Communications on Applied Mathematics and Computation ›› 2024, Vol. 6 ›› Issue (1): 340-353.doi: 10.1007/s42967-023-00253-1
• ORIGINAL PAPERS • Previous Articles Next Articles
John Jurkiewicz, Peter Hinow
Received:
2022-08-19
Revised:
2023-01-04
Published:
2024-04-16
Contact:
John Jurkiewicz,E-mail:jurkiew4@uwm.edu
E-mail:jurkiew4@uwm.edu
Supported by:
John Jurkiewicz, Peter Hinow. A Population Dynamics Approach to the Distribution of Space Debris in Low Earth Orbit[J]. Communications on Applied Mathematics and Computation, 2024, 6(1): 340-353.
[1] ApolloSat.com.:U.S. Satellite Destroyed in Space Collision (2022). Access at https://apollosat.com/space-collision/. Accessed 1 Aug 2021 [2] Bonnal, C., McKnight, D., Phipps, C., Dupont, C., Missonnier, S., Lequette, L., Merle, M., Rommelaere, S.:Just in time collision avoidance-a review. Acta Astronaut. 170, 637-651 (2020) [3] Brouwer, D.:Solution of the problem of artificial satellite theory without drag. Astron. J. 64, 378-396 (1959) [4] Carnegie Endowment for International Peace:The dangerous fallout of Russia's anti-satellite missile test (2022). Access at https://carnegieendowment.org. Accessed 20 June 2022 [5] Gast, R.:Ein All für alle (Die Zeit, 07-23-2022, in German) (2022) [6] Hoots, F.R.:Reformulation of the Brouwer geopotential theory for improved computational efficiency. Celest. Mech. 24, 367-375 (1981) [7] Johnston, E.:List of satellites in geostationary orbit (2022). Access at https://www.satsig.net/sslist.htm. Accessed 20 May 2022 [8] Kessler, D.J., Cour-Palais, B.G.:Collision frequency of artificial satellites:the creation of a debris belt. J. Geophys. Res. 83, 2637-2646 (1978) [9] Klima, R., Bloembergen, D., Savani, R., Tuyls, K., Wittig, A., Sapera, A., Izzo, D.:Space debris removal:learning to cooperate and the price of anarchy. Front. Robot. AI 5, 54 (2018) [10] Lemaitre, A., Hubaux, C.:Space debris long term dynamics. In:Celletti, A., Locatelli, U., Ruggeri, T., Strickland, E. (eds.) Mathematical Models and Methods for Planet Earth. INdAM, vol. 6, pp. 113-121. Springer, Cham (2013) [11] Liou, J.-C.:An active debris removal parametric study for LEO environment remediation. Adv. Space Res. 47, 1865-1876 (2011) [12] Liou, J.-C., Hall, D.T., Krisko, P.H., Opiela, J.N.:LEGEND-a three-dimensional LEO-to-GEO debris evolutionary model. Adv. Space Res. 34, 981-986 (2004) [13] Lyddane, R.H.:Small eccentricities or inclinations in the Brouwer theory of the artificial satellite. Astron. J. 68, 555-558 (1963) [14] McInnes, C.R.:An analytical model for the catastrophic production of orbital debris. ESA J. 17, 293-305 (1993) [15] NASA:LEGEND:3D/OD evolutionary model (2022). orbitaldebris.jsc.nasa.gov. Accessed 20 Nov 2022 [16] Nikolaev, S., Phillion, D., Springer, H.K., deVries, W., Jiang, M., Pertica, A., Henderson, J., Horsley, M., Olivier, S.:Brute force modeling of the Kessler syndrome. In:Advanced Maui Optical and Space Surveillance Technologies Conference (AMOS), Maui, HI, September 2012 (2012) [17] Okubo, A.:Diffusion and Ecological Problems:Mathematical Models. Springer, Berlin (1980) [18] Reynolds, R.C., Eichler, P.:A comparison of debris environment projections using the EVOLVE and CHAIN models. Adv. Space Res. 16, 127-135 (1995) [19] Riesing, K., Kahoy, K.:Orbit determination from two-line element sets for ISS-deployed CubeSats. In:29th Annual AIAA/USA Conference on Small Satellites (2015) [20] Rossi, A.:Population models of space debris. In:Knežević, Z., Milani, A. (eds.) Dynamics of Populations of Planetary Systems, vol. 197 of Proceedings IAU Colloquium, pp. 427-438. International Astronomical Union, Paris (2005) [21] Space.com:A rogue 3-ton piece rocket debris just collided with the moon (2022). Access at