Question

The moon has a mass of 7.34 × 10^22 kg and a radius of 1.74 × 10^6 meters. If you have a mass of 66 kg, how strong is the force between you and the moon?

Answer 1

106.8 N

Explanation:

We have the following:

Mass of moon = 7.34*10^22 kg

Radius of moon = 1.74*10^6 m

Newton’s Law of Universal Gravitation states:

`\begin{gathered} F_G=(G\cdot m_1\cdot m_2)/(r^2) \\ \text{ where, } \\ G=6.6743*10^(-11)\frac{N\cdot m^2}{\text{ kg}} \end{gathered}`

Mass 1 is the mass of the moon and mass 2 would be the mass of the person (66 kg), we replace and calculate the gravitational force:

`\begin{gathered} F_G=(6.6743\cdot10^(-11)\cdot7.34*10^(22)\cdot66)/((1.74*10^6)^2) \\ F_G=106.8\text{ N} \end{gathered}`

Therefore, the gravitational force is 106.8 N