This looked clever. "Primitive" advanced astronomy!

Demonstrating the Elliptical Orbit of Mars using Naked Eye Data

Kevin Krisciunas (Submitted on 18 Oct 2016 (v1), last revised 30 Dec 2018 (this version, v2))

Over the course of 3.1 years we determined the position of Mars on 75 dates using a handheld cross staff and two to five bright reference stars of known right ascension and declination on each occasion. On average the observed positions of Mars are within +/- 11 arc minutes of the true ecliptic latitudes and ecliptic longitudes. After deriving the two dates of opposition to the Sun, we were able to carry out a two stage analytical experiment on Mars' orbit. From the 2015/2016 data we obtain a value of the eccentricity of 0.093 +/- 0.012. The 2015/2016 data can be fit reasonably well by adopting a circular orbit for the Earth, but the 2017/2018 data must be fit with an ellipse for Mars and an ellipse for the Earth. Applying the two ellipse model to the 2015/2016 data, we obtain an RMS error of the ecliptic longitudes of only +/- 7.5 arc minutes. While Kepler was able to derive the shape of Mars' orbit while relying on data of Tycho Brahe accurate to +/- 2 arc minutes, today we may assume an elliptical orbit, and we can show that much less accurate data are consistent with an ellipse having an eccentricity equal to the modern accepted value of 0.0934, within the errors.