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# By what factor would your weight change if Earth’s diameter were doubled and its mass were also doubled?

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The gravitational force can be described by the formula:

$\begin{gather} F_g = \dfrac{GMm}{r^2} \end{gather}$

If the Earth's diameter would be doubled, and the mass was also doubled, we calculate for the change in the gravitational force you will experience using Eq (1) as follows:

\begin{align*} F_g &= \dfrac{G(2M)m}{(2r)^2} \\ &= \dfrac{2GMm}{4r^2} \\ &= \boxed{2F_g} \end{align*}

Since the gravitational force will be double in magnitude, this means that your weight will also be doubled

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