Pith. sign in

REVIEW 2 major objections 5 minor 31 references

Areostationary Satellite Station Keeping Via a Natural Motion Trajectory and Predictive Control

T0 review · 2 major / 5 minor · reviewed 2026-08-02 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read A Mars-areostationary satellite can be held on station with about 3.4 m/s of fuel per year by tracking a natural drift orbit instead of a fixed longitude.

desk verdict Smart use of a Martian libration limit cycle as an MPC reference, but the fuel-saving claim is not apples-to-apples with the ±0.2°-window comparators; the abstract overstates the result. read the letter →

arxiv 2603.00781 v2 pith:6YZVZMOE submitted 2026-02-28 physics.space-ph math.OC

Nathan A. Gall , Robert D. Halverson , Ryan J. Caverly This is my paper
classification physics.space-phmath.OC
keywords areostationaryMarsorbitstationkeepingmodelpredictivecontrolnaturalmotiontrajectorylimitcycleconvexoptimizationgravitationalperturbations
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper tries to show that a Mars-areostationary satellite can be kept on station far more cheaply if the controller tracks a natural, fuel-free oscillation in radial and east-west motion rather than holding a fixed longitude. Mars's lumpy gravity creates a slow limit cycle around each stable longitude, swinging the satellite about ±1° in longitude over roughly 127 days; linearizing around this free trajectory reduces station keeping to a convex quadratic program. The claimed annual fuel cost is 3.418 m/s, the lowest of any convex-optimization-based AMO station-keeping policy and comparable to a computationally expensive nonlinear MPC, with robustness to thrust, mass, and estimation errors. The savings come with the caveat that the satellite is allowed to drift up to about 1.2° in longitude from the nominal slot.

What carries the argument

The key object is the natural motion trajectory (NMT): a fuel-free limit cycle in the satellite's radial and along-track motion about a stable areostationary longitude, produced by the fifth-order spherical-harmonic gravity field of Mars. Two such limit cycles exist, centered at 17.92°W and 167.83°E. The paper derives a discrete-time linear time-varying (LTV) model by linearizing the full nonlinear dynamics about this trajectory, with the reference control set to zero; this LTV model is what turns the station-keeping problem into a convex quadratic program solvable in real time.

What would settle it

Simulate the same MPC policy with the station-keeping window enforced relative to the fixed 17.92°W longitude (a strict ±0.2° box) while keeping the natural-motion model; if the annual Δv rises to roughly 4 m/s (the value of the prior LTV policy), the claimed improvement is entirely due to relaxing the window, not to the natural-motion model. Alternatively, measure the actual free trajectory with a Mars-orbiting satellite; if its period or amplitude diverges from the predicted 127-day / ±1° figure, the model's benefit disappears.

Watch

Extended reading notes

Core claim

The central discovery is that a satellite at one of Mars's stable areostationary longitudes naturally follows a bounded, periodic limit cycle in the radial and east-west directions under the influence of Mars's non-uniform gravity, with no thrust. This trajectory, which drifts about a degree in longitude over about 127 days, exists because the radial gravitational perturbation is nearly three orders of magnitude stronger than the other perturbations and couples into east-west motion. The authors build a linear time-varying prediction model by linearizing the full nonlinear dynamics about this limit cycle, then use model predictive control to keep the satellite within a small window around th

Load-bearing premise

The fuel savings rest on the premise that a Mars relay or navigation satellite may be allowed to drift up to about ±1.2° in longitude from its nominal slot, since the station-keeping window is defined relative to the drifting natural trajectory, not to the fixed areostationary longitude.

