大氣阻力會顯著影響低地球軌道衛星，造成軌道衰減與軌道參數變化。小型衛星常依賴兩行軌道根數（TLE）進行事後軌道分析。然而，IRIS-F2/F3 的相對運動無法僅以單一固定漂移率假設充分解釋。因此，本研究探討 TLE 資料是否能與實際操作紀錄相互對應，並辨識在哪些條件下，觀測到的漂移變化可作為差分阻力效應的替代指標。

本研究提出一套依據不同狀態進行分段的分析流程。首先，將 TLE、衛星健康資訊與太空天氣資料進行標準化、品質篩選，並依時間順序整合成完整資料序列。接著，依據操作狀態將資料分類為高阻力與低阻力區段。透過軌道傳播模型與 TLE 分析，萃取軌道衰減指標、半長軸變化、平均運動變化以及漂移相關指標。這些指標並非直接的物理量測結果，而是用來反映有效阻力變化的替代指標，並可作為後續軌道預測與比較分析的依據。

本研究的主要創新在於建立一套結合歷史 TLE 資料與實際操作紀錄的姿態狀態分段分析架構，用以探討不同姿態狀態下的阻力影響。研究結果顯示，在遙測資料有限的情況下，姿態狀態分段能有效從歷史 TLE 資料中萃取出具有意義的阻力相關行為。相較於未分段的整體分析，此方法也能更清楚呈現名義狀態與高阻力狀態之間的差異。

Atmospheric drag causes orbital decay and parameter variation in Low Earth Orbit satellites. Small satellites often rely on Two-Line Element (TLE) data for post-orbit analysis, though relative motion between satellites cannot be captured by a single constant drift assumption. This study examines whether TLE-derived behavior matches operational records and identifies when observed drift can serve as a differential-drag proxy.

The thesis proposes a workflow that divides the data into state-dependent segments. TLE, Beacon, and space-weather information are normalized, quality-controlled, chronologically arranged, and classified into high- and low-drag segments. SGP4 and TLE analysis yield orbit-decay indicators, semi-major axis, mean motion, and drift proxies. These indicators are treated as effective drag proxies, rather than direct physical measurements, to support orbit prediction and comparison.

The main contribution is an attitude-state segmented framework that integrates historical TLE data with operational records of IRIS-F2 and IRIS-F3 cubesates to investigate drag effects. The results show that attitude-state segmentation effectively extracts significant drag-related behavior from historical TLE data, especially with limited telemetry. It also highlights distinct differences between nominal and high-drag states compared to non-segmented analysis.

