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Maria

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Estudos Gerais04/09/2025

v = 2πr / T F_g = F_c F_g = G m_1 m_2 / R^2 F_c = v^2 m_r / ...

v = 2πr / T F_g = F_c F_g = G m_1 m_2 / R^2 F_c = v^2 m_r / r_i G m_2 / R^2 = 4π^2 r_i / T^2 -> G m_2 / R^2 = 4π^2 r_i / T^2 G / R^3 = 4π^2 / T^2 (m_1 m_2) -> T^2 = 4π^2 R^3 / (G m_1 m_2)

Me ajude a meio que "refazer" o caminha que Kepler fez para chegar na tarceira lei

v = 2πr / T
F_g = F_c
F_g = G m_1 m_2 / R^2
F_c = v^2 m_r / r_i
G m_2 / R^2 = 4π^2 r_i / T^2 -> G m_2 / R^2 = 4π^2 r_i / T^2
G / R^3 = 4π^2 / T^2 (m_1 m_2) -> T^2 = 4π^2 R^3 / (G m_1 m_2)
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