CoChat
Sign Up
Cited by 9Space Satellite Systems and ControlSpacecraft Dynamics and ControlSpacecraft Design and Technology

Decay time estimate for LEO spacecraft

Open access
Niccolai, Lorenzo, Mengali, Giovanni·2024·Acta Astronautica
DOI 10.1016/j.actaastro.2024.09.045
Open this paper in CoChat — free account

Abstract

The growing concerns posed by orbital debris represent a serious threat to the future of space operations in low Earth orbit. With the goal of limiting the formation of new debris, space agencies are proposing international guidelines that satellites should be able to deorbiting within 25 years of the end of their operational life. Orbital decay is typically caused by atmospheric drag, so estimating the decay time of a satellite subject to drag is critical to assessing whether the guidelines are met. However, such estimate is a very challenging task because of the difficulty of accurately modeling atmospheric properties and because of the coupling of orbital dynamics with spacecraft attitude. In this paper, a simplified algorithm based on the King-Hele formulation is proposed to rapidly estimate the decay time of an orbiting satellite without imposing any assumptions on the spacecraft’s nominal size, mass, geometry or attitude. The algorithm accounts for the effect of solar activity level variations on atmospheric properties and drag coefficient through an iterative procedure and can be applied to any object in orbit. Numerical tests show that the predictions in terms of decay times are very accurate for satellites that are quite different in size and geometry, including the presence of an aerodynamic drag augmentation system such as a drag sail. • This work proposes a quick method for estimating the decay time of a LEO spacecraft. • The influence of different spacecraft and…

Integrity signals

Registry

Crossref · 10.1016/j.actaastro.2024.09.045

Cites

1 of 1 references verified0 citation errors · 0 not checkable

Statistics

Recomputing p-values needs the paper’s full text.

Claims the paper makes

We couldn’t retrieve this paper’s full text, so its claims and self-check weren’t run. The registry and citation checks still apply.

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • The drag coefficient C is ∼2 for roughly spherical spacecraft in low Earth orbit.

    “Since the drag coefficient C is ∼2 for roughly spherical spacecraft in low Earth orbit (L. Niccolai & G. Mengali 2024), and the density of the Martian exosphere at Phobos’s altitude is similar to the density of Earth’s exosphere at LEO altitude (N. Østgaard et al. 2003; P. D. Feldman et al. 2011), we set the drag coefficient C at 2.”

    From Phobos is not Hollow (2026) · cites this paper as L. Niccolai & G. Mengali 2024

