Semi-analytical model for the calculation of solar radiation pressure and its effects on a LEO satellite with predicting the change in position vectors using machine learning techniques

Mamta Gulati; Pranava Seth

REVIEW 5 major objections 6 minor 21 references

Semi-analytical model for the calculation of solar radiation pressure and its effects on a LEO satellite with predicting the change in position vectors using machine learning techniques

T0 review · 5 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read The paper claims that solar radiation pressure on a LEO satellite can be computed with a simple cannonball model and that a linear-regression model can predict the resulting position shift to within 0.027% mean absolute error.

desk verdict A clean tutorial on SRP basics and ground tracks, but the ML validation is circular, the HPOP comparison is missing, and a misattributed Starlink example undercuts confidence. read the letter →

arxiv 2411.17626 v1 pith:DIGPBW5I submitted 2024-11-26 cs.CE

Pranava Seth , Mamta Gulati This is my paper · ORCID

classification cs.CE

keywords AstrodynamicsOrbitalPerturbationsSolarRadiationPressureTrajectorychangesMachineLearningLEOsatellitescannonballmodellinearregression

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 claims that the perturbation of a low-Earth-orbit satellite by solar radiation pressure can be captured by a lightweight 'cannonball' model and that the resulting change in position can be predicted with a simple linear-regression machine-learning model. Using a 550 km circular, sun-synchronous orbit and a 15 kg satellite, the authors compute the SRP acceleration from a year of ephemeris data, apply it as a perpendicular perturbation so that only the orbital inclination changes, and train a regressor on the SRP acceleration plus mass and area-to-mass ratio to output the perturbed Z position. They report a mean absolute percentage error of 0.0266%, which they take as validation of the model. The motivation is practical: accurate, fast trajectory-change estimates for the growing number of LEO satellites using a computationally light pipeline that can run alongside mission planning.

What carries the argument

The load-bearing object is the cannonball model of solar radiation pressure, which treats the satellite as a sphere with one effective cross-sectional area and a single reflectivity coefficient. Its acceleration formula is $\vec{a}_{\mathrm{SRP}} = \frac{C_r P_0 A\, \mathrm{AU}^2}{M} \frac{\vec{r} - \vec{R}_{\mathrm{geos}}}{|\vec{r} - \vec{R}_{\mathrm{geos}}|^3}$ (with an eclipse shadow factor $\nu$ available but set to the no-eclipse value), and the companion perturbation equation $\delta i(t) = \frac{1}{n a}\int W \cos(u)\,dt$ converts the perpendicular SRP acceleration into an inclination change. These feed a generated dataset whose features are $\vec{a}_{\mathrm{SRP}}$, satellite mass $M$, and area-to-mass ratio $A/M$, with the $X,Y,Z$ position vectors as targets, on which the paper trains linear regression with gradient descent. That combination is what makes the pipeline semi-analytical: the physics of SRP is handled by closed-form equations, while the machine-learning step learns the mapping from SRP input to perturbed position.

What would settle it

Propagate the same 550 km circular sun-synchronous orbit over several days with a full force model that includes radial and tangential SRP components, J2, and atmospheric drag, and record whether semi-major axis and eccentricity change; if they change measurably while the paper's inclination-only model predicts no change, the central perturbation premise is contradicted.

Watch

Extended reading notes

Core claim

On its own terms, the paper's central finding is that a custom software module implementing the cannonball model for solar radiation pressure, with a reflectivity coefficient $C_r = 1 + \varepsilon$ and emissivity $\varepsilon = 0.30$, produces SRP acceleration values that agree with an established high-precision orbit propagator, and that when this acceleration is applied purely perpendicular to a circular orbit, the only perturbed Keplerian element is the inclination, per $\delta i(t) = \frac{1}{n a}\int_{t_0}^{t} W \cos(u)\,dt$. A linear-regression model trained on $\vec{a}_{\mathrm{SRP}}$, mass, and area-to-mass ratio predicts the resulting $Z$ position vector with a MAPE of $0.02662153353165422\%$, which the authors present as evidence that the combined analytical-machine-learning pipeline works for rapid satellite trajectory assessment. The paper also validates its ground-track computation against a reference LEO satellite's TLE and compares ground-station revisit times across Indian subcontinent sites.

