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

• A. The charges on the objects and the distance between them
• B. Only the distance between the objects, because gravity does not depend on mass
• C. The two masses and the square of the distance: $F=Gm{m}_1{m}_2{r}^2$
• D. The two masses and the distance between their centers: $F=G\frac{m{m}_1{m}_2}{r^2}$

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 proportional to the product of their masses and inversely proportional to the square of the distance between them.
2. Identify the variables involved: \(m_1\) and \(m_2\) represent the masses of the two objects, and \(r\) is the distance between the centers of these masses.
3. Write the formula for the gravitational force as: \[F = G \frac{m_1 m_2}{r^2}\] where \(G\) is the gravitational constant.
4. Understand that the force depends directly on both masses — increasing either mass increases the force — and depends inversely on the square of the distance, meaning that as the distance increases, the force decreases rapidly.
5. Note that charges on the objects do not affect gravitational force, and gravity always depends on mass, so the correct variables determining the magnitude of gravitational force are the two masses and the distance between their centers.