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

Answer:

$G=\frac{Fr^2}{m_1m_2}$

Step-by-step explanation:

Since our equation is $F=\frac{Gm_1m_2}{r^2}$ and we want to solve for G, first we divide both sides by the product $m_1m_2$, which gives:

$\frac{F}{m_1m_2}=\frac{Gm_1m_2}{m_1m_2r^2}=\frac{G}{r^2}$

So we are left with:

$\frac{F}{m_1m_2}=\frac{G}{r^2}$

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

$\frac{Fr^2}{m_1m_2}=\frac{Gr^2}{r^2}=G$

Which gives us our final formula:

$G=\frac{Fr^2}{m_1m_2}$