Cites

Flagged first, then by citations

Research works printed but not linked: 72

  1. Sweeting, 1996, Earth observation using low cost micro/minisatellites, Acta Astronaut., 39, 823, 10.1016/S0094-5765(97)00066-0 · DOI
  2. Wekerle, 2017, Status and trends of smallsats and their launch vehicles - An up-to-date review, J. Aerosp. Technol. Manage., 9, 269, 10.5028/jatm.v9i3.853 · DOI
  3. Niccolai, 2019, A review of smart dust architecture, dynamics, and mission applications, Prog. Aerosp. Sci., 106, 1, 10.1016/j.paerosci.2019.01.003 · DOI
  4. Twiggs, 2000, Space system developments at Stanford University: From launch experience of microsatellites to the proposed future use of picosatellites, Proc. SPIE, 4136, 79, 10.1117/12.406646 · DOI
  5. Kestilä, 2013, Aalto-1 nanosatellite - technical description and mission objectives, Geosci Instrum Methods Data Syst, 2, 121, 10.5194/gi-2-121-2013 · DOI
  6. Dalbins, 2023, Interplanetary student nanospacecraft: development of the LEOdemonstrator ESTCube-2, Aerospace, 10, 10.3390/aerospace10060503 · DOI
  7. Rossi, 2020, Short-term space safety analysis of LEO constellations and clusters, Acta Astronaut., 175, 476, 10.1016/j.actaastro.2020.06.016 · DOI
  8. Ren, 2021, The interaction between the LEO satellite constellation and the space debris environment, Appl. Sci., 11, 10.3390/app11209490 · DOI
  9. Zhang, 2022, LEO mega constellations: Review of development, impact, surveillance, and governance, Space: Sci. Technol., 2022
  10. Kessler, 1978, Collision frequency of artificial satellites: the creation of a debris belt, J. Geophys. Res., 83, 2637, 10.1029/JA083iA06p02637 · DOI
  11. Liou, 2006, Risks in space from orbiting debris, Science, 311, 340, 10.1126/science.1121337 · DOI
  12. Liou, 2008, Instability of the present LEO satellite populations, Adv. Space Res., 41, 1046, 10.1016/j.asr.2007.04.081 · DOI
  13. Kessler, 1991, Collisional cascading: The limits of population growth in low earth orbit, Adv. Space Res., 11, 63, 10.1016/0273-1177(91)90543-S · DOI
  14. Liou, 2006, Collision activities in the future orbital debris environment, Adv. Space Res., 38, 2102, 10.1016/j.asr.2005.06.021 · DOI
  15. Kessler, 2010, The kessler syndrome: Implications to future space operations, Adv. Astronaut. Sci., 137, 47
  16. Liu, 2022, Space debris detection and positioning technology based on multiple star trackers, Appl. Sci., 12, 10.3390/app12073593 · DOI
  17. Bonnal, 2020, Just in time collision avoidance - A review, Acta Astronaut., 170, 637, 10.1016/j.actaastro.2020.02.016 · DOI
  18. Katz, 2024, Can a satellite dodge space debris?, Acta Astronaut., 222, 174, 10.1016/j.actaastro.2024.06.007 · DOI
  19. Bombardelli, 2021, Space occupancy in low-Earth orbit, J. Guid. Control Dyn., 44, 684, 10.2514/1.G005371 · DOI
  20. Zhao, 2020, Survey on research and development of on-orbit active debris removal methods, Sci. China Technol. Sci., 63, 2188, 10.1007/s11431-020-1661-7 · DOI
  21. Bianchi, 2024, Preliminary design of a space debris removal mission in LEO using a solar sail, Adv. Space Res., 73, 4254, 10.1016/j.asr.2024.01.024 · DOI
  22. F. Schäfer, M. Lambert, E. Christiansen, S. Kibe, H. Stokes, H.G. Reimerdes, S.A. Meshcheryakov, F. Angrilli, H. Zengyao, The Inter-Agency Space Debris Coordination Committee (IADC) protection manual, in: 4th European Conference on Space Debris, Darmstadt, Germany, 2005.
  23. M. Yakovlev, The IADC space debris mitigation guidelines and support document, in: 4th European Conference on Space Debris, Darmstadt, Germany, 2005.
  24. Levin, 2012, Wholesale debris removal from LEO, Acta Astronaut., 73, 100, 10.1016/j.actaastro.2011.11.014 · DOI
  25. Sánchez-Arriaga, 2017, Comparison of technologies for deorbiting spacecraft from low-Earth-orbit ad end of mission, Acta Astronaut., 138, 536, 10.1016/j.actaastro.2016.12.004 · DOI
  26. Visagie, 2015, Drag sails for space debris mitigation, Acta Astronaut., 109, 65, 10.1016/j.actaastro.2014.12.013 · DOI
  27. Niccolai, 2024, Performance estimate of a spin-stabilized drag sail for spacecraft deorbiting, Appl. Sci., 14, 10.3390/app14020612 · DOI
  28. D.L. Oltrogge, C. Chao, Stardardized approaches for estimating orbit lifetime after end-of-life, in: AAS/AIAA Astrodynamics Specialist Conference, Mackinac Island (MI), USA, 2007.
  29. Kerr, 2018, Incorporating solar activity into general perturbation analysis of atmospheric friction, J. Guid. Control Dyn., 41, 1320, 10.2514/1.G003229 · DOI
