Answer:
[tex]G=\frac{Fr^2}{m_1m_2}[/tex]
Step-by-step explanation:
Since our equation is [tex]F=\frac{Gm_1m_2}{r^2}[/tex] and we want to solve for G, first we divide both sides by the product [tex]m_1m_2[/tex], which gives:
[tex]\frac{F}{m_1m_2}=\frac{Gm_1m_2}{m_1m_2r^2}=\frac{G}{r^2}[/tex]
So we are left with:
[tex]\frac{F}{m_1m_2}=\frac{G}{r^2}[/tex]
Now we multiply both sides by [tex]r^2[/tex], which gives:
[tex]\frac{Fr^2}{m_1m_2}=\frac{Gr^2}{r^2}=G[/tex]
Which gives us our final formula:
[tex]G=\frac{Fr^2}{m_1m_2}[/tex]
