Cavendish is said to have "weighed Earth" because his determination of \(G\) provided the first value for the planet's mass \(m_{\mathrm{E}}\). Given that the radius of Earth is about \(6400 \mathrm{~km}\) and given the value of \(G\) in Eq. 13.5, determine \(m_{\mathrm{F}}\).

Data from Eq. 13.5

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G = 6.6738 x 10 N m/kg.