zbMATH — the first resource for mathematics

Study of collision probability considering a non-uniform cloud of space debris. (English) Zbl 1449.70030
Summary: 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.
70M20 Orbital mechanics
70F05 Two-body problems
70F07 Three-body problems
70F15 Celestial mechanics
70F16 Collisions in celestial mechanics, regularization
Full Text: DOI
[1] Anon (2002) Space debris mitigation guidelines. Technical report IADC-issue 1, rev 1, Inter-Agency Space Debris Coordination Committee (IADC), 2002
[2] Kessler, Dj; Cour-Palais, Bg, Collision frequency of artificial satellites: the creation of a debris belt, J Geophys Res, 83, A6, 2637-2646 (1978)
[3] Öpik EJ, Lindsay EM (1951) Collision probabilities with the planets and the distribution of interplanetary matter. In: Proceedings of the Royal Society of London, Series A, Mathematical and physical scinces, Vol 54, Section A, no 12. pp 165-199
[4] Su, S-Y; Kessler, D., Contribution of explosion and future collision fragments to the orbital debris environment, Adv Space Res, 5, 2, 25-34 (1985)
[5] Kessler, Dj, Collision probability at low altitudes resulting from elliptical orbits, Adv Space Res, 10, 393-396 (1990)
[6] Letizia F, Colombo C, Lewis HG (2015) Small debris fragments contribution to collision probability for spacecraft in low earth orbits. In: Space Safety is No Accident, Springer, pp. 379-387
[7] Letizia, F., Extension of the density approach for debris cloud propagation, J Guid Control Dyn, 41, 12, 2650-2656 (2018)
[8] Letizia F, Colombo C, Lewis HG, McInnes CR (2013) Space debris cloud evolution in low earth orbit. In: 64th International Astronautical Congress, China. 23-27 Sep 2013, IAC-13. A6. p 12
[9] Rossi, A.; Valsecchi, G.; Alessi, E., The criticality of spacecraft index, Adv Space Res, 56, 3, 449-460 (2015)
[10] Letizia F, Colombo C, Lewis H, Krag H (2017) Extending the ECOB space debris index with fragmentation risk estimation. In: 7th European Conference on Space Debris, 17-21 April 2017. European Space Agency (ESA), Darmstadt, Germany
[11] Colombo C, Letizia F, Trisolini M, Lewis HG, Chanoine A, Duvernois P, Austin J, Lemmens S (2017a) Life cycle assessment indicator for space debris. In: 7th European Conference on Space Debris. ESA Space Debris Office, v 7, issue 1. Darmstadt
[12] Rossi, A.; Cordelli, A.; Pardini, C.; Anselmo, L.; Farinella, P., Modelling the space debris evolution: two new computer codes, Adv Astronaut Sci, 89, 1217-1217 (1995)
[13] Gor’Kavyi, Nikolai N.; Ozernoy, Leonid M.; Mather, John C.; Taidakova, Tanya, Quasi‐Stationary States of Dust Flows under Poynting‐Robertson Drag: New Analytical and Numerical Solutions, The Astrophysical Journal, 488, 1, 268-276 (1997)
[14] Mcinnes, C. R., 4527 simple analytic model of the long-term evolution of nanosatellite constellations, J Guid Control Dyn, 23, 2, 332-338 (2000)
[15] Lewis, Hg; Swinerd, G.; Williams, N.; Gittins, G., Damage: a dedicated geo debris model framework, Eur Space Agency Publ ESA SP, 473, 373-378 (2001)
[16] Colombo and McInnes (2012) Orbital dynamics of earth-orbiting ’smart dust’ spacecraft under the effects of solar radiation pressure and aerodynamic drag, In: AIAA/AAS Astrodynamics Specialist Conference, 2-5 August 2010. AIAA 2010-7656, Toronto, Ontario, Cananda. 10.2514/6.2010-7656
[17] Pardini, C.; Anselmo, L., Review of past on-orbit collisions among cataloged objects and examination of the catastrophic fragmentation concept, Acta Astronautica, 100, 30-39 (2014)
[18] White, Adam E.; Lewis, Hugh G., The many futures of active debris removal, Acta Astronautica, 95, 189-197 (2014)
[19] Opiela JN, Hillary E, Whitlock DO, Hennigan M, ESCG (2012) Debris Assessment Software-User’s Guide, Lyndon B. Johnson Space Center, Tech Rep, 2012
[20] Klinkrad, H., Space debris—models and risk analysis (2006), Berlin, Heidelberg: Springer, Berlin, Heidelberg
