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

• A. The distance and the objects' velocities, but not their masses
• B. The masses, the distance, and the electric charges on the objects
• C. The two masses and the distance between their centers: $F=G\frac{m_1{m}_2}{r^2}$
• D. Only the masses of the objects; the distance does not matter

Answer: (C)

Verified step by step guidance

1. Recall Newton's law of universal gravitation, which states that the gravitational force between two objects depends on their masses and the distance between them.
2. Identify the variables involved: the masses of the two objects, denoted as \(m_1\) and \(m_2\), and the distance between their centers, denoted as \(r\).
3. Write down the formula for the gravitational force: \(F = G \frac{m_1 m_2}{r^2}\), where \(G\) is the gravitational constant.
4. Understand that the force is directly proportional to the product of the two masses, meaning if either mass increases, the force increases.
5. Recognize that the force is inversely proportional to the square of the distance between the objects, so as the distance increases, the force decreases rapidly.