If astronauts measure the time it takes an object to fall 1 m on the Moon to be about 1.1 s, what is the mass of the Moon?

To determine the mass of the Moon based on the falling time of an object, you can use the formula for the gravitational acceleration on the surface of a celestial body, which is given by ( g = \frac{G \cdot M}{R^2} ). In this equation, ( g ) is the gravitational acceleration, ( G ) is the gravitational constant ((6.674 \times 10^{-11} , \text{m}^3/\text{kg} \cdot \text{s}^2)), ( M ) is the mass of the Moon, and ( R ) is the radius of the Moon.

Given that the time to fall 1 meter on the Moon is approximately 1.1 seconds, we can first determine the acceleration ( g ) using the equation of motion for constant acceleration:

[ d = \frac{1}{2} g t^2 ]

where ( d ) is the distance (1 m), and ( t ) is the time (1.1 s). Rearranging gives:

[ g = \frac{2d}{t^2} = \frac{2 \cdot 1,\text{