[21] Kessler DJ, Johnson NL, Liou J-C, Matney M (2010) The Kessler syndrome: implications to future space operations. In: 33rd Annual AAS Guidance and Control Conference, AAS 10-016, Advances in the Astronomical Sciences, vol 137. pp 47-62
[22] Liou J, Matney M, Anz-Meador P, Kessler D, Jansen M, Theall J (2001) The new NASA orbital debris engineering model ORDEM2000. In: Proceedings of the Third European Conference on Space Debris, ESA SP-473. pp 309-313
[23] Longman, Rw; Schneider, Am, Use of Jupiter’s moons for gravity assist, J Spacecr Rockets, 7, 5, 570-576 (1970)
[24] Longuski, Jm; Williams, Sn, The last grand tour opportunity to Pluto, J Astronaut Sci, 39, 359-365 (1991)
[25] Kresák, L., On a criterion concerning the perturbing action of the Earth on meteor streams, Bull Astron Inst Czechoslov, 5, 45 (1954)
[26] D’Amario, La; Byrnes, Dv; Stanford, Rh, Interplanetary trajectory optimization with application to galileo, J Guid Control Dyn, 5, 5, 465-471 (1982)
[27] Prado, Afba; Broucke, R., Transfer orbits in the Earth-Moon system using a regularized model, J Guid Control Dyn, 19, 4, 929-933 (1996) · Zbl 0888.70019
[28] Formiga JKS, Prado A (2011) Orbital characteristics due to the three-dimensional swing-by in the Jun- Jupiter system. In: Proceeding CIMMACS’11/ISP’11 Proceedings of the 10th WSEAS international conference on Computational Intelligence, Man-Machine Systems and Cybernetics, and proceedings of the 10th WSEAS international conference on Information Security and Privacy, Jakarta, Indonesia, December 01-03, 2011. pp 61-69
[29] Gomes, Vm; Prado, Fba; Golebiewska, J., Dynamics of space particles and spacecrafts passing by the atmosphere of the earth, Sci World J, 2013, 489645 (2013)
[30] Formiga, Jks; Dos Santos, Dps, Orbital maneuvers to reach and explore a triple asteroid, Comput Appl Math, 35, 3, 893-905 (2016) · Zbl 1348.70024
[31] Broucke, Ra; Prado, Afba, Jupiter swing-by trajectories passing near the earth, Adv Astronaut Sci, 82, 2, 1159-1176 (1993)
[32] Formiga, Jks; Gomes, Vm; De Moraes, Rv, Orbital effects in a cloud of space debris making a close approach with the earth, Comput Appl Math, 37, 133-143 (2017) · Zbl 1429.70019
[33] Gomes, Vm; Oliveira, Gmc; Prado, Afba; Sanchez, Dm, Orbital effects in a cloud of space debris making a close approach with the earth, Comput Appl Math, 35, 663-673 (2016) · Zbl 1401.70019
[34] Gomes, Vm; Formiga, Jks; Moraes, Rv, A study of the impact of the initial energy in a close approach of a cloud of particles, WSEAS Trans Appl Theor Mech, 3, 869-878 (2008)
[35] Gomes, Vm; Formiga, Jks; Moraes, Rv, A study of the impact of the initial energy in a close approach of a cloud of particles, WSEAS Trans Math, 9, 811-820 (2010)
[36] Gomes, Vm; Formiga, Jks; Moraes, Rv, Studying close approaches for a cloud of particles considering atmospheric drag, Math Prob Eng (Print), 2013, 1-10 (2013)
[37] Araujo, Ran; Winter, Oc; Prado, Afba, Sphere of influence and gravitational capture radius, Mon Noti R Astron Soc (Print), 391, 675-684 (2008)
[38] Formiga, Jorge Kennety S.; Prado, Antonio F. B. A., Studying sequences of resonant orbits to perform successive close approaches with the Moon, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 37, 4, 1391-1404 (2014)
[39] Dos Santos, Dp; Prado, Afba; Rocco, Em, The study of the asymmetric multiple encounters problem and its application to obtain jupiter gravity assisted Maneuvers, Math Probl Eng, 2013, 745637 (2013)
[40] Broucke R (1988) The Celestial mechanics of gravity assist. In: AIAA/AAS Astrodynamics Conference, Minneapolis, MN, Aug 15-17, 1988, Technical Papers (A88-50352 21-13). American Institute of Aeronautics and Astronautics, Washington, DC, pp 69-78
[41] Letizia, F.; Colombo, C.; Lewis, Hg, Collision probability due to space debris clouds through a continuum approach, J Guid Control Dyn, 39, 10, 2240-2249 (2016)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.