Load-bearing premise

The premise the result rests on is that solar radiation pressure acts only perpendicular to the orbital plane and that the orbit is exactly circular, so Eq. (10) produces only an inclination change; if radial or tangential SRP acts, or if atmospheric drag and J2 are present, the semi-major axis and eccentricity also evolve, and the trained model would miss those dominant perturbing effects.

Editorial extensions

If this is right

SRP acceleration for a LEO satellite can be computed quickly from mass, effective area, reflectivity, and ephemeris data, without a full finite-element or N-plate model.
For circular orbits, a perpendicular-only SRP treatment reduces the perturbation analysis to a single scalar change in inclination, making trajectory correction inexpensive.
A linear-regression surrogate trained on SRP acceleration and mass/area features predicts the perturbed Z position with a MAPE of about 0.027%, suggesting that similar fast surrogates could support near-real-time trajectory updates.
The same pipeline can be reused for other LEO satellites by changing mass, area, reflectivity, and ephemeris inputs, with the ML model retrained on the new satellite's data.

Reading between the lines

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

An extension the paper leaves implicit is to activate the eclipse shadow factor, which is present in the model but set to the no-eclipse case; testing on dawn-dusk orbits with frequent eclipses would likely show larger position errors, since the reported accuracy assumes constant illumination.
Because the regression features include mass and area-to-mass ratio as constants for a single satellite, the reported accuracy only reflects interpolation in the SRP acceleration; a stronger test would train on multiple satellites with different masses and areas to see whether the linear hypothesis generalizes.
In a realistic LEO environment, SRP is usually a secondary perturbation relative to atmospheric drag and the J2 oblateness effect; the inclination-only result should be read as a controlled physics demonstration rather than a complete trajectory model, and adding drag and J2 is the obvious next step.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The paper is a tidy walkthrough of orbital elements, ground track generation, and a revisit-time comparison for Indian ground stations, with a visual check against a Starlink TLE. That part is fine as a tutorial. But the core claim - that the 0.0266% MAPE validates a machine-learning position predictor - does not hold up. The ML dataset is generated by incrementing the same a_SRP values and feeding them through the same Eq. 10 used to produce the ground truth, so the test set is not independent. Figure 8 shows Z varying nearly linearly with a_SRP, so linear regression trivially fits its own generator. The MAPE is a self-consistency check, not a validation. The physical model also has a load-bearing inconsistency: Eq. 9 gives the full SRP acceleration vector, but the perturbation analysis keeps only the perpendicular component W and says radial and tangential are disregarded. The paper never explains how W is extracted from Eq. 9 or why those components would vanish for realistic Sun-satellite geometry. The claim that inclination is the only affected element follows only under that assumption, which is not justified for LEO. The HPOP validation is asserted but never shown - no figure, no error metric - so the only external check is the ground track comparison, which is visual. There is also a notation slip: R_geos is described as the geocentric position of the Earth rather than the Sun, and the motivating SpaceX example misattributes the Starlink losses to SRP when the public record points to atmospheric drag from a geomagnetic storm. Credit where due: the authors are transparent about their simplifications (no eclipses, circular orbit), the code is on GitHub, and the revisit-time table could be useful for a first-pass mission design exercise. But the central validation is circular, and the physical inconsistency between Eq. 9 and the perpendicular-only assumption is not minor. Who gets value from this? Maybe a student learning how to string together SPICE, RK4, and a basic SRP calculation. As a research contribution, the evidence does not support the claims. I would desk-reject rather than spend referee time on a revision. If the authors fixed the circularity by testing on an independent propagator and justifying the perpendicular-only assumption, the tutorial portion might merit a teaching-oriented outlet.

Referee Report

5 major / 6 minor

Summary. The paper develops a custom Python module for computing solar radiation pressure (SRP) acceleration on a LEO satellite using the cannonball model, then analyzes orbital perturbations (restricted to inclination change under the assumption of a circular orbit and perpendicular-only SRP), compares ground station revisit times, and trains a linear regression model to predict position-vector changes from the SRP acceleration. The central quantitative claim is a MAPE of 0.0266% for predicted Z position, and the authors state validation against MATLAB's HPOP and Orbitron ground tracks.