Editorial extensions

If this is right

  • If the natural-motion-tracking policy is right, autonomous AMO station keeping can be performed with an annual fuel cost of roughly 3.4 m/s, making long-lived relay and navigation satellites at Mars more feasible.
  • The 127-day, ±1° natural oscillation means a satellite can be allowed to drift in longitude without breaking a communication requirement; a 1° longitude deviation changes a surface receiver's elevation by about 1.2°.
  • The LTV model linearized about the limit cycle eliminates the need to cancel the dominant radial and east-west perturbations, so nearly all fuel goes to north-south station keeping.
  • The policy degrades gracefully under 15% thrust errors, 20% mass error, missing time-varying third-body ephemerides, and a one-hour computation delay, each adding less than 4% fuel; however, 100 m / 0.1 m/s navigation errors increase fuel use roughly 2.6-fold.
  • Because the optimization is a convex quadratic program, on-board implementation is plausible, in contrast to the comparable nonlinear MPC.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper's window-relaxation caveat implies that the Δv advantage over prior policies is partly a measure of the cost of enforcing a tight longitude window; a mission that absolutely requires ±0.2° at a fixed longitude would not see the full saving.
  • The natural-motion idea might transfer to Earth's geostationary orbit, where similar longitude-dependent gravity terms and stable points exist, potentially giving GEO station keeping a fuel-free drift reference.
  • One testable extension is to run the same policy at the other stable longitude (167.83°E) to check whether the limit cycle and annual Δv are symmetric; the paper only simulates 17.92°W.
  • The reported fuel cost is essentially the minimum north-south drift compensation; comparing it to the analytically required Δv for inclination control would separate unavoidable cost from control-law inefficiency.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. The paper proposes a station-keeping MPC strategy for areostationary Mars orbit (AMO) satellites. It identifies a natural-motion limit cycle in the radial and longitudinal dynamics near the stable longitude 17.92° W, caused primarily by Mars' gravity harmonics, and uses this trajectory as a fuel-free reference. A discrete-time LTV prediction model is obtained by linearizing the nonlinear dynamics about this trajectory, and a soft-constrained QP is solved at each 1-hour step. In one-year nonlinear simulations with GMM2B gravity (to fifth order), third-body and SRP perturbations, the proposed policy reports an annual Δv of 3.418 m/s, almost entirely in the North-South direction, together with robustness tests for thrust uncertainty, mass uncertainty, unavailable time-varying perturbations, a one-hour computation delay, and navigation errors. The paper claims that this is the lowest annual Δv of any convex AMO station-keeping policy in the literature.

Significance. The central idea—using a natural limit cycle as a reference so that the controller does not actively cancel the dominant radial and East-West harmonic perturbations—is interesting and, if confirmed on an apples-to-apples basis, would be a genuine advance: it offers convex QP tractability with fuel consumption close to that of nonlinear MPC (3.418 vs. 3.423 m/s). The robustness study is a real strength; it goes beyond prior AMO MPC papers by quantifying sensitivity to thrust bias, mass uncertainty, missing ephemeris knowledge, computation delay, and navigation noise, and it reports the Δv decomposition by axis. However, the headline fuel-efficiency claim is currently not established because the comparison in Table 2 uses different station-keeping windows for the proposed policy and the baselines. The paper needs a same-window comparison or an explicit sensitivity study before the 'lowest convex AMO station-keeping Δv' claim can be supported.

