In Newton's law of universal gravitation, the magnitude of the gravitational force between two point masses is $F=G\frac{m{}_{1}m{}_2}{r^2}$. Which two factors determine the value of $F$ for a given pair of objects?

• A. The acceleration due to gravity $g$ at the surface and the objects' speeds
• B. The electric charges on the objects and the distance $r$
• C. The two masses $m{}_1$ and $m{}_2$, and the distance between their centers $r$
• D. The volumes of the objects and the temperature of the surrounding space

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 given by the formula: \[F = G \frac{m_1 m_2}{r^2}\] where \(G\) is the gravitational constant, \(m_1\) and \(m_2\) are the masses of the two objects, and \(r\) is the distance between their centers.
2. Identify the variables in the formula that directly affect the magnitude of the gravitational force: these are the two masses \(m_1\) and \(m_2\), and the distance \(r\) between them.
3. Understand that the gravitational force increases with larger masses and decreases as the distance between the masses increases, specifically with the square of the distance.
4. Note that other factors such as acceleration due to gravity at the surface, electric charges, volumes, or temperature do not appear in the formula and therefore do not determine the gravitational force between two masses.
5. Conclude that the two factors determining the gravitational force \(F\) for a given pair of objects are the masses \(m_1\) and \(m_2\), and the distance \(r\) between their centers.