Demonstrating the Elliptical Orbit of Mars using Naked Eye Data

TL;DR

This study used naked eye observations over 3.1 years to demonstrate Mars's elliptical orbit, estimating its eccentricity as approximately 0.093, aligning with modern values despite less precise data.

Contribution

It shows that even with relatively imprecise naked eye data, the elliptical nature of Mars's orbit can be confirmed and its eccentricity accurately estimated.

Findings

Observed Mars positions within +/- 11 arc minutes of true positions.

Estimated Mars's orbital eccentricity as 0.093 +/- 0.012.

Data fit well with elliptical orbit models, confirming Kepler's findings.

Abstract

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 ellptical 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.