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Study of collision probability considering a non-uniform cloud of space debris

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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.

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Acknowledgements

The authors wish to express their appreciation for the support provided by Grants \(\#2016/15675-1\), \(\#2017/04643-4\) from São Paulo Research Foundation (FAPESP) and Institute of Science and Technology, UNESP - São Paulo State University.

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Authors and Affiliations

  1. Institute of Science and Technology, São Paulo State University (UNESP), São José dos Campos, São Paulo, Brazil

    Jorge Kennety Silva Formiga & Fabiana A. Fiore

  2. São Paulo State University (UNESP), São João da Boa Vista, São Paulo, Brazil

    Denilson Paulo Souza dos Santos

  3. Federal University of So Paulo (UNIFESP)S, São José dos Campos, São Paulo, Brazil

    Rodolpho Vilhena de Moraes

  4. National Institute for Space Research(INPE), São José dos Campos, São Paulo, Brazil

    Antonio Fernando Bertachini A. Prado

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  1. Jorge Kennety Silva Formiga
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  2. Denilson Paulo Souza dos Santos
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  3. Fabiana A. Fiore
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  4. Rodolpho Vilhena de Moraes
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  5. Antonio Fernando Bertachini A. Prado
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Correspondence to Jorge Kennety Silva Formiga.

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Communicated by Jose Alberto Cuminato.

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Formiga, J.K.S., Santos, D.P.S.d., Fiore, F.A. et al. Study of collision probability considering a non-uniform cloud of space debris. Comp. Appl. Math. 39, 21 (2020). https://doi.org/10.1007/s40314-019-0997-z

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