An Image Analysis Method for Calculating the Moon’s Orbital Eccentricity

Abstract

In this work we describe a teaching proposal to calculate the eccentricity of the Moon’s trajectory by applying a geometrical technique. The values of the ratios between the Earth-Moon distance and the diameter of the Moon at apogee and at perigee were calculated from a kinematic model associated with a geometrical technique of image analysis. The experimental data were collected from two videos of the Moon’s movement in positions close to the apogee and perigee. We chose two frames of both videos, and by means of image analysis we obtained a geometrical parameter for each video and by means of a kinematic model we defined a physical parameter. Then, by combining both parameters we calculated the maximal and minimum apparent diameters, which were used to calculate the eccentricity. Finally, we compared our results with values of literature.

Fotografias de Io, seu diâmetro e sua distância de Júpiter

“…O conhecimento adquirido pelo estudante interessado é conquistado seguindo a diretriz da aprendizagem ativa [15], pois esse artigo é uma proposta de materialização daquela pedagogia com tendência tecnológica contemporânea [16,17]. Esse trabalho se junta a outros trabalhos publicados [18,19], que diferem ligeiramente deste aqui apresentado, mas seguem a mesma metodologia, isto é, incluindo análises de imagens, triangulações e uma modelagem cinemática simplificada, mas que mostram que modelos cinemáticos e geométricos simples nos fornecem valores com precisão muito boa para calcular parâmetros astronômicos importantes como distância entre planetas, entre luas e seus planetas e diâmetros de planetas ou luas.…”

The Moon, a disk or a sphere?

“…In this context, the role of science education and, specifically, astronomy teaching, is fundamental to promote the acknowledgment of scientific research methods and their use as a tool to understand the current world [11][12][13][14][15][16][17][18][19][20]. Accordingly, we present a physical modeling activity that allows students to determine the differences between a disk and a sphere using pure scientific criteria.…”

The Moon, a disk or a sphere?

“…Flat Earth movement is being defended once again by people who are unaware of scientific procedures and insist on defending opinions without scientific evidence [6][7][8][9][10]. In this context, the role of science education and, specifically, astronomy teaching, is fundamental to promote the acknowledgment of scientific research methods and their use as a tool to understand the current world [11][12][13][14][15][16][17][18][19][20]. Accordingly, we present a physical modeling activity that allows students to determine the differences between a disk and a sphere using pure scientific criteria.…”