{"id":1261,"date":"2023-12-05T10:23:46","date_gmt":"2023-12-05T13:23:46","guid":{"rendered":"https:\/\/revistabrasileiradefisica.com\/rbf\/?p=1261"},"modified":"2023-12-05T10:23:46","modified_gmt":"2023-12-05T13:23:46","slug":"sobre-a-equivalencia-entre-as-leis-de-kepler-e-a-lei-da-gravitacao-de-newton","status":"publish","type":"post","link":"https:\/\/revistabrasileiradefisica.com\/rbf\/2023\/12\/05\/sobre-a-equivalencia-entre-as-leis-de-kepler-e-a-lei-da-gravitacao-de-newton\/","title":{"rendered":"Sobre a equival\u00eancia entre as leis de Kepler e a lei da gravita\u00e7\u00e3o de Newton"},"content":{"rendered":"\r\n

On the equivalence between Kepler's laws and Newton's law of gravitation\r\n<\/em><\/h4>\r\n\r\n\r\n\r\n

DOI<\/strong>: 10.5281\/zenodo.10260768<\/a><\/em><\/p>\r\n\r\n\r\n\r\n

Allan Kenedy Santos Silva<\/strong>
ORCID<\/a> | <\/em> Lattes<\/a> | <\/em> E-mail<\/a><\/em><\/p>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n

Resumo: <\/strong>Johannes Kepler, por meio das observa\u00e7\u00f5es feitas por Tycho Brahe, elaborou tr\u00eas leis que regem o movimento dos planetas em torno do Sol. Anos mais tarde, Isaac Newton formulou a lei da gravita\u00e7\u00e3o universal e, a partir dela, derivou as leis de Kepler. Neste texto mostramos como se pode inferir a lei da gravita\u00e7\u00e3o a partir das leis de Kepler, e como estas s\u00e3o consequ\u00eancias dela. Em outras palavras, mostraremos que as leis de Kepler e a lei da gravita\u00e7\u00e3o de Newton s\u00e3o matematicamente equivalentes.<\/em>
Palavras-chave: <\/strong>leis de Kepler; lei da gravita\u00e7\u00e3o universal; coordenadas polares.<\/em><\/p>\r\n\r\n\r\n\r\n

Abstract: <\/strong>Johannes Kepler, through the observations made by Tycho Brahe, developed three laws that govern the movement of planets around the Sun. Years later, Isaac Newton formulated the law of universal gravitation and, from it, derived Kepler's laws. In this text we show how the law of gravitation can be inferred from Kepler's laws, and how these are consequences of it. In other words, we will show that Kepler's laws and Newton's law of gravitation are mathematically equivalent.
Keywords:<\/strong> Kepler's laws; law of universal gravitation; polar coordinates<\/p>\r\n\r\n\r\n\r\n

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