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Figure 1. Path, in green, of the apparent position of the North Celestial Pole (i.e. the center of star trails) as a function of time in ICRS coordinates. For reference, a few dates are identified in Julian years. Most of the secular motion along RA=0h is due to the precession of the Earth’s axis; the rest, as well as the slow 18.6 year east-west variation, is due to nutation. The annual “loops” are caused by the aberration of the positions of the stars (shown here fixed at their ICRS positions from Gaia DR2). Detection of the loops constitutes observational proof of Earth’s orbital motion, and measurement of their amplitude constitutes a measurement of the astronomical unit.

Fortunately, Polaris sits ∼ 45′ from the North Celestial Pole, and so should not interfere with the measurement for Northern observers. The rotational and eccentric orbital motion of the Earth is smaller than its circular orbital motion by two orders of magnitude, so can both be ignored, as can polar motion, which is a < 1′′ effect. The Celestial Poles are at |b| = 27◦, and so finding nearby stars should not pose too large a problem; there are multiple stars with g< 17 within 2′ of the North Celestial Pole for the next several years at least. Despite my aspirations, I have not found the time to even begin the project. I nonetheless feel that it is a rich project in observational astronomy and fundamental physics, and a pleasingly didactic exercise appropriate for upper- division undergraduate and graduate astronomy and physics laboratory classes. True, it cannot be completed in a single semester, but its complexity and length may be justified by the novelty of proving heliocentrism with nothing but a small telescope and camera. I therefore publish this Research Note to disseminate the idea in hopes that I might receive word in a few years of a triumphant astronomy class’s proof of heliocentrism, along with their best estimates of the astronomical unit and precession. 3

This Research Note has made use of NASA’s Astrophysics Data System; Astropy, a community-developed core Python package for astronomy (Astropy Collaboration et al. 2013); and Gaia (Gaia Collaboration et al. 2016) DR2 (Gaia Collaboration 2018). 4

REFERENCES

Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., Gaia Collaboration. 2018, VizieR Online Data Catalog, et al. 2013, A&A, 558, A33 1345 Bradley, J. 1727, Philosophical Transactions of the Royal Gaia Collaboration, Prusti, T., de Bruijne, J. H. J., et al. 2016, A&A, 595, A1 Society of London Series I, 35, 637