major comments (2)
  1. [V.C, Table 2] The headline comparison is not apples-to-apples. The proposed policy constrains the spacecraft to within ±0.2° of the natural motion trajectory, which the text says results in 'roughly up to ±1.2° of longitudinal deviation from 17.92° West.' The LTI-MPC [20], LTV-MPC [22], and nMPC [21,23] baselines instead enforce a static ±0.2° window about the fixed stable longitude. This is a sixfold difference in allowable longitude excursion, and station-keeping Δv is strongly dependent on the deadband. The 3.418 m/s result versus 4.175 and 4.350 m/s could therefore be due almost entirely to the relaxed constraint rather than to the natural-motion reference or the LTV linearization. No experiment in the paper varies the window size while holding the controller type fixed. The paper should either (a) run the proposed policy with an absolute ±0.2° longitude window, (b) relax the baseline policies to
  2. [III.C and Eq. (6)] The existence of the natural motion trajectory is asserted on the basis of Fig. 1 and a narrative about harmonic perturbations, but no quantitative validation is provided that this is a true limit cycle. The zero-fuel reference in Eq. (6) and the LTV linearization in Eq. (10) are built entirely on this assumption. If the trajectory is actually a slowly evolving drift, the 'fuel-free' premise collapses. The authors should provide at least a return-map or Floquet stability check, the period and amplitude of the cycle, and a brief sensitivity study to the GMM2B gravity-model truncation order. This would also help resolve the ambiguity between the abstract's 'within one degree' and the body's 'up to ±1.2°.'
minor comments (5)
  1. [Abstract / V.C] The abstract says the natural motion trajectory maintains the satellite 'within one degree of longitude,' but V.C says the proposed policy can result in 'roughly up to ±1.2° of longitudinal deviation from 17.92° West.' Please state the exact allowable longitude envelope (one-sided or two-sided) and reconcile these numbers.
  2. [V.D] The computation-time robustness case imposes a one-hour delay but does not report actual CPU solve times or hardware. Since the novelty includes 'computationally tractable for on-board implementation,' a measure of wall-clock time per MPC step (even on a simulated flight-class processor) would substantiate this claim.
  3. [V.D / Table 3] The robustness study covers actuator, mass, ephemeris, delay, and navigation errors but omits gravity-field coefficient uncertainty. Because the natural motion trajectory is derived from GMM2B, it would be useful to test sensitivity to, e.g., truncation order or coefficient perturbations in the predicted reference trajectory.
  4. [Table 2 and Refs. [20]-[23]] All baseline convex MPC policies are from the authors' prior work. An independent implementation or an external baseline would strengthen the comparison, especially because the window convention differs.
  5. [IV] No proof of recursive feasibility or closed-loop stability is given for the soft-constrained QP without terminal cost. The one-year simulations are compelling empirical evidence, but a short comment on the assumptions under which stability is expected (or a reference to the relevant MPC stability framework) would be appropriate.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular derivation found; the natural-motion reference and MPC are self-contained, but the fuel-efficiency comparison is not apples-to-apples because the proposed policy allows larger absolute longitude drift.

full rationale

The central derivation is not circular: the natural motion trajectory is obtained by numerically solving Eq. (6) under the GMM-2B gravity model from an external source (Ref. [26]), not fitted to any fuel target; the LTV prediction model in Eqs. (7)-(11) is a first-order Taylor expansion about that trajectory; and the reported 3.418 m/s annual Δv is a simulation outcome of the nonlinear dynamics, not a fitted parameter renamed as a prediction. The paper does rely on the authors' own prior MPC policies [20,22] as the only convex-optimization baselines for the 'lowest Δv' superlative, which is a literature and benchmarking limitation rather than a derivation-circularity issue. The most material weakness is explicitly acknowledged in Section V.C: 'the proposed policy maintains the spacecraft within ±0.2° of the natural motion trajectory, resulting in roughly up to ±1.2° of longitudinal deviation from 17.92° West.' Because the comparators enforce a fixed ±0.2° window about the true AMO longitude, the headline fuel comparison is unfair and should be re-run with matched absolute windows. However, this does not make the derivation circular: the controller's fuel savings are a physical consequence of tracking a computed fuel-free limit cycle, and the paper is transparent about the looser absolute station-keeping window. No load-bearing step reduces by construction to its own input, so no significant circularity is present; score 2 reflects the minor self-citation in the baseline comparison and the acknowledged benchmark mismatch.

Assumptions & free parameters 7 free parameters · 5 assumptions · 0 invented entities

The central result rests on the fidelity of the GMM2B gravity model truncated at degree 5, the choice of perturbation set, and the unproven-but-numerically-supported existence of the limit cycle. The MPC tuning parameters (N, R, S) are chosen by hand, not fitted to achieve the reported Δv.

