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The mathematical model used here to describe the gravitational force between two masses is known as the **inverse square law** model. This type of model is characterized by a relationship where a quantity (in this case, the gravitational force \( F_g \)) is inversely proportional to the square of the distance (\( r \)) between two objects.

### Explanation:

The given equation for the gravitational force is:

\[ F_g(r) = G \frac{m_1 m_2}{r^2} \]

where:
- \( F_g \) is the gravitational force between two masses (in Newtons).
- \( G \) is the gravitational constant (\( 6.673 \times 10^{-11} \, \text{N} \cdot \text{m}^2 / \text{kg}^2 \)).
- \( m_1 \) is the mass of the first object (in kilograms).
- \( m_2 \) is the mass of the second object (in kilograms).
- \( r \) is the distance between the centers of the two masses (in meters).

### Key Characteristics of the Inverse Square Law Model:
1. **Inverse Proportionality to the Square of Distance:**
   The gravitational force \( F_g \) decreases with the square of the distance \( r \) between the two masses. This means that if the distance between the masses is doubled, the gravitational force is reduced to one-fourth of its original value.
   
2. **Direct Proportionality to the Product of the Masses:**
   The gravitational force \( F_g \) is directly proportional to the product of the two masses \( m_1 \) and \( m_2 \). If either mass is increased, the gravitational force increases proportionally.

### Application:
This inverse square law model is a fundamental principle in physics, describing not only gravitational forces but also other phenomena such as the intensity of light and sound, and electric field strength, which all diminish in proportion to the square of the distance from the source.

### Summary:
The type of mathematical model used here is the inverse square law model, which describes how the gravitational force between two masses decreases with the square of the distance between them while being directly proportional to the product of the two masses.

Do you want further details or have any questions? Here are some related questions to explore:

1. How does the gravitational force change if the distance between two masses is tripled?
2. What would happen to the gravitational force if the mass of one object is doubled and the distance remains the same?
3. Can you describe other physical phenomena that follow the inverse square law?
4. How would you experimentally verify the inverse square law for gravitational force?
5. What is the significance of the gravitational constant \( G \)?
6. How does the inverse square law apply to the intensity of light from a point source?
7. Can the gravitational force between two masses ever be zero? Explain under what conditions.
8. How does the inverse square law relate to Kepler's laws of planetary motion?

**Tip:** The inverse square law is a powerful tool in physics and astronomy, allowing scientists to understand and predict the behavior of forces and fields over varying distances. Familiarity with this concept can provide deeper insights into many natural phenomena.

Explore the mathematical model describing gravitational force between two masses using the inverse square law. Learn about its application in physics and its implications on force calculations. Suitable for advanced high school students and physics enthusiasts.

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