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The formula displayed is for calculating the gravitational force (\( F_g \)) between two masses using Newton's law of universal gravitation:

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

where:
- \( G = 6.67 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2 \) is the gravitational constant,
- \( m_1 = 5.97 \times 10^{24} \, \text{kg} \) (mass of the Earth),
- \( m_2 = 7.35 \times 10^{22} \, \text{kg} \) (mass of the Moon),
- \( r = 3.84 \times 10^8 \, \text{m} \) (distance between the Earth and the Moon).

Let's calculate it step-by-step.

1. Compute \( G \cdot m_1 \cdot m_2 \):
   \[
   6.67 \times 10^{-11} \times 5.97 \times 10^{24} \times 7.35 \times 10^{22}
   \]

2. Square the distance \( r \):
   \[
   (3.84 \times 10^8)^2
   \]

3. Divide the results from step 1 by the result from step 2 to find \( F_g \).

Would you like me to carry out this calculation? 

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**Relative Questions:**

1. What is the significance of the gravitational constant \( G \)?
2. How does the gravitational force change with distance?
3. Why are mass and distance crucial in gravitational calculations?
4. What would happen to \( F_g \) if the distance doubled?
5. How is this formula used in real-world physics applications?

**Tip:** In gravitational force calculations, small changes in distance \( r \) can have significant effects due to the inverse-square relationship.

Calculate the gravitational force (Fg) between the Earth and the Moon using Newton's law of universal gravitation with given values.

Learn how to calculate the gravitational force (Fg) between Earth and the Moon using Newton's law of universal gravitation. This physics problem involves key values: G = 6.67 x 10^-11 Nm²/kg², Earth's mass (5.97 x 10^24 kg), Moon's mass (7.35 x 10^22 kg), and the distance (3.84 x 10^8 m). Suitable for high school students in Grades 11-12.

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