# Orbital WCS and stellar positioning — working outline - Updated 2026-10-15; **bullet outline only**, replacing full manuscript text as the active presentation. - Working title: **Orbital evolution of the TESS focal-plane mapping: physical contributions and limits to stellar positioning**. - Main question: which observed changes are predicted by known physics, which are conditionally described by telemetry, and what positional accuracy is independently demonstrated? - Terminology: measured displacement ≠ prediction error ≠ absolute position error; empirical correction ≠ established physical cause. - Figure numbers below retain the existing six-figure plan; supplementary panels can be linked beneath each figure on the webpage. ## 1. Motivation and scope ### 1.1 Why orbital image motion needs explanation - Science-camera guide-star centroids feed spacecraft pointing control; apparent guide fields change with observer velocity. - Optical/distortion evolution and attitude changes both affect the same stellar positions. - Existing literature establishes aberration and guiding mechanisms; novelty must come from observed decomposition and independent positional validation. - Pointing knowledge, closed-loop stability, long-exposure motion and WCS accuracy are different observables. ### 1.2 What this study claims - Sector 20 header-WCS characterization across four cameras and sixteen CCDs. - Deeper centroid/profile tests on C3/CCD3 with explicitly narrower image and temporal coverage. - Candidate conditional physical/thermal correction, with startup and endpoint failures retained. - Accurate positions remain a measured validation objective; no blanket all-CCD precision claim from a one-frame pilot. ## 2. Data and measurement definitions ### 2.1 Input identity and reference frames - Freeze cadence, exposure-time convention, velocity reference, catalogue epoch/proper motion and image generation. - Distinguish full-FFI, crop-local and PSF-profile coordinates; preserve source IDs. - Record Moon-contaminated/flagged intervals and actual camera availability. - Historical mixed catalogue epochs: retain as a diagnosed limitation; use a corrected new generation for accuracy tests. ### 2.2 What a stellar position means - Separate fitted PSF origin, Gaussian-defined profile centre and catalogue-to-detector WCS. - Include explicit chromatic displacement; reference colour is not necessarily zero shift for centred quadratic colour terms. - Define fixed Gaussian support, weighting and background treatment before comparing models. - Distinguish native-pixel Gaussian fits from Gaussian fits to dense effective-profile samples. ### 2.3 Validation populations - Label header probes, fitted stars, held-source stars, held pixels and held time blocks separately. - Hold source/neighbour regions out of initialization and model fitting; retain exact existing `held_fixed` contracts where applicable. - Keep same-source comparisons on fixed pixel support and one image generation. - Report spatial/colour/brightness/phase coverage and correlated uncertainty; do not convert ensemble scatter into absolute accuracy. ## 3. Physical and empirical description of orbital motion ### 3.1 Observer velocity and common attitude - Compute aberration using Earth plus spacecraft velocity; identify sign and reference conventions explicitly. - Show measured and predicted spatial vector fields before reducing them to RMS. - Fit or measure the common attitude and label it as supplied information. - **Figure 1:** full focal-plane motion, physical velocity contribution and remaining field. ### 3.2 Guiding response and what is identifiable - Use literature to motivate aberrated guide-field tracking and guide-camera selection effects. - Compare common rotation with camera-relative spatial modes. - Do not identify fitted effective guide weights with actual onboard weights. - Resolve commanded-attitude/quaternion references before treating telemetry as independent truth. - Supplement to Figure 1: guiding timeline and control-loop schematic, labelled literature versus flight-data inference. ### 3.3 Thermal association - Separate scale, shear and higher-order changes from global pointing. - Compare time-only and temperature-informed models on the same support. - Show sensor histories alongside the measured spatial mode. - Distinguish conditional temperature slope from a material expansion coefficient. - **Figure 2:** thermal histories, withheld distortion-error curves and matching spatial prediction-error maps. ### 3.4 Beginning and end of orbit - Test whole endpoint intervals with an explicit training buffer. - Distinguish large accumulated displacement from poor prediction. - Treat startup thermal history, changing gradients, guiding and measurement bias as competing explanations. - Retain the separate orbit-48 startup analysis for cameras 2–4. - **Figure 3:** separate pointing predictions and startup limits; Figure 2 contains the distortion errors. ## 4. Measurement-convention controls ### 4.1 Saved ePSF origin conversion - Apply a coordinate conversion to saved profiles; preserve predicted pixels rather than retraining. - Show actual profiles and Gaussian residuals with the inferred spatial correction. - Test support sensitivity and pathological profiles explicitly. - **Figure 4:** original versus Gaussian-origin endpoint motion and its profile evidence. ### 4.2 Temporal estimator consistency - Compare legacy and trained positions on fixed stars across the historical temporal coverage. - Separate static differences, frame translations, cell structure and individual-star scatter. - Flag shared initialization, training membership, crop coverage and historical catalogue epoch inconsistency. - **Figure 5:** temporal consistency tracks plus per-star fields and image stamps; not absolute accuracy. ## 5. Toward independently accurate positions ### 5.1 Same-image pilot - Show only the verified pilot's actual source count, image generation, heldout status and spatial footprint. - Compare explicit common-centre estimators on identical images and pixels. - Show data/model/residual stamps, signed position vectors and uncertainty. - State whether results test estimator consistency, injection recovery or independent predictive accuracy. - **Figure 6, development:** same-image positional pilot; unmeasured endpoint/all-camera extensions visibly marked. ### 5.2 Accuracy completion test - Extend the validated procedure to reserved startup/interior/end frames in both orbits. - Compare a simple affine baseline, current mapping and physical/thermal correction on identical reserved observations. - Derive any permitted registration on training stars only; keep absolute and translation-removed scores separate. - Fix acceptance tolerance before final testing; report coherent mode bounds, tails and measurement/catalogue uncertainty. - Match claim coverage to tested CCDs; one CCD per camera does not certify sixteen CCDs. ## 6. Explanation, remaining ambiguity and paper boundary ### 6.1 What is explained - Known velocity-aberration physics supplies a testable spatial prediction. - Measured attitude removes common motion but is not itself a predictive physical explanation. - Temperature adds conditional predictive information; Gaussian recentering does not remove the tested bulk startup evolution. - Summarize component status using EXPLANATION_LEDGER.md. ### 6.2 What would discriminate remaining causes - Matched-temperature warming/cooling and component-gradient contrasts. - Independent camera-contrast/attitude test with verified quaternion conventions. - Frozen-model test on a preselected second thermal/guiding regime. - Common-image held-source positioning with corrected catalogue epochs. ### 6.3 Scope and conclusion bullets - Paper 1 retains single-image de-crowding/chromatic ePSF fitting; cite rather than duplicate that novelty. - This paper owns orbital mapping evolution and independently tested positional correction. - Paper 2 retains temporal photometry, detrending and astrophysical signal preservation. - Claim only the calibrated domain and supported physical attribution; unresolved startup terms remain a documented result.