The acceleration due to gravity ($g$) on a celestial body is calculated using the formula:

$g = \frac{G \cdot M}{R^2}$

Where:

• $G$ is the gravitational constant: $6.674 \times 10^{-11} \, \text{m}^3 \, \text{kg}^{-1} \, \text{s}^{-2}$,
• $M$ is the mass of the Moon: $7.35 \times 10^{22} \, \text{kg}$,
• $R$ is the radius of the Moon: $1.74 \times 10^6 \, \text{m}$.

Step 1: Substitute the values into the formula:

$g = \frac{(6.674 \times 10^{-11}) \cdot (7.35 \times 10^{22})}{(1.74 \times 10^6)^2}$

Step 2: Simplify the denominator:

$(1.74 \times 10^6)^2 = 3.0276 \times 10^{12}$

Step 3: Calculate the numerator:

$(6.674 \times 10^{-11}) \cdot (7.35 \times 10^{22}) = 4.90659 \times 10^{12}$

Step 4: Divide the numerator by the denominator:

$g = \frac{4.90659 \times 10^{12}}{3.0276 \times 10^{12}}$

$g \approx 1.62 \, \text{m/s}^2$

Final Answer:

The acceleration due to gravity on the Moon is approximately:

$g \approx 1.62 \, \text{m/s}^2$

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Would you like more details on the calculation process? Here are some related questions to expand on this topic:

1. How does the acceleration due to gravity on the Moon compare to Earth?
2. What factors influence the acceleration due to gravity on a celestial body?
3. How would you calculate the weight of an object on the Moon?
4. How does the Moon’s gravity affect objects in orbit around it?
5. What are some examples of the Moon’s lower gravity affecting lunar exploration?

Tip: Always use scientific notation carefully when dealing with astronomical calculations to avoid errors.