Eratosthenes’ Experiment under Moonlight

In the present work we carried out Eratosthenes’ experiment using the full Moon as light source, in other words, we carried out the experiment at night. The measurements were conducted in the cities of Goiânia-GO and Carolina-MA. The collected data were interpreted using three different models: i) the model with the same longitude (the Eratosthenes’ standard model); ii) the generalized model for cities separated in both latitude and longitude; iii) the generalized model supplemented with the value of the latitude of the northernmost city (the city of Carolina). The values obtained in the three models, $R_1=(6.3\pm 0.1)\times {10}^{3}km$, $R_2=(6.2\pm 0.2)\times {10}^{3}km$ and $R_3=(6.2\pm 0.2)\times {10}^{3}km$, are in full agreement with the average volumetric radius of the Earth, $R_{NASA}=6.371\times {10}^{3}km$. This comparison shows the coherence of the models as well as the good quality of the experimental data. We hope that this work is going to stimulate debates about theoretical models and experimental implementations aimed to estimate sizes and distances on Earth and in the Solar System.

Keywords:
Earth Circumference; Earth Radius; Eratosthenes’ Experiment; Full Moon; Ancient Astronomy