[1] CubeSat Design Specification, Revision 14.1, The CubeSat Program, California Polytechnic State University, San Luis Obispo, CA, USA, 2022.
[2] D. A. Vallado, Fundamentals of Astrodynamics and Applications, 4th ed. Microcosm Press, 2013.
[3] H. D. Curtis, Orbital Mechanics for Engineering Students, 3rd ed. Heinemann, 2014. Butterworth
[4] W. H. Clohessy and R. S. Wiltshire, “Terminal guidance system for satellite rendezvous,” vol. 27, no. 9, pp. 653–658, Sep. 1960, doi: 10.2514/8.8704. [Online]. Available: https://arc.aiaa.org/doi/10.2514/8.8704
[5] H. Schaub and K. T. Alfriend, “J2 invariant relative orbits for spacecraft formations,” Celestial Mechanics and Dynamical Astronomy, vol. 79, no. 2, pp. 77–95, Feb. 2001, doi: 10.1023/A:1011161811472. [Online]. Available: https://doi.org/10.1023/A: 1011161811472
[6] D. Pérez and R. Bevilacqua, “Differential drag spacecraft rendezvous using an adaptive Lyapunov control strategy,” Acta Astronautica, vol. 83, pp. 196–207, Feb. 2013. [Online]. Available: https://doi.org/10.1016/j.actaastro.2012.09.005
[7] L. Dell׳Elce and G. Kerschen, “Optimal propellantless rendez-vous using differential drag,” Acta Astronautica, vol. 109, pp. 112–123, Apr. 2015. [Online]. Available: https://doi.org/10.1016/j.actaastro.2015.01.011
[8] C. L. Leonard, W. M. Hollister, and E. V. Bergmann, “Orbital formation keeping with differential drag,” Journal of Guidance, Control, and Dynamics, vol. 12, no. 1, pp. 108–113, Jan. 1989, doi: 10.2514/3.20374. [Online]. Available: https: //doi.org/10.2514/3.20374
[9] B. S. Kumar, A. Ng, K. Yoshihara, and A. De Ruiter, “Differential drag as a means of spacecraft formation control,” IEEE Transactions on Aerospace and Electronic Systems, vol. 47, no. 2, pp. 1125–1135, Apr. 2011, doi: 10.1109/TAES.2011.5751247. [Online]. Available: https://doi.org/10.1109/TAES.2011.5751247
[10] C. Foster, J. Mason, V. Vittaldev, L. Leung, V. Beukelaers, L. Stepan, and R. Zimmerman, “Constellation phasing with differential drag on Planet Labs satellites,” Journal of Spacecraft and Rockets, vol. 55, no. 2, pp. 473–483, Mar. 2018, doi: 10.2514/1.A33927. [Online]. Available: https://doi.org/10.2514/1.A33927
[11] C. L. Leonard, “Formationkeeping of Spacecraft via Differential Drag,” M.S. thesis, Dept. of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA, USA, Jul. 1986. [Online]. Available: https://ntrs.nasa.gov/api/citations/19870004033/ downloads/19870004033.pdf
[12] R. Bevilacqua and M. Romano, “Rendezvous Maneuvers of Multiple Spacecraft Using Differential Drag Under J2 Perturbation,” J. Guid. Control Dyn., vol. 31, no. 6, pp. 1595–1607, Nov. 2008, doi: 10.2514/1.36362. [Online]. Available: https://doi.org/10.2514/1.36362
[13] B. S. Kumar, “Differential Drag as a Means of Spacecraft Formation Control,” in Proc. IEEE Aerosp. Conf., Big Sky, MT, USA, 2007, pp. 1–12, doi: 10.1109/AERO.2007.352790. [Online]. Available: https://doi.org/10.1109/AERO.2007. 352790
[14] O. Ben-Yaacov and P. Gurfil, “Long-Term Cluster Flight of Multiple Satellites Using Differential Drag,” Journal of Guidance, Control, and Dynamics, vol. 36, no. 6, pp. 1731–1740, Nov. 2013. [Online]. Available: https://arc.aiaa.org/doi/10.2514/1.61496
[15] G. Gaias, J.-S. Ardaens, and O. Montenbruck, “Model of J2 perturbed satellite relative motion with time-varying differential drag,” Celestial Mechanics and Dynamical Astronomy, vol. 123, no. 4, pp. 411–433, Aug. 2015, doi: 10.1007/s10569-015-9643-2. [Online]. Available: https://doi.org/10.1007/s10569-015-9643-2
[16] M. K. Ben-Larbi, T. Jusko, and E. Stoll, “Input-output linearized spacecraft formation control via differential drag using relative orbital elements,” Advances in Space Research, vol. 67, no. 11, pp. 3444–3461, Jun. 2021, doi: 10.1016/j.asr.2020.12.005. [Online]. Available: https://doi.org/10.1016/j.asr.2020.12.005
[17] L. Mazal, D. Pérez, R. Bevilacqua, and F. Curti, “Spacecraft rendezvous by differential drag under uncertainties,” Journal of Guidance, Control, and Dynamics, vol. 39, no. 8, pp. 1721–1733, Aug. 2016, doi: 10.2514/1.G001785. [Online]. Available: https://doi.org/10.2514/1.G001785
[18] C. Riano-Rios, R. Bevilacqua, and W. Dixon, “Differential drag-based multiple spacecraft maneuvering and on-line parameter estimation using integral concurrent learning,” Acta Astronautica, vol. 174, pp. 189–203, Sep. 2020, doi: 10.1016/j.actaastro.2020.04.059. [Online]. Available: https://doi.org/10.1016/j.actaastro.2020.04.059
[19] C. Riano-Rios, R. Bevilacqua, and W. E. Dixon, “Adaptive control for differential drag-based rendezvous maneuvers with an unknown target,” Acta Astronautica, vol. 181, pp. 733–740, Apr. 2021, doi: 10.1016/j.actaastro.2020.03.011. [Online]. Available: https://doi.org/10.1016/j.actaastro.2020.03.011
