What must you know in order to calculate the gravitational force between two objects?

Options

A. their mass
B. the distance between them
C. both of the above
D. none of these

Answer

To calculate the gravitational force between two objects, you need to know the following:

1. **Mass of the Objects**: You need to know the mass of both objects involved in the gravitational interaction. Let's denote the masses as \( m_1 \) and \( m_2 \).

2. **Distance Between the Objects**: You also need to know the distance between the centers of the two objects. This distance is usually denoted as \( r \).

3. **Gravitational Constant**: The universal gravitational constant \( G \) is also required, which is a constant value used in the calculation of gravitational force.

The formula to calculate the gravitational force \( F \) between two objects is given by Newton's Law of Universal Gravitation:

\[ F = G \frac{m_1 \times m_2}{r^2} \]

Where:
- \( F \) is the gravitational force,
- \( G \) is the universal gravitational constant (approximately \( 6.674 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \)),
- \( m_1 \) and \( m_2 \) are the masses of the two objects,
- \( r \) is the distance between the centers of the two objects.

### Step-by-Step Solution:

1. **Identify the Masses**: Determine the mass of the first object (\( m_1 \)) and the mass of the second object (\( m_2 \)).
- Hint: Look for the weight or mass information provided for each object.

2. **Measure the Distance**: Measure or find out the distance (\( r \)) between the centers of the two objects.
- Hint: This distance is crucial and should be measured in meters for standard calculations.

3. **Use the Gravitational Constant**: Remember the value of the universal gravitational constant (\( G \)).
- Hint: This is a known constant and does not change; you can find it in textbooks or reliable online resources.

4. **Apply the Formula**: Substitute the values of \( m_1 \), \( m_2 \), \( r \), and \( G \) into the formula \( F = G \frac{m_1 \times m_2}{r^2} \).
- Hint: Ensure that your units are consistent (e.g., masses in kilograms, distance in meters).

5. **Calculate the Gravitational Force**: Perform the calculation to find the gravitational force (\( F \)).
- Hint: Use a calculator for accuracy, especially when dealing with large or small numbers.