Question

What is the DISTANCE between a 20 kg cannonball and a 0.01 kg marble if the gravitational attraction between a 20 kg cannonball and a marble is 0.48 x 10^-10 N?

Answer 1

According to Newton's law of gravitation, gravitational force between two objects of mass $m_1, m_2$, located at distance $R$ between each other is $F = \frac{G m_1 m_2}{R^2}$, where $G = 6.674 \cdot 10^{-11} m^3 kg^{-1} s^{-2}$ is the universal gravitational constant.

Using the last formula, the distance between the cannonball and marble is:$R = \sqrt{\frac{ G m_1 m_2}{F}} = \sqrt{\frac{6.67 \cdot 10^{-11} m^3 kg^{-1} s^2 \cdot 20 kg\cdot 0.01 kg}{0.48 \cdot 10^{-10} N}} \approx 0.53 m$