contestada

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.

Respuesta :

AMB000

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]