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Propagates a circular two-body orbit from altitude, inclination, RAAN, and initial orbital phase; rotates Earth at a fixed sidereal rate; and samples ground-station elevation. It ignores eccentricity, perturbations, epoch-dependent Greenwich angle, refraction, ellipsoid shape, terrain, and antenna m

Propagates two caller-supplied Cartesian states with constant velocity, analytically finds the clamped time of closest approach, and compares miss distance with combined hard-body radius. It ignores gravity, covariance, maneuver uncertainty, tracking error, and nonlinear dynamics and is not an opera

Treats cells at or above a caller threshold as foreground, labels four-neighbor connected components, and reports area, bounding box, peak, and mean value. It does not ingest imagery, calibrate backscatter, remove speckle, geolocate pixels, classify objects, or infer real-world meaning.

Checks wind, gust, lightning distance, precipitation, cloud fraction, and temperature against caller-supplied limits and reports every failed rule. It does not retrieve observations, forecast weather, interpret vehicle-specific rules, detect upper-level winds, or authorize a launch.

Uses da/dt = -rho×sqrt(mu×a)/ballistic_coefficient for a circular orbit, holds density and ballistic coefficient constant, and linearly projects altitude over a bounded horizon. Real density changes rapidly with altitude and solar activity; the result is not a lifetime prediction or maneuver plan.

Combines caller-supplied AIS gap duration, unmatched satellite detections, night-observation fraction, and position discrepancy into a bounded score. It does not identify a vessel, link detections, establish illegal activity, or replace maritime intelligence review.

Maps a caller-supplied Kp value to conventional G0–G5 bands, maps Dst to declared disturbance bands, and combines severity with geomagnetic latitude and infrastructure class. It does not retrieve observations, forecast a storm, model local ground conductivity, or predict equipment failure.

Computes mean NDVI and an ordinary least-squares daily NDVI trend, then applies yield = intercept + mean_coefficient×mean_NDVI + trend_coefficient×daily_trend. It does not derive NDVI from imagery, account for crop stage or weather, or provide an agronomically calibrated forecast unless the caller s

Sums enhancement_ppm×pixel_area, multiplies by wind speed, plume orientation, and a caller-supplied conversion factor, and reports the resulting proxy and optional kg/h estimate. It does not retrieve satellite data, remove background, solve atmospheric transport, determine source location, or valida

Fits ordinary least squares to log radiance by year, converts the slope to annual radiance change, and applies a caller-supplied economic elasticity. Night lights are an imperfect proxy affected by sensors, saturation, electrification, outages, policy, and conflict; this is not an official economic