https://www.space.com/rogue-rocket-stage-hit-moon-today Accessed 20 June 2022 [22] Space.com:Starlink satellites:everything you need to know about the controversial internet megaconstellation (2022). Access at https://www.space.com/spacex-starlink-satellites.html. Accessed 10 Dec 2022 [23] Takahashi, K., Charles, C., Boswell, R.W., Ando, A.:Demonstrating a new technology for space debris removal using a bidirectional plasma thruster. Sci. Rep. 8, 14417 (2018) [24] US Space Command:Space-track.org (2010). Space-Track.org. Accessed 8 Aug 2022 [25] Zhang, B., Wang, Z., Zhang, Y.:Discrete evolution model based on mean spatial density for space debris environment. Astrophys. Space Sci. 364, 70 (2019) |
[1] | King-Yeung Lam, Ray Lee, Yuan Lou. Population Dynamics in an Advective Environment [J]. Communications on Applied Mathematics and Computation, 2024, 6(1): 399-430. |
[2] | Shuang Liu, Xinfeng Liu. Exponential Time Differencing Method for a Reaction- Diffusion System with Free Boundary [J]. Communications on Applied Mathematics and Computation, 2024, 6(1): 354-371. |
[3] | Tingting Li, Jianfang Lu, Pengde Wang. Stability Analysis of Inverse Lax-Wendroff Procedure for High order Compact Finite Difference Schemes [J]. Communications on Applied Mathematics and Computation, 2024, 6(1): 142-189. |
[4] | Yu Wang, Min Cai. Finite Difference Schemes for Time-Space Fractional Diffusion Equations in One- and Two-Dimensions [J]. Communications on Applied Mathematics and Computation, 2023, 5(4): 1674-1696. |
[5] | N. N. Nazarenko, A. G. Knyazeva. Mathematical Modeling of Biological Fluid Flow Through a Cylindrical Layer with Due Account for Barodiffusion [J]. Communications on Applied Mathematics and Computation, 2023, 5(4): 1365-1384. |
[6] | Xiaoying Han, Habib N. Najm. Modeling Fast Diffusion Processes in Time Integration of Stiff Stochastic Differential Equations [J]. Communications on Applied Mathematics and Computation, 2022, 4(4): 1457-1493. |
[7] | Hasnaa Alzahrani, George Turkiyyah, Omar Knio, David Keyes. Space-Fractional Diffusion with Variable Order and Diffusivity:Discretization and Direct Solution Strategies [J]. Communications on Applied Mathematics and Computation, 2022, 4(4): 1416-1440. |
[8] | Ren-jun Qi, Zhi-zhong Sun. Some Numerical Extrapolation Methods for the Fractional Sub-diffusion Equation and Fractional Wave Equation Based on the L1 Formula [J]. Communications on Applied Mathematics and Computation, 2022, 4(4): 1313-1350. |
[9] | F. S. Mousavinejad, M. FatehiNia, A. Ebrahimi. P-Bifurcation of Stochastic van der Pol Model as a Dynamical System in Neuroscience [J]. Communications on Applied Mathematics and Computation, 2022, 4(4): 1293-1312. |
[10] | Jun-Feng Yin, Yi-Shu Du. A Class of Preconditioners Based on Positive-Definite Operator Splitting Iteration Methods for Variable-Coefficient Space-Fractional Diffusion Equations [J]. Communications on Applied Mathematics and Computation, 2021, 3(1): 157-176. |
[11] | Wenhui Guan, Xuenian Cao. A Numerical Algorithm for the Caputo Tempered Fractional Advection-Diffusion Equation [J]. Communications on Applied Mathematics and Computation, 2021, 3(1): 41-59. |
[12] | Yubo Yang, Fanhai Zeng. Numerical Analysis of Linear and Nonlinear Time-Fractional Subdiffusion Equations [J]. Communications on Applied Mathematics and Computation, 2019, 1(4): 621-637. |
[13] | Kamran Kazmi, Abdul Khaliq. A Split-Step Predictor-Corrector Method for Space-Fractional Reaction-Diffusion Equations with Nonhomogeneous Boundary Conditions [J]. Communications on Applied Mathematics and Computation, 2019, 1(4): 525-544. |
Viewed | ||||||||||||||||||||||||||||||||||||||||||||||
Full text 30
|
|
|||||||||||||||||||||||||||||||||||||||||||||
Abstract 210
|
|
|||||||||||||||||||||||||||||||||||||||||||||