Question

Newton’s law of universal gravitation, F=Gm1m2/r²,measures the force of gravity between two masses m1 and m2,where r is the distance between the centers of the masses, and G is the universal gravitational constant. Solve this equation for G.

Answer 1

`G=(Fr^2)/(m_1m_2)`

Explanation:

Since our equation is
`F=(Gm_1m_2)/(r^2)` and we want to solve for G, first we divide both sides by the product
`m_1m_2`, which gives:

`(F)/(m_1m_2)=(Gm_1m_2)/(m_1m_2r^2)=(G)/(r^2)`

So we are left with:

`(F)/(m_1m_2)=(G)/(r^2)`

Now we multiply both sides by
`r^2`, which gives:

`(Fr^2)/(m_1m_2)=(Gr^2)/(r^2)=G`

Which gives us our final formula:

`G=(Fr^2)/(m_1m_2)`