[20] C. Traub, G. H. Herdrich, and S. Fasoulas, “Influence of energy accommodation on a robust spacecraft rendezvous maneuver using differential aerodynamic forces,” CEAS Space Journal, vol. 12, no. 1, pp. 43–63, 2020, doi: 10.1007/s12567-019-00258-8. [Online]. Available: https://doi.org/10.1007/s12567-019-00258-8
[21] D. A. Vallado, P. Crawford, R. Hujsak, and T. S. Kelso, “Revisiting spacetrack report #3,” in AIAA/AAS Astrodynamics Specialist Conference and Exhibit, 2006.
[22] C. Levit and W. Marshall, “Improved orbit predictions using two-line elements,” Advances in Space Research, vol. 47, no. 7, pp. 1107–1115, Apr. 2011, doi: 10.1016/j.asr.2010.10.017. [Online]. Available: https://doi.org/10.1016/j.asr.2010.10.017
[23] P. Kovář, P. Puričer, and K. Kovářová, “Study of the Two-Line Element Accuracy by 1U CubeSat with a GPS Receiver,” Sensors, vol. 22, no. 8, p. 2902, Apr. 2022, doi: 10.3390/s22082902. [Online]. Available: https://doi.org/10.3390/s22082902
[24] C. Foster, H. Hallam, and J. Mason, “Orbit Determination and Differential-drag Control of Planet Labs Cubesat Constellations,” in Proc. AIAA/AAS Astrodynamics Specialist Conf., Vail, CO, USA, Aug. 2015, pp. 1–13, doi: 10.48550/arXiv.1509.03270. [Online]. Available: https://arxiv.org/abs/1509.03270
[25] B. R. Bowman, W.KentTobiska, F. A. Marcos, and C. Valladares, “The JB2006 empirical thermospheric density model,” Journal of Atmospheric and Solar-Terrestrial Physics, vol. 70, no. 5, pp. 774–793, 2008, doi: 10.1016/j.jastp.2007.10.002. [Online]. Available: https://doi.org/10.1016/j.jastp.2007.10.002
[26] J. M. Picone, A. E. Hedin, D. P. Drob, and A. C. Aikin, “Nrlmsise-00 empirical model of the atmosphere: Statistical comparisons and scientific issues,” Journal of Geophysical Research: Space Physics, vol. 107, no. A12, pp. SIA 15–1–SIA 15–16, 2002, doi: 10.1029/2002JA009430. [Online]. Available: https://doi.org/10.1029/2002JA009430
[27] J. Wertz, Spacecraft Attitude Determination and Control, ser. Astrophysics and Space Science Library. Springer Netherlands, 2012.
[28] C. Traub, M. K. Ben-Larbi, F. Turco, A. J. Große Siestrup, J. Harbeck, E. Stoll, and D. Lück, “Revealing the impact of operational constraints on aerodynamic collision avoidance maneuvers: In-flight results from the BEESAT-4 CubeSat,” Acta Astronautica, vol. 234, pp. 296–313, 2025, doi: 10.1016/j.actaastro.2025.04.038. [Online]. Available: https://doi.org/10.1016/j.actaastro.2025.04.038
[29] A. W. Koenig, T. Guffanti, and S. D’Amico, “New State Transition Matrices for Spacecraft Relative Motion in Perturbed Orbits,” Journal of Guidance, Control, and Dynamics, vol. 40, no. 7, pp. 1749–1768, 2017, doi: 10.2514/1.G002409. [Online]. Available: https://doi.org/10.2514/1.G002409
[30] Space-Track.org, “Two-Line Element Sets,” https://www.space-track.org.
[31] T. S. Kelso, “CelesTrak,” https://celestrak.org.
[32] S. Hull, A. Shelton, and D. Richardson, “Differential drag demonstration: A post-mission experiment with the eo-1 spacecraft,” in Proceedings of the IAA Conference on Space Situational Awareness (ICSSA), no. GSFC-E-DAA-TN47408. Orlando, FL, United States: International Academy of Astronautics, 2017, Conference Paper.
[33] T. E. Berger, M. Dominique, G. Lucas, M. Pilinski, V. Ray, R. Sewell, E. K. Sutton, J. P. Thayer, and E. Thiemann, “The thermosphere is a drag: The 2022 starlink incident and the threat of geomagnetic storms to low earth orbit space operations,” Space Weather, vol. 21, no. 3, p. e2022SW003330, 2023, doi: 10.1029/2022SW003330. [Online]. Available: https://doi.org/10.1029/2022SW003330
[34] D. M. Oliveira and E. Zesta, “Satellite orbital drag during magnetic storms,” Space Weather, vol. 17, no. 11, pp. 1510–1533, 2019. [Online]. Available: https: //doi.org/10.1029/2019SW002287
[35] NOAASpaceWeatherPrediction Center, “F10.7 cm radio emissions,” https://www.swpc.noaa.gov/phenomena/f107-cm-radio-emissions.
[36] J. Matzka, C. Stolle, Y. Yamazaki, O. Bronkalla, and A. Morschhauser, “The geomagnetic kp index and derived indices of geomagnetic activity,” Space Weather, vol. 19, no. 5, p.e2020SW002641, 2021. [Online]. Available: https://doi.org/10.1029/2020SW002641
[37] NOAASpaceWeatherPredictionCenter,“Solarcycle25progression,”https://www.swpc.noaa.gov/products/solar-cycle-progression.
[38] Bruinsma, Sean, “The DTM-2013 thermosphere model,” Journal of Space Weather and Space Climate, vol. 5, p. A1, 2015.
[39] E. Belloni, S. Silvestrini, J. Prinetto, and M. Lavagna, “Relative and absolute on-board optimal formation acquisition and keeping for scientific activities in high-drag low-orbit environment,” Advances in Space Research, vol. 73, no. 11, pp. 5595–5613, 2024.
[40] T. Scruggs and N. Fitz-Coy, “Average cross-sectional area of idealized debrisat fragments using icosahedron motivated orientation vectors,” in Proc. 7th European Conference on Space Debris, Darmstadt, Germany, 2017, pp. 18–21