Spacecraft Formation Guidance Law using a State Transition Matrix With Gravitational, Drag and Third-Body Perturbations
Bibliographic record
Abstract
There has been a growing interest in spacecraft formation-flying for space science applications. Such missions will require an accurate and efficient dynamics model, within the guidance system, to calculate and control the desired relative motion. This paper achieves an accurate analytical solution of relative motion between two spacecraft using relative classical orbital elements. The analytical solution is obtained by propagating the relative orbital elements forward in time, while taking into account gravitational field up to the fifth harmonic, third-body and drag, and calculating the relative motion in the local-vertical-local-horizontal reference frame at each time-step. Specifically, the solution proposed in this paper requires only a single matrix multiplication with the initial orbital elements and the desired time to compute the relative motion, since the solution utilized Jacobian matrices evaluated at the target spacecraft's initial orbital elements which need only be calculated once. The analytical solution was observed to accurately describe the relative motion when compared with a numerical simulator, yielding errors on the order of meters for separation distances on the order of thousands of meters. Additionally, the solution maintained accurate tracking performance when used within a back-propagation guidance law.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".