Analytical Model for the Propagation of Small-Debris-Object Clouds After Fragmentations

Current debris evolutionary models usually neglect fragments smaller than 10 cm because of the high computational effort they add to the simulation. However, small-debris objects can also be dangerous to operational satellites. This work proposes an analytical approach to describe the evolution of a cloud of small fragments generated by a collision in low Earth orbit. The proposed approach considers the cloud globally and derives its evolution analytically, in terms of the change in the spatial density under the effect of atmospheric drag. As a result, the analytical approach allows the representation of small fragments and noticeably reduces the computational time under 10% compared to the numerical propagation of all the fragment trajectories. For altitudes above 800 km, the relative error compared to the numerical method is lower than 10%.

[1]  Luciano Anselmo,et al.  Review of past on-orbit collisions among cataloged objects and examination of the catastrophic fragmentation concept☆ , 2014 .

[2]  Hugh G. Lewis,et al.  Collision Probability Due to Space Debris Clouds Through a Continuum Approach , 2016 .

[3]  Holger Krag,et al.  A simplified approach to analyze the space debris evolution in the low earth orbit , 2014 .

[4]  Joshua Ashenberg.  Formulas for the phase characteristics in the problem of low-Earth-orbital debris , 1994 .

[5]  R McinnesC,et al.  An Analytical Model for the Catastrophic Production of Orbital Debris. , 1993 .

[6]  N. Fitz-Coy,et al.  DebriSat - A Planned Laboratory-Based Satellite Impact Experiment , 2013 .

[7]  H. Klinkrad,et al.  The sensitivity of the ESA DELTA model , 2002 .

[8]  Colin R. McInnes,et al.  Wave-like patterns in an elliptical satellite ring , 2013 .

[9]  Ruediger Jehn.  Dispersion of debris clouds from on-orbit fragmentation events , 1990 .

[10]  J. Liou.  An active debris removal parametric study for LEO environment remediation , 2011 .

[11]  N. Johnson,et al.  NASA's new breakup model of evolve 4.0 , 2001 .

[12]  A. Rossi,et al.  Long Term Evolution of Earth Orbiting Debris , 1997 .

[13]  C. Pardini,et al.  MODELLING THE SPACE DEBRIS EVOLUTION : TWO NEW COMPUTER , 1995 .

[14]  Colin R. McInnes.  Simple Analytic Model of the Long-Term Evolution of Nanosatellite Constellations , 2000 .

[15]  Yulin Zhang,et al.  An analytic method of space debris cloud evolution and its collision evaluation for constellation satellites , 2016 .

[16]  G. B. Valsecchi,et al.  Fragmentation Consequence Analysis for LEO and GEO Orbits , 2015 .

[17]  Hugh G. Lewis,et al.  Multidimensional extension of the continuity equation method for debris clouds evolution , 2016 .

[18]  Heiner Klinkrad,et al.  Comparison of debris flux models , 2002 .

[19]  Alessandro Rossi,et al.  Space debris , 2011, Scholarpedia.

[20]  John C. Mather,et al.  A New Approach to Dynamical Evolution of Interplanetary Dust , 1997 .

[21]  Marlon E. Sorge,et al.  Satellite Fragmentation Modeling with IMPACT , 2008 .

[22]  D. Vallado.  Fundamentals of Astrodynamics and Applications , 1997 .

[23]  Adam E. White,et al.  The many futures of active debris removal , 2014 .

[24]  Florent Deleflie,et al.  Semi-analytical theory of mean orbital motion for geosynchronous space debris under gravitational influence , 2009 .

[25]  James E. Gentle.  Estimation of Functions , 2009 .

[26]  Ukraine,et al.  Quasi-Stationary States of Dust Flows under Poynting-Robertson Drag: New Analytical and Numerical Solutions , 1997 .

[27]  D. McKnight.  A phased approach to collision hazard analysis , 1990 .

[28]  P H Krisko.  The predicted growth of the low-Earth orbit space debris environment — an assessment of future risk for spacecraft , 2007 .

[29]  Hugh G. Lewis,et al.  DAMAGE: a dedicated GEO debris model framework , 2001 .

[30]  James Lee Foster,et al.  The analytic basis for debris avoidance operations for the International Space Station , 2001 .

[31]  V. A. Chobotov.  Dynamics of orbiting debris clouds and the resulting collision hazard to spacecraft , 1990 .