
                         close approach that modifies the trajectory of every single 
                         particle that belongs to the cloud. This study makes simulations 
                         considering separately two different clouds based on the patched 
                         conics model to obtain the new trajectories of each particle and 
                         to analyze the density of the whole cloud. Then it is possible to 
                         map the new distribution of the orbital elements of the fragments 
                         that constituted the cloud, using the distribution as initial 
                         conditions. After calculating the spatial density for the whole 
                         cloud, it is possible to obtain the cumulative collision 
                         probability for one space vehicle that crosses the cloud. These 
                         pieces of information are important when planning satellite 
                         missions where a spacecraft passes close to a cloud of this type, 
                         because we can determine values to study the risks of collision 
                         and the possible maneuvers that need to be made to avoid them.",
                  doi = "10.1007/s40314-019-0997-z",
                  url = "http://dx.doi.org/10.1007/s40314-019-0997-z",
                 issn = "2238-3603",
             language = "en",
           targetfile = "
        urlaccessdate = "19 abr. 2021"