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elena-14-01-66 [18.8K]
3 years ago
5

Newton’s law of universal gravitation, F=Gm1m2/r²,measures the force of gravity between two masses m1 and m2,where r is the dist

ance between the centers of the masses, and G is the universal gravitational constant. Solve this equation for G.
Mathematics
1 answer:
Pavel [41]3 years ago
6 0

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}

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