In Newton's law of universal gravitation, the magnitude of the gravitational force between two point masses is $F=G\frac{m\_1m\_2}{r^2}$. Which two factors determine how strong the gravitational force is between the two objects (assuming $G$ is constant)?

• A. The distance between the objects and the temperature of the objects
• B. The distance between the objects and the volume of the objects
• C. The masses of the two objects and their electric charges
• D. The masses of the two objects and the distance between their centers

Answer: (D)

Verified step by step guidance

1. Recall Newton's law of universal gravitation, which states that the magnitude of the gravitational force \(F\) between two point masses \(m_1\) and \(m_2\) is given by the formula: \[F = G \frac{m_1 m_2}{r^2}\] where \(G\) is the gravitational constant and \(r\) is the distance between the centers of the two masses.
2. Identify the variables in the formula that affect the gravitational force: the masses \(m_1\) and \(m_2\), and the distance \(r\) between the objects.
3. Understand that \(G\) is a constant and does not change the force based on the objects themselves, so it is not a factor that varies with the objects' properties.
4. Note that the force is directly proportional to the product of the two masses, meaning if either mass increases, the force increases proportionally.
5. Note that the force is inversely proportional to the square of the distance between the objects, meaning if the distance increases, the force decreases by the square of that increase.