According to 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 variables determine the value of $F$ (assuming $G$ is constant)?

• A. The electric charges of the objects and the distance $r$
• B. Only the distance $r$ between the masses
• C. The masses $m{}_1$ and $m{}_2$ and the acceleration due to gravity $g$
• D. $m{}_1$, $m{}_2$, and $r$

Answer: (D)

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 affect the gravitational force \(F\). Since \(G\) is a constant, the variables that determine \(F\) are \(m_1\), \(m_2\), and \(r\).
3. Understand that the force is directly proportional to the product of the two masses \(m_1\) and \(m_2\), meaning if either mass increases, the force increases proportionally.
4. Recognize that the force is inversely proportional to the square of the distance \(r\) between the masses, so as \(r\) increases, the force decreases by the square of that distance.
5. Note that other quantities such as electric charges or acceleration due to gravity \(g\) do not appear in this formula and therefore do not determine the gravitational force between the two masses.