  30. Frey, 2019, Extension of the King-Hele orbit contraction method for accurate, semi-analytical propagation of non-circular orbits, Adv. Space Res., 64, 1, 10.1016/j.asr.2019.03.016 · DOI
  31. Giudici, 2024, Density-based evolutionary model of the space debris environment in low-earth orbit, Acta Astronaut., 219, 115, 10.1016/j.actaastro.2024.03.008 · DOI
  32. 2013, The new COSPAR International Refernece Atmosphere (CIRA2014): overview, Space Res. Today, 188, 4, 10.1016/j.srt.2013.11.005 · DOI
  33. Picone, 2002, NRLMSISE-00 empirical model of the atmosphere: Statistical comparisons and scientific issues, J. Geophys. Res. Space Phys., 107, 10.1029/2002JA009430 · DOI · Paper page
  34. March, 2021, Gas-surface interactions modelling influence on satellite aerodynamics and thermosphere mass density, J. Space Weather Space Clim., 11, 1
  35. Mehta, 2023, Satellite drag coefficient modeling for thermosphere science and mission operations, Adv. Space Res., 72, 5443, 10.1016/j.asr.2022.05.064 · DOI
  36. Trisolini, 2018, Spacecraft design optimisation for demise and survivability, Aerosp. Sci. Technol., 77, 638, 10.1016/j.ast.2018.04.006 · DOI
  37. Chen, 2024, Aerodynamic analysis of deorbit drag sail for cubesat using DSMC method, Aerospace, 11, 10.3390/aerospace11040315 · DOI
  38. B.R. Bowman, K. Moe, Drag coefficient variability at 175-500km from the orbit decay analysis of spheres, in: AAS/AIAA Astrodynamics Specialist Conference, No. AAS 05-257, Lake Tahoe (CA), USA, 2005.
  39. Qi, 2013, Periodic variations of drag coefficient for the ANDE spherical satellites during lifetime, Chin. J. Space Sci., 33, 525, 10.11728/cjss2013.05.525 · DOI
  40. K. Moe, B.R. Bowman, The effects of surcace composition and treatment on drag coefficients of spherical satellites, in: AAS/AIAA Astrodynamics Specialist Conference, No. AAS 05-258, Lake Tahoe (CA), USA, 2005.
  41. B. Cotten, I. Bennett, R.E. Zee, On-orbit results from the CanX-7 drag sail deorbit mission, in: 31st Annual AIAA/USU Conference on Small Satellites, Logan (UT), USA, 2017.
  42. Black, 2020, DragSail systems for satellite deorbit and targeted reentry, J. Space Saf. Eng., 7, 397, 10.1016/j.jsse.2020.07.030 · DOI
  43. Miguel, 2021, Deorbiting spacecraft with passively stabilised attitude using a simplified quasi-rhombic-pyramid sail, Adv. Space Res., 67, 2561, 10.1016/j.asr.2020.03.028 · DOI
  44. Zhang, 2022, Attitude stability analysis and configuration design of pyramid drag sail for deorbit missions, J. Aerosp. Eng., 35, 10.1061/(ASCE)AS.1943-5525.0001479 · DOI
  45. Casalino, 2022, Approximate optimal LEO transfers with J2 perturbation and dragsail, Acta Astronaut., 192, 379, 10.1016/j.actaastro.2021.12.006 · DOI
  46. D. Stelzl, P. Seefeldt, M. Killian, L. Hofmann, G. Puttich, X. Lopez-Corralez, C. Garcia Mora, J. Pimpi, M. Schuhbaur, O. Stolz, P. Lindenmaier, T. Spröwitz, T. Cardone, E.K. Pfeiffer, The ADEO space sail products, in: The 6th International Symposium on Space Sailing, ISSS, New York (NY), USA, 2023.
  47. Serfontein, 2021, Drag augmentation systems for space debris mitigation, Acta Astronaut., 188, 278, 10.1016/j.actaastro.2021.05.038 · DOI
  48. Anuta, 1984, Landsat-4 MSS and Thematic Mapper data quality and information content analysis, IEEE Trans. Geosci. Remote Sens., GE-22, 222, 10.1109/TGRS.1984.350595 · DOI
  49. D.H. Oza, D.J. Niklewski, C.E. Doll, G.D. Mistretta, R.C. Hart, Improved solution accuracy for Landsat-4 (TDRSS-user) orbit determination, in: Flight Mechanics/Estimation Theory Symposium, Greenbelt (MD), USA, 1994.
  50. Zandbergen, 1997, ERS-1 and ERS-2 tandem mission: Orbit determination, prediction and maintenance, Adv. Space Res., 19, 1649, 10.1016/S0273-1177(97)00319-0 · DOI
  51. Andersen, 1998, Precise ERS-2 orbit determination using SLR, PRARE, and RA observations, J. Geod., 72, 421, 10.1007/s001900050181 · DOI
  52. A.W.P. Thomson, T.D.G. Clark, E. Clarke, Improved predictions of solar and geomagnetic activity with application to ESA/LEO satellite operations, in: Space Weather Workshop: Looking Towards a Future European Space Weather Programme, Noordwijk, The Netherlands, 2001.
  53. M. Baker, P. Collins, R. Dyer, F. Murolo, The MetOp-A satellite: One year of routine operations, in: SpaceOps Conference, Heidelberg, Germany, 2008.