free parameters (7)
  • Prediction horizon N = 18
    Section V.A: chosen through tuning to ensure satisfactory performance.
  • Control weight R = 5.6e5 * I
    Section V.A: chosen to emphasize minimization of control effort.
  • Slack weight S = 100 * I
    Section V.A: chosen to strictly enforce the station-keeping window with a soft constraint.
  • Longitude window λmax = 0.2° relative to natural trajectory
    Section V.A: defined as the maximum deviation from the natural motion trajectory; this is a mission requirement, not derived.
  • Latitude window φmax = 0.05°
    Section V.A: same as above.
  • Maximum thrust fmax = 50 mN per axis
    Section V.A: low-thrust propulsion assumption.
  • SRP constant = 4.5e-6
    Section V.A: modeling input for solar radiation pressure.
assumptions (5)
  • domain assumption GMM2B spherical harmonic coefficients up to degree 5 adequately model Mars' gravity for AMO dynamics.
    Section III.B: coefficients from GMM2B [26] used up to fifth order, citing Ref. [23] that higher orders are negligible.
  • ad hoc to paper The natural motion trajectory is a limit cycle of Eq. (6) with only radial and along-track harmonic perturbations; its existence is established by numerical simulation, not proof.
    Section III.C: 'This motion is shown in Fig. 1' — no analytical proof of periodicity is given.
  • domain assumption Third-body perturbations (Phobos, Deimos, Sun) and solar radiation pressure are modeled with the given constants, and are assumed small enough that the LTV linearization about the limit cycle is accurate.
    Section III.B and V.A.
  • standard math The first-order Taylor expansion and zero-order hold discretization produce a prediction model accurate over the 1-hour sample period.
    Section III.D, Eqs. (7)–(10).
  • ad hoc to paper The MPC soft-constrained QP with no terminal cost is stabilizing for this system; no formal stability proof is provided.
    Section IV: the objective contains no state penalty and no terminal cost.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Areostationary Satellite Station Keeping Via a Natural Motion Trajectory and Predictive Control." pith.science (2026). https://pith.science/paper/6YZVZMOE

@misc{pith2026260300781,
  author       = {Pith},
  title        = {Pith review of: Areostationary Satellite Station Keeping Via a Natural Motion Trajectory and Predictive Control},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6YZVZMOE}},
  note         = {Machine review of arXiv:2603.00781}
}
read the original abstract

Areostationary Mars orbit (AMO) satellites will play an important role in future expeditions to the Martian surface due to their strength as navigation and communication satellites. Perturbative forces experienced by an AMOR satellite will cause it to drift from its nominal orbit, necessitating station keeping. This note presents a novel approach to AMO station keeping that bridges the gap seen in prior predictive control methods between fuel-efficiency and computational-efficiency. The method proposed in this notes involves the discovery and use of a fuel-free natural motion trajectory that maintains the satellite within one degree of longitude from a areostationary orbit. Two of these natural motion trajectories exist as limit cycles about Mars' stable equilibrium longitudes. They are the resulting motion in the presence of Mars' non-homogeneous gravitational field, accounting for Keplerian and higher-order gravitational perturbations. The proposed MPC policy uses a linear time-varying (LTV) dynamic model that is derived by linearizing the satellite's dynamics relative to the appropriate natural motion trajectory. The result is a station keeping policy that minimizes the fuel consumed, maintains thrust and station-keeping constraints, and is computationally tractable for on-board implementation as a quadratic program.

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

31 extracted references · 14 canonical work pages

  1. [20]

    Station Kee ping of Satellites in Areostationary Mars Orbit Using Model Predictive Control,

    Halverson, R., Weiss, A., and Caverly, R., “Station Kee ping of Satellites in Areostationary Mars Orbit Using Model Predictive Control,” AAS/AIAA Space Flight Mechanics Meeting , 2021. AAS 593-602

    2021

  2. [22]

    Station Keep ing of Areostationary Mars Orbit Satellites Using Linear Ti me-Varying Model Predictive Control,

    Gall, N., Halverson, R., and Caverly, R., “Station Keep ing of Areostationary Mars Orbit Satellites Using Linear Ti me-Varying Model Predictive Control,” AAS/AIAA Astrodynamics Specialist Conference, 2024. AAS 24-356

    2024

  3. [1]

    Predictive Station Keeping of Areostat ionary Satellites Using Natural Motion Trajectories,

    Gall, N. A., and Caverly, R. J., “Predictive Station Keeping of Areostat ionary Satellites Using Natural Motion Trajectories,” 2025 Regional Student Conferences, 2025. https://doi.org/10.2514/6.2025-99106, AIAA 2025 -99106

    work page doi:10.2514/6.2025-99106 2025

  4. [2]

