The acceleration due to gravity at the moon's surface is `1.67 ms^(-2)`. If the radius of the moon is `1.74 xx 10^(6) m`, calculate the mass of the moon.

Explanation

To find the mass of the moon using the given acceleration due to gravity and the radius, we can use the formula for gravitational acceleration:

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

Where:
- \( g \) is the acceleration due to gravity (1.67 m/s²)
- \( G \) is the universal gravitational constant (\( 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))
- \( M \) is the mass of the moon (which we need to find)
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