Significance. If fully supported, the work would offer a lightweight, accessible SRP module and a fast ML surrogate for trajectory perturbations, which could be useful for LEO mission planning and education. Strengths include the use of standard astrodynamics references, a complete pipeline from ephemeris data to ground-track visualization, and detailed revisit-time calculations. However, the paper's main load-bearing validation is circular, and the missing independent comparison makes the claimed accuracy unverifiable; the modeling assumptions exclude radial and tangential SRP components, which are physically important in LEO.

major comments (5)

[Section 4, Figure 8] The reported MAPE of 0.0266% does not validate the model, because the training and test data are both generated by the same deterministic semi-analytical model (Section 4, Eq. 10) from the same a_SRP feature, so the linear regressor is only fitting the generator's own curve; the near-linear relation in Figure 8 makes this result tautological. The claimed comparison with MATLAB HPOP (Section 3, Figure 6 caption) is not shown anywhere in the manuscript, so it cannot serve as an independent check.
[Section 3, Eq. (9)] The notation is internally inconsistent: the text states that R_geos denotes 'the geocentric position of the Earth,' but the denominator |r - R_geos|^3 and the SRP context require R_geos to be the geocentric position of the Sun; moreover, the roles of the barycentric Earth and Moon coordinates in the bullets are not explained, making the calculation irreproducible from the text.
[Section 4, Eq. (10)] The perturbation analysis discards radial and tangential SRP components and assumes a perfectly circular orbit, so only inclination changes; however, Eq. (9) produces an acceleration along the Sun-satellite vector that has nonzero radial and tangential components, which in LEO drive significant changes in semi-major axis and eccentricity. The training dataset is therefore not a faithful SRP-perturbed trajectory, and the ML model trained on it cannot capture the dominant SRP effects.
[Section 2.1] The statement that the state vectors and trajectory 'were validated through simulations in MATLAB using identical parameters' is not supported by any figure, table, or error metric in the paper, so the trajectory validation is unverifiable; the comparison with Starlink-4566/Orbitron is also only visual.
[Section 4] The ML feature set is limited to a_SRP (with mass and area-to-mass ratio held constant), and the target is the Z position for a circular orbit with only inclination perturbed; this setup does not support the abstract's claim that the model 'can adaptively learn and refine predictions based on historical data and real-time input,' and no generalization test is provided.

minor comments (6)

[Throughout] There are numerous typographical errors, including 'eﬀect' for 'effect', 'pertuberbed' in Section 4, 'alogorithm' and 'comaprison' in Section 2.1, and 'the the JPL' in Section 3.
[Abstract] Abstract: 'it's effects' should be 'its effects.'
[Section 3] Section 3: 'The ephemeris was obtained from the the Jet Propulsion Laboratory' contains a duplicated 'the.'
[Section 4] Section 4: The MAPE is quoted to an excessive number of significant figures (0.02662153353165422%) without any uncertainty estimate.
[Section 1] The GitHub link in the abstract is public, but Section 1 states that access will be granted upon request after review; this inconsistency prevents reviewers from checking the code during the review process.
[Section 4] Section 4: The value a_SRP = 0.00994 km/day^2 is used in Figure 7, but the units of Eq. (9) are not stated; consistent SI or specified units should be used throughout.

Circularity Check

1 steps flagged · score 7.0 of 10

The 0.0266% MAPE validates the ML model against its own generator, not against independent data; the ML prediction reduces by construction to the same Eq. 10 dataset used to train it.

fitted input called prediction [Section 4 (Orbital Perturbation Analysis under Solar Radiation Pressure and Satellite Attitude Prediction using Machine Learning; dataset generation and Figure 8)]
"Further, a training dataset was generated by utilizing the perturbed orbital components, with the major objective column being the state vectors. ... The dataset generated via the identical methodology as previously elucidated and have been divided into two sets in an 80:20 ratio randomly. ... The Mean Absolute Percentage Error (MAPE) was used as the main metric, which came out to 0.02662153353165422%, validating the successful working of the model."

