Lab 05: Astrometry and Motion

Apparatus and Setup

You will use ../data/asteroid_astrometry.csv, three sequential images of a fast-moving object with a 15-minute interval between exposures, each with a measured pixel centroid and a matched sky position from a plate solution.

Materials and Data

Procedure

1. From images 1 and 2, compute the pixel separation and the sky separation (arcsec), then the plate scale (arcsec/pixel).
2. From images 2 and 3, independently repeat the same calculation as a consistency check on the plate scale.
3. Compare the two plate-scale estimates. If they agree to within a few percent, you have a validated plate scale; if not, identify a likely cause (centroiding error, non-linear distortion, a typo in the coordinates).
4. Using the 15-minute interval between images 1 and 2, compute the object’s angular rate of motion in arcsec/minute.
5. State whether this rate is consistent with a slow-moving main-belt asteroid or a faster-moving near-Earth object, given that typical main-belt rates are well under 1 arcsec/minute near opposition.

Analysis and Uncertainty

Report both plate-scale estimates and their percent difference. Report the derived angular rate with an explicit statement of what centroiding precision (in pixels) would be needed to measure that rate to 10% accuracy over this time baseline.

Deliverables

• Two independent plate-scale determinations (images 1–2 and images 2–3) with arithmetic shown.
• Percent agreement between the two estimates.
• Angular rate of motion in arcsec/minute, with a classification (main-belt vs. near-Earth pace) and justification.

Assessment Criteria

• Correct pixel and sky separations for both image pairs.
• Plate-scale estimates near 0.81 and 0.83 arcsec/pixel (accept reasonable rounding).
• Correct angular rate and a physically reasonable classification with justification.

References and Provenance

• OpenStax Astronomy 2e (local reference copy: references/openstax-astronomy-2e.pdf), Chapter 19.2 (surveying the stars, astrometric fundamentals).
• Dataset: materials/ASTR210/data/asteroid_astrometry.csv, logged in reference-log.md; the 15-minute image cadence is an instructor-provided observing-log value.