In Newton's law of universal gravitation, $F=\frac{G{m}_1{m}_2}{r^2}$, which two factors determine the magnitude of the gravitational force between two objects?

• A. The masses of the two objects and the distance between their centers
• B. The masses of the two objects and the acceleration due to gravity at Earth's surface
• C. The electric charges of the objects and the distance between their centers
• D. The volumes of the two objects and the distance between their surfaces

Answer: (A)

Verified step by step guidance

1. Recall Newton's law of universal gravitation, which states that the gravitational force \(F\) between two masses is given by the formula: \[F = \frac{G m_1 m_2}{r^2}\] 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 masses \(m_1\) and \(m_2\), and the distance \(r\) between the centers of the two objects.
3. Understand that the gravitational force is directly proportional to the product of the two masses, meaning if either mass increases, the force increases proportionally.
4. Recognize that the gravitational force is inversely proportional to the square of the distance between the centers of the masses, so as the distance increases, the force decreases rapidly.
5. Conclude that the two factors determining the magnitude of the gravitational force are the masses of the two objects and the distance between their centers.