The training and test sets are both outputs of the same deterministic semi-analytical chain: a_SRP is computed with Eq. 9, artificially incremented, and fed into Eq. 10 to produce perturbed orbital elements and position vectors. Because the 20% validation split is drawn from that same generator, the test data are not independent of the training data. The linear regressor is therefore fitting the generator's own output curve, and the quoted MAPE of 0.0266% measures only how well y_pred = w*x + b reproduces that synthetic curve. Calling this 'validating the successful working of the model' presents a self-consistency check as external prediction skill.

full rationale

The paper has independent, non-circular components: the ground track comparison against Orbitron validates the basic propagator, and Eq. 9 is the standard cannonball-model SRP acceleration. However, the ML 'prediction' of perturbed position vectors is trained and tested on data generated by the authors' own semi-analytical model using the identical methodology. The reported MAPE therefore demonstrates only that a linear regressor can approximate the output of Eq. 10 for a single varying feature a_SRP; it is not evidence that the model predicts real SRP-perturbed satellite positions. The paper also states that only perpendicular SRP is considered, so the synthetic ground truth omits radial and tangential SRP effects, but that is a modeling limitation rather than a circular step. The lone claimed external validation against MATLAB HPOP is mentioned but never shown, so it does not provide independent support. Because the central quantitative evidence for the ML model reduces by construction to a fit of its own data generator, a score of 7 is appropriate.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The SRP calculation rests on the standard cannonball model (Eq. 9) and a set of simplifying choices: perpendicular-only SRP, perfectly circular orbit, shadow factor nu=1. The ML component fits linear regression weights on a dataset produced by the same propagator, so no independent physical grounding is added. No invented entities are introduced.

free parameters (4)

emissivity = 0.30
Chosen by hand in Section 3; determines Cr = 1 + emissivity and scales the SRP force linearly.
satellite mass = 15 kg
Set for the hypothetical satellite in Section 3; the computed SRP acceleration is inversely proportional to this value.
effective cross-sectional area A (area-to-mass ratio) = not reported
A/M enters Eq. 9 and is an input feature for the ML model, but the paper never states A's value, so the absolute SRP acceleration cannot be reproduced.
linear regression weights w and bias b = not reported
Fit by gradient descent on the generated dataset (Eqs. 11-14); no coefficients or intercept are reported, only the resulting MAPE.

assumptions (5)

domain assumption Newtonian two-body dynamics with RK4 propagation in the J2000 ECI frame accurately represents the satellite's unperturbed trajectory.
Used throughout Section 2.1 to propagate state vectors and ground tracks; no verification of integration error or force model completeness is provided.
domain assumption The cannonball model (Eq. 9) with emissivity 0.30 and Cr = 1 + emissivity adequately models SRP on the simulated satellite.
Invoked in Section 3; the paper cites refs [8-14] for the model but provides no quantitative comparison of the resulting acceleration with the claimed MATLAB HPOP validation.
ad hoc to paper Only the perpendicular (out-of-plane) component of SRP acts, and the orbit is perfectly circular, so inclination is the only Keplerian element that changes.
Stated in Section 4: 'only SRP acting in perpendicular directions have been considered, whereas tangential and radial directions have been disregarded'. This restriction drives Eq. 10 and the ML training data.
ad hoc to paper The shadow factor nu is set to 1 (no eclipses) for the entire one-year SRP calculation.
Section 3: 'we have considered the no ecllipse shadow condition in our calculations to monitor the acceleration pattern due to SRP over the course of an entire year'. This overestimates SRP for a real LEO orbit that passes through Earth's shadow.
domain assumption Sun-synchronous polar orbital elements (i=98.6 deg, omega=180 deg, Omega=7 deg, altitude 550 km) and a 15 kg mass with emissivity 0.30 represent a typical LEO satellite.
Assumed in Section 2.1 and used for all simulations; no sensitivity analysis is given.

