To calculate an object's weight, we have weight = mass * gravitational field strength (W = mg). From this, we see that an object with a greater mass (e.g. a hammer compared with a feather) has a greater weight, and since weight is the force that causes falling, we might expect that it will fall faster.

However, this does not happen. If we want to work out the acceleration of an object, we use Newton's second law, force = mass * acceleration (F = ma). Since weight is the force acting on the hammer or feather, we can equate our expression for the weight, mg, to ma:

ma = mg

We can then divide both sides of this equation by m, yielding

a = g

And therefore, the acceleration a doesn't depend on m, the object's mass. For this reason, a hammer and a feather will fall with the same acceleration on the Moon, as long as there are no other forces.