According to Newton's law of universal gravitation, the magnitude of the gravitational force between two point masses depends on which two factors?

• A. The sum of the two masses and the distance between their centers (specifically it varies as $\frac{m+M}{r^2}$)
• B. The product of the two masses and the square of the distance between their centers (specifically it varies as $mM{r}^2$)
• C. The product of the two masses and the distance between their centers (specifically it varies as $\frac{mM}{r^2}$)
• D. The difference of the two masses and the distance between their centers (specifically it varies as $\frac{m-M}{r^2}$)

Answer: (C)

Verified step by step guidance

1. Recall Newton's law of universal gravitation, which states that the gravitational force \(F\) between two point masses is proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
2. Express this relationship mathematically as: \(F = G \frac{m M}{r^{2}}\), where \(G\) is the gravitational constant, \(m\) and \(M\) are the two masses, and \(r\) is the distance between their centers.
3. Understand that the force depends on the product \(m \times M\), not the sum or difference of the masses, because gravitational attraction increases with both masses involved.
4. Note that the force varies inversely with the square of the distance \(r\), meaning if the distance doubles, the force becomes one-fourth as strong.
5. Therefore, the two key factors determining the magnitude of the gravitational force are the product of the two masses and the square of the distance between their centers.