Concurso:
Universidade do Estado do Pará (UEPA)
Disciplina:
Astronomia
Hiparco de Nicéa conseguiu determinar a distância Terra-Lua (DTL) pela observação de um eclipse lunar. Durante o Eclipse do século, como ficou conhecido, que ocorreu em 27 de julho de 2018, um grupo de estudantes resolveu reproduzir esse método e fazer a estimativa da distância Terra-lua. Sabese que o semi-diâmetro do Sol é d (como mostra a figura abaixo), RT é o raio da Terra, Tsinódico é o mês sinódico e Teclipse foi o tempo em que a Lua esteve na umbra, produzida pela Terra. Ao desprezar a paralaxe diária do sol (ângulo a), foi possível obter uma expressão para determinar a distância Terra-Lua (DTL) dada por
![Imagem associada para resolução da questão](data:image/png;base64, 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)