    Mars Network for Enabling Low-Cost Missions ,

    Hastrup, R. C., Bell, D. J., Cesarone, R. J., Edwards, C. D ., Ely, T. A., Guinn, J. R., Rosell, S. N., Srinivasan, J. M., a nd Townes, S. A., “Mars Network for Enabling Low-Cost Missions ,” Acta Astronautica, Vol. 52, No. 2–6, 2003, pp. 227–235. https://doi.org/0.1016/S0094-5765(02)00161-3

    2003

  5. [3]

    Small Areostationary Telecommunications Orbiter Concepts for Mars in the 2020s,

    Lock, R. E., Edwards, C. D., Nicholas, A. K., Woolley, R., and Bell, D. J., “Small Areostationary Telecommunications Orbiter Concepts for Mars in the 2020s,” IEEE Aerospace Conference, 2016, pp. 1–12. https://doi.org/10.1109/AERO.2016.750 0899

    work page doi:10.1109/aero.2016.750 2016

  6. [4]

    Proximity Link Design and Per- formance Options for a Mars Areostationary Relay Satellite ,

    Edwards, C. D., Bell, D. J., Biswas, A., Cheung, K.-M., an d Lock, R. E., “Proximity Link Design and Per- formance Options for a Mars Areostationary Relay Satellite ,” IEEE Aerospace Conference , 2016, pp. 1–10. https://doi.org/10.1109/AERO.2016.7500680

    arXiv 2016

  7. [5]

    CDMA Comm unication System for Mars Areostationary Relay Satellite,

    Babuscia, A., Divsalar, D., and Cheung, K. M., “CDMA Comm unication System for Mars Areostationary Relay Satellite, ” IEEE Aerospace Conference, 2017, pp. 1–10. https://doi.org/10.1109/AERO.2017.794 3941

    work page doi:10.1109/aero.2017.794 2017

  8. [6]

    S pace and Earth Terminal Sizing for Future Mars Missions,

    Breidenthal, J., Xie, H., Lau, C.-W., and MacNeal, B., “S pace and Earth Terminal Sizing for Future Mars Missions,”SpaceOps Conference, 2018. https://doi.org/10.2514/6.2018-2426, AIAA 2018- 2426

    work page doi:10.2514/6.2018-2426 2018

Show all 31 references
  1. [7]

    Mars Con stellation Design and Low-Thrust Deployment Us- ing Nonlinear Orbit Control,

    Pontani, M., Pustorino, M., and Teofilatto, P., “Mars Con stellation Design and Low-Thrust Deployment Us- ing Nonlinear Orbit Control,” The Journal of the Astronautical Sciences , Vol. 69, 2022, pp. 1691–1725. https://doi.org/10.1007/s40295-022-00352-w

    2022 doi

  2. [8]

    Analysis of Or bit Determination From Earth-Based Tracking for Relay Satellites in a Perturbed Areostationary Orbit,

    Romero, P., Pablos, B., and Barderas, G., “Analysis of Or bit Determination From Earth-Based Tracking for Relay Satellites in a Perturbed Areostationary Orbit,” Acta Astronautica , Vol. 136, 2017, pp. 434–442. https://doi.org/10.1016/j.actaastro.2017.04.002. 14

    2017 doi

  3. [9]

    Areostationary Mars Orbi t: Dynamics, Control, and Applications,

    Matthieu, F., and Yuying, L., “Areostationary Mars Orbi t: Dynamics, Control, and Applications,” IFAC-PapersOnLine, Vol. 59, No. 20, 2025, pp. 488–493. https://doi.org/10.101 6/j.ifacol.2025.11.198

    2025

  4. [10]

    M., Handbook of Geostationary Orbits , Microcosm, Inc., Dordrecht, The Netherlands, 1994

    Soop, E. M., Handbook of Geostationary Orbits , Microcosm, Inc., Dordrecht, The Netherlands, 1994

    1994

  5. [11]

