Chapter 8, Problem 8.2E

The force of attraction due to gravity follows an equation similar to Coulomb’s law:

$F=G\frac{m_1{m}_2}{r^2}$

Where $m_1$ and $m_2$ are the masses of the objects, $r$ is the distance between the objects, and $G$ is the gravitational constant, which equals $6.67\times {10}^{-11}{\text{N m}}^{\text{2}}/{\text{kg}}^{\text{2}}$.

(a) Calculate the force of gravitational attraction between Earth and the Sun if the mass of Earth equals $5.97\times {10}^{24}\text{kg}$, the mass of the Sun is $1.984\times {10}^{30}\text{kg}$, and the average distance between them is $1.494\times {10}^8\text{km}$.

(b) Assuming that the Sun and Earth would have the same magnitude but opposite charges, what charge is necessary to provide a coulombic force that equals the gravitational force between the Sun and Earth? How many moles of electrons is that? To put your answer in perspective, consider that if earth were composed of pure iron, it would contain about ${10}^{26}\text{moles}$ of $\text{Fe}$ atoms.