  54. S. Pessina, P. Righetti, J. Branco, V.M. Moreno Villa, T.V. Peters, MetOp-A long term free-dynamics attitude analysis, for improved re-entry prediction, in: 26th International Symposium on Space Flight Dynamics, Matsusyama, Japan, 2017.
  55. Reigber, 2002, CHAMP mission status, Adv. Space Res., 30, 129, 10.1016/S0273-1177(02)00276-4 · DOI
  56. Schmitt, 2000, CHAMP attitude and orbit control system, Acta Astronaut., 46, 327, 10.1016/S0094-5765(99)00227-1 · DOI
  57. Visser, 1999, Gravity field determination with GOCE and GRACE, Adv. Space Res., 23, 771, 10.1016/S0273-1177(99)00154-4 · DOI
  58. J. Herman, D. Presti, A. Codazzi, C. Belief, Attitude control for GRACE the first low-flying satellite formation, in: 18th Intertnational Symposium on Space Flight Dynamics, (548), ESA, Munich, Germany, 2004, pp. 27–32.
  59. Mehta, 2013, Drag coefficient modeling for GRACE using Direct Simulation Monte Carlo, Adv. Space Res., 52, 2035, 10.1016/j.asr.2013.08.033 · DOI
  60. Vellutini, 2020, Monitoring the final orbital decay and the re-entry of Tiangong-1 with the Italian SST ground sensor network, J. Space Saf. Eng., 7, 487, 10.1016/j.jsse.2020.05.004 · DOI
  61. S. Sommer, V. Karamanavis, F. Schlichtaber, T. Patzelt, J. Rosebrock, D. Cerutti-Maori, L. Leushacke, Analysis of the attitude motion and cross sectional area of Tiangong-1 during its uncontrolled re-entry, in: 1st NEO and Debris Detection Conference, Darmstadt, Germany, 2019.
  62. L. Sagniéres, M.K. Jorgensen, I. Sharf, Simulating the rotational dynamics of Tiangong-1 for re-entry analysis, in: 8th European Conference on Space Debris, Darmstadt, Germany, 2021.
  63. Corpino, 2016, E-st@r-I experience: Valuable knowledge for improving the e-st@r-II design, Acta Astronaut., 121, 13, 10.1016/j.actaastro.2015.12.027 · DOI
  64. D.E. Rowland, J. Hill, P. Uribe, J. Klenzing, F. Hunsaker, M. Fowle, K. Simms, H. Hancock, M. Saulino, D. Guzman, A. Willingham, A. Weatherwax, The NSF Firefly CubeSat mission: Rideshare mission to study energetic electrons produced by lightning, in: IEEE Aerospace Conference, AERO, Big Sky (MT), USa, 2011, http://dx.doi.org/10.1109/AERO.2011.5747231. · DOI
  65. Angelopoulos, 2020, The ELFIN mission, Space Sci. Rev., 216, 10.1007/s11214-020-00721-7 · DOI
  66. D.L. Oltrogge, K. Leveque, An evaluation of CubeSat orbital decay, in: 25th Annual AIAA/USU Conference on Small Satellites, Logan (UT), USA, 2011.
  67. Murcia Piñeros, 2021, Analysis of the orbit lifetime of CubeSats in low earth orbits including periodic variation in drag due to attitude motion, Adv. Space Res., 67, 902, 10.1016/j.asr.2020.10.024 · DOI
  68. Pardini, 2020, Comparison and accuracy assessment of semi-empirical atmosphere models through the orbital decay of spherical satellites, J. Astronaut. Sci., 49, 255, 10.1007/BF03546321 · DOI
  69. König, 1996, GFZ-1: A small laser satellite mission for gravity field model improvement, Geophys. Res. Lett., 23, 3143, 10.1029/96GL02574 · DOI
  70. Johnson, 2011, NanoSail-D: A solar sail demonstration mission, Acta Astronaut., 68, 571, 10.1016/j.actaastro.2010.02.008 · DOI
  71. Vincent, 2017, The CanX-7 nanosatellite ADS-B mission: A preliminary assessment, Positioning, 8, 1, 10.4236/pos.2017.81001 · DOI
  72. E. Eiler, A. Abraham, Characterizing the reentry prediction uncertainty of Tiangong-1, in: AAS/AIAA Astrodynamics Specialist Conference, Snowbird (UT), USA, 2018.

Cited by

Sorted by citations

Authors
Niccolai, L., & Mengali, G.
Affiliations
University of Pisa (IT)
Corresponding author
Niccolai, Lorenzo
ORCID
Venue
Acta Astronautica
Publisher
Elsevier BV
Published
2024-12
Volume
225
Pages
601-614
ISSN
0094-5765 (ISSN-L)
DOI
10.1016/j.actaastro.2024.09.045
OpenAlex
W4402812817
Cited by
9
References
1
Citations by year
2026: 6 · 2025: 3
FWCI
1.56
Type
journal article
Language
en
Open access
Licence
Locations
  • Acta Astronautica (publishedVersion, cc-by)
  • CINECA IRIS Institutial research information system (University of Pisa) (submittedVersion, cc-by-nc-nd)
Funders
University of Pisa (PRA_2022_1)
Topics
  • Physical Sciences › Engineering › Aerospace Engineering › Space Satellite Systems and Control
  • Physical Sciences › Engineering › Aerospace Engineering › Spacecraft Dynamics and Control
  • Physical Sciences › Engineering › Aerospace Engineering › Spacecraft Design and Technology
Keywords
low Earth orbit satellites, space debris, atmospheric drag, solar activity effects, air density, scale height, drag coefficient, drag sail

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review