    Geostationary Satellite Station-Keeping Using Convex Optimization,

    De Bruijn, F. J., Theil, S., Choukroun, D., and Gill, E., “Geostationary Satellite Station-Keeping Using Convex Optimization,” Journal of Guidance, Control, and Dynamics , Vol. 39, No. 3, 2016, pp. 605–616. https://doi.org/10.251 4/1.G001302

    2016

  6. [12]

    Long-Term Electric-Propulsion Geos tationary Station-Keeping via Integer Programming,

    Gazzino, C., Arzelier, D., Louembet, C., Cerri, L., Pit tet, C., and Losa, D., “Long-Term Electric-Propulsion Geos tationary Station-Keeping via Integer Programming,” Journal of Guidance, Control, and Dynamics , Vol. 42, No. 5, 2019, pp. 976–991. https://doi.org/10.2514/1.G003644

    2019 doi

  7. [13]

    Electric Satellite Station Keeping, Attitude Control, and Momentum Management by MPC,

    Caverly, R. J., Di Cairano, S., and Weiss, A., “Electric Satellite Station Keeping, Attitude Control, and Momentum Management by MPC,” IEEE Transactions on Control Systems Technology , Vol. 29, No. 4, 2020, pp. 1475–1489. https://doi.org/10.1109/TCST.2020.3014601

    2020

  8. [14]

    Combined Long-Term Collision Avoidanc e and Stochastic Station-Keeping in Geostationary Earth Orbit,

    De Vittori, A., Pavanello, Z., Di Lizia, P., McMahon, J. , and Armellin, R., “Combined Long-Term Collision Avoidanc e and Stochastic Station-Keeping in Geostationary Earth Orbit,” Journal of Guidance, Control, and Dynamics , Vol. 48, No. 4, 2025, pp. 840–854. https://doi.org/1...

    2025 doi

  9. [15]

    Optimal Longitudes Determination for the Station Keeping of Areostationary Satellites,

    Silva, J. J., and Romero, P., “Optimal Longitudes Determination for the Station Keeping of Areostationary Satellites,” Planetary and Space Science, Vol. 87, 2013, pp. 14–18. https://doi.org/10.1016/j.pss .2012.11.013

    2013 doi

  10. [16]

    St ation-Keeping Maneuvers to Control the Inclination Evolut ion of Areostationary Satellites,

    Romero, P., Barderas, G., and García-Roldán, J. M., “St ation-Keeping Maneuvers to Control the Inclination Evolut ion of Areostationary Satellites,” Journal of Guidance, Control, and Dynamics , Vol. 38, No. 11, 2015, pp. 2223–2227. https://doi.org/10.2514/1.G001162

    2015 doi

  11. [17]

    Model Predictive Control in Aerosp ace Systems: Current State and Opportunities,

    Eren, U., Prach, A., Koçer, B. B., Raković, S. V ., Kayaca n, E., and Açıkmeşe, B., “Model Predictive Control in Aerosp ace Systems: Current State and Opportunities,” Journal of Guidance, Control, and Dynamics, Vol. 40, No. 7, 2017, pp. 1541–1566. https://doi.org/10.2514/1.G002507

    2017 doi

  12. [18]

    Real-Time Optimization and Model Predictive Control for Aerospace and Automotive Applications,

    Di Cairano, S., and Kolmanovsky, I. V ., “Real-Time Optimization and Model Predictive Control for Aerospace and Automotive Applications,” American Control Conference, 2018, pp. 2392–2409. https://doi.org/10.23919/ACC.201 8.8431585

    2018 doi

  13. [19]

    Safe and Constrained Rendezvous, Proximity Operations , and Docking,

    Petersen, C., Caverly, R. J., Phillips, S., and Weiss, A ., “Safe and Constrained Rendezvous, Proximity Operations , and Docking,” American Control Conference, 2023, pp. 3645–3661. https://doi.org/10.23919/ACC5577 9.2023.10155826

    2023

  14. [21]

    A Compari son of Linear Quadratic and Nonlinear Model Predic- tive Control Applied to Station Keeping of Satellites in Are ostationary Mars Orbits,

