Measure motion from a moving observer

Astrometry measures where an object appears relative to a reference coordinate system. A calibrated image places detector pixels on the sky using comparison stars. The result needs a timestamp and the observer’s location: an angular position without those conditions cannot fully describe the observation.

A single direction defines a line of sight. It does not by itself say how far along that line an object lies. Repeated positions reveal apparent motion, but a short sequence can remain consistent with several distances and orbits. Precision in one measured quantity should not be confused with certainty about every inferred quantity.

NEOSSat moves around Earth while observing. That changing viewpoint contributes parallax, an apparent displacement relative to more distant objects. The target’s own motion and the observer’s motion must both be considered. The position of the observatory is part of the measurement rather than a detail added after the orbit fit.

For a simple small-angle model, the angular shift in radians is approximately the baseline perpendicular to the line of sight divided by target distance. The model assumes a distant target relative to that baseline and isolates the viewpoint change. A real moving-object analysis also accounts for target motion, precise timing and geometry.

Imagine a perpendicular baseline of 1,000 kilometres and a target 1,000,000 kilometres away. The model gives 0.001 radians. Doubling the target distance halves the predicted shift to 0.0005 radians; doubling the baseline at the original distance doubles the shift. These are invented values illustrating a relationship, not a NEOSSat orbit solution.

The preserved Wirtanen image is a real example of a moving view. The mission team stacked 70 images across one third of NEOSSat’s orbit on December 2, 2018. Its curved apparent trace includes the effect of observer parallax. It should not be read as a photograph of the comet physically following that curved line through three-dimensional space.

Parallax depends on viewpoint and distance

Follow-up observations can extend the time span, add a different viewpoint or recover a target when other telescopes cannot view it. Each contribution can constrain a family of possible trajectories. Its value depends on the measurement errors and geometry, rather than on the number of frames alone.

Use a fictional uncertainty exercise: one short arc leaves a broad range of possible distances. A second well-timed sequence reduces that range but still permits multiple trajectories. The justified conclusion is that the range narrowed. It is not yet a unique orbit, and certainly not a numerical Earth-impact probability without the additional analysis that such a claim requires.

Keep the measured angular positions, uncertainties, timestamps and observer coordinates with the solution. A revised reference catalogue or corrected timing can change the inferred orbit. That traceability allows researchers to improve an earlier result without pretending that the original images contained information they did not measure.