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Cite this review

Pith. "Pith review of Semi-analytical model for the calculation of solar radiation pressure and its effects on a LEO satellite with predicting the change in position vectors using machine learning techniques." pith.science (2026). https://pith.science/paper/DIGPBW5I

@misc{pith2026241117626,
  author       = {Pith},
  title        = {Pith review of: Semi-analytical model for the calculation of solar radiation pressure and its effects on a LEO satellite with predicting the change in position vectors using machine learning techniques},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DIGPBW5I}},
  note         = {Machine review of arXiv:2411.17626}
}

read the original abstract

The rapid increase in the deployment of Low Earth Orbit (LEO) satellites, catering to diverse applications such as communication, Earth observation, environmental monitoring, and scientific research, has significantly amplified the complexity of trajectory management. The current work focuses on calculating and analyzing perturbation effects on a satellite's anticipated trajectory in LEO, considering Solar Radiation Pressure (SRP) as the main perturbing force. The acceleration due to SRP and it's effects on the satellite was calculated using a custom-built Python module mainly based on the hypothesis of the cannonball model. The study demonstrates the effectiveness of the proposed model through comprehensive simulations and comparisons with existing analytical and numerical methods. Here, the primary Keplerian orbital characteristics were employed to analyze a simulated low-earth orbit LEO satellite, initially visualizing the satellite's trajectory and ground tracks at a designated altitude. The study also focuses on a comparative analysis of ground stations, primarily considering the main regions of the subcontinent, with revisit time as the key parameter for comparison. In the end, we combine analytical techniques with Machine Learning (ML) algorithms to predict changes in the position vectors of the satellite. Using ML techniques, the model can adaptively learn and refine predictions based on historical data and real-time input, thus improving accuracy over time. In addition, the incorporation of analytical methods allows for a deeper understanding of the underlying physics governing satellite motion, enabling more precise adjustments and corrections.

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Reference graph

Works this paper leans on

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

[1] [1]

Eshagh, M., Najaﬁ Alamdari, M.: Perturbations in orbital elements of a low earth orbiting satellite. J. Earth Space Phys. 33, 1–12 (2007)

work page 2007

[2] [2]

In: 42nd COSPAR Scientiﬁc Assembly, vol

Nwankwo, V.U.J., Chakrabarti, S.K., Weigel, B.: The eﬀect of solar fo rcing in- duced atmospheric perturbations on leo satellites’ nominal aerody namic drag. In: 42nd COSPAR Scientiﬁc Assembly, vol. 42, pp. 1–1218 (2018)

work page 2018

[3] [3]

In: AGU Fall Meeting Abstracts, vol

Pilinski, M., Sutton, E., Bernstein, V., Tobiska, W.K., McGranaghan, R.: Mod- eling low-earth orbit satellite trajectories: Atmospheric density sp eciﬁcation and vehicle environment interactions. In: AGU Fall Meeting Abstracts, vol. 2021, pp. 31–03 (2021)

work page 2021

[4] [4]

Alexandria Engineering Journal 60(2), 2661–2676 (2021) https://doi.org/10.1016/j.aej.2020.12.056

Flores, R., Burhani, B.M., Fantino, E.: A method for accurate and e ﬃcient propa- gation of satellite orbits: A case study for a molniya orbit. Alexandria Engineering Journal 60(2), 2661–2676 (2021) https://doi.org/10.1016/j.aej.2020.12.056

work page doi:10.1016/j.aej.2020.12.056 2021

[5] [5]

Tosun, B.: Computation of satellite orbits by using numerical meth ods (2020)

work page 2020

[6] [6]

Dover, Mineola (1971)

Bate, R.R., Mueller, D.D., White, J.E.: Fundamentals of Astrodynamic s. Dover, Mineola (1971)

work page 1971

[7] [7]

MATLAB Cen tral File Exchange

Mahooti, M.: High precision orbit propagator (2023). MATLAB Cen tral File Exchange

work page 2023

[8] [8]

Internat ional Journal of 18 Aerospace Engineering vol

List, M., Bremer, S., Rievers, B., Selig, H.: Modelling of solar radiation pressure eﬀects: Parameter analysis for the microscope mission. Internat ional Journal of 18 Aerospace Engineering vol. 2015 , 14 (2015) [gr-gc]

work page 2015