    Halverson, R. D., Weiss, A., and Caverly, R., “A Compari son of Linear Quadratic and Nonlinear Model Predic- tive Control Applied to Station Keeping of Satellites in Are ostationary Mars Orbits,” AIAA SciTech Forum , 2023. https://doi.org/10.2514/6.2023-2000, AIAA 2023-2000. 15

    2023 doi

  15. [23]

    Autonomous Station Keeping of Satellites in Areostationary Mars Orbit: A Predictive Control Approach,

    Halverson, R. D., Weiss, A., Lundin, G., and Caverly, R. J., “Autonomous Station Keeping of Satellites in Areostationary Mars Orbit: A Predictive Control Approach, ” Acta Astronautica , Vol. 230, 2025, pp. 1–15. https://doi.org/10.1016/j.actaastro.2025.01.064

    2025 doi

  16. [24]

    T., Vadali, S

    Alfriend, K. T., Vadali, S. R., Gurfil, P., How, J. P., and Breger, L. S., Spacecraft Formation Flying: Dynamics, Control, and Navigation, 1st ed., Elsevier, Oxford, UK, 2010

    2010

  17. [25]

    G., and Hoots, F., Applied Orbit Perturbation and Maintenance , 2 nd ed., Aerospace Press, American Institute of Aeronautics & Astronautics, Reston, V A, 2018

    Chao, C.-C. G., and Hoots, F., Applied Orbit Perturbation and Maintenance , 2 nd ed., Aerospace Press, American Institute of Aeronautics & Astronautics, Reston, V A, 2018

    2018

  18. [26]

    An Improve d Solution of the Gravity Field of Mars (GMM-2B) From Mars Glob al Surveyor,

    Lemoine, F. G., Smith, D. E., Rowlands, D. D., Zuber, M. T ., Neumann, G. A., Chinn, D. S., and Pavlis, D. E., “An Improve d Solution of the Gravity Field of Mars (GMM-2B) From Mars Glob al Surveyor,” Journal of Geophysical Research: Planets , Vol. 106, No. E10, 2001, pp. 2335...

    2001 doi

  19. [27]

    Technical Note: Perturbations on a Stationary Satellite by the Longitude-Dependent terms in Mars’ Gravitational Field,

    Alvarellos, J. L., “Technical Note: Perturbations on a Stationary Satellite by the Longitude-Dependent terms in Mars’ Gravitational Field,” The Journal of the Astronautical Sciences , Vol. 57, No. 4, 2009, pp. 701–715. https://doi.org/10.1007/BF03321524

    2009 doi

  20. [28]

    Discretization Perfor- mance and Accuracy Analysis for the Rocket Powered Descent G uidance Problem,

    Malyuta, D., Reynolds, T., Szmuk, M., Mesbahi, M., Acik mese, B., and Carson, J. M., “Discretization Perfor- mance and Accuracy Analysis for the Rocket Powered Descent G uidance Problem,” AIAA SciTech Forum , 2019. https://doi.org/10.2514/6.2019-0925, AIAA 2019-0925

    2019 doi

  21. [29]

    The Comp lex-Step Derivative Approximation,

    Martins, J. R., Sturdza, P., and Alonso, J. J., “The Comp lex-Step Derivative Approximation,” ACM Transactions on Mathe- matical Software, Vol. 29, No. 3, 2003, pp. 245–262. https://doi.org/10.114 5/838250.838251

    2003

  22. [30]

    Complex Step Jacobian,

    Cao, Y ., “Complex Step Jacobian,” , 2025. URL https://www.mathworks.com/matlabcentral/fileexchange/18176-complex-step-jacobian, MATLAB Central File Exchange, Retrieved February 26, 2025

    2025

  23. [31]

    Complex-step-compatible atan2(),

    Ricciardi, A., “Complex-step-compatible atan2(),” , 2025. URL https://www.mathworks.com/matlabcentral/fileexchange/101193-complex-step-comp MATLAB Central File Exchange, Retrieved February 26, 2025. 16

    2025

Pith tools

Reviewed August 2, 2026 · model on record in the stance chip above.