Question

The mass of the moon is 7.36×1022kg and its distance to the Earth is 3.84×108m. What is the gravitational force of the moon on the earth?

Answer 1

The gravitational force is F =
`2\,*\,10^(20)\,N`

Step-by-step explanation:

To answer this question we need to recall Newton's Universal Law of Gravitation for the force "F" exerted from one object to the other:

`F=G\,(m_1\,*\,m_2)/(d^2)`

where G is the Universal gravitational constant =
`6.674\,* \,10^(-11)\,\,(m^3)/(kg\,s^2)`

`m_1`, and
`m_2` are the masses of the two bodies/objects attracting each other via gravitational force. In our case, one is the mass of the Earth =
`5.972\,*\,10^(24)\, kg`

and the other one,the mass of the Moon =
`7.36\,*\,10^(22)\,kg`

and lastly, "d" is the distance between to two objects. In our case:

d =
`3.84\,*\,10^8\,m`

Since all these quantities are given in SI units, when we use them in the formula, our answer will result in the SI units of force "N" (Newtons):

`F=6.674\,*10^(-11)\,(5.972\,10^(24)\,7.36\,10^(22))/((3.84\,10^8)^2) \,N\\F=1.989\,*\,10^(20)\,N\\`

which can be rounded to: F =
`2\,*\,10^(20)\,N`