Gravitational Force and Distance Relationship

The problem is to visualize the relationship between the gravitational force between two objects and the distance between them. According to Newton's law of gravitation, the gravitational force between two masses decreases as the distance between them increases. We aim to graph this relationship, where the distance is plotted on the x-axis and the gravitational force is plotted on the y-axis.

### Solution:

The solution involves:

1. **Gravitational Force Formula**:

   The gravitational force between two objects is given by the formula:

   F = (G * m1 * m2) / r²

   Where:

   - F is the gravitational force,

   - G is the gravitational constant (6.674 × 10⁻¹¹ N·m²/kg²),

   - m1 and m2 are the masses of the two objects,

   - r is the distance between the two objects.

2. **Masses**:

   In this solution, the masses of the two objects are given as:

   - m1 = 0.5 kg,

   - m2 = 1.5 kg.

3. **Distance Range**:

   The distance between the objects varies from 100 meters to 1000 meters, in steps of 50 meters. The gravitational force will be calculated for each of these distances.

4. **Gravitational Force Calculation**:

   The gravitational force is calculated using the formula for each value of r, and the results are stored in a list.

5. **Graphical Representation**:

   The graph is then plotted with the distances on the x-axis and the corresponding gravitational forces on the y-axis. This helps visualize how the force decreases as the distance increases.

### Key Observations from the Plot:

- The plot should show a **decreasing curve**, illustrating that the gravitational force decreases as the distance between the objects increases.

- The relationship is an inverse square law, meaning the force diminishes rapidly as the distance increases.

- The force is very high at smaller distances and decreases significantly as the distance increases.

Thus, this solution effectively models the behavior of gravitational force with respect to distance, providing insights into the relationship between these two variables.