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?

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.