The mass of the Moon

How much mass does the Moon contain? In order to know it, you can exploit the mutual attraction of Earth and Moon. Under the action of the gravitational force, these bodies move according to the three Kepler's laws. You will later learn these laws, which rule the motion of a body around a second one. 

When two bodies of comparable mass orbit one around the other, Kepler's third law states that a relation exists between the orbital period of the two bodies, their mean distance and their masses. This law is true also in the case of the Earth-Moon system. Using this law you can therefore find the mass of the Moon, when the mass of the Earth, the orbital period of the Moon, and the mean Earth-Moon distance are known. 
You already know these data, and with Kepler's third law one finds that the Moon has a mass which is 0.012 times that of the Earth (that is, about one hundredth). Now that you know the mass and the radius of the Moon, you can find how strong is the gravitational force on the surface of our natural satellite.   
The force is proportional to the mass, so if the Moon were replaced with the Earth under your feet, you would notice a gravitational force equal to about one hundredth that of the Earth. But the Moon is smaller than the Earth, so you can get closer to its center. In that case, you know that the force increases as the inverse square of the distance. The ratio between the sizes of the two bodies is about 3.7, so the ratio between the two gravitational forces is about 13.7 (3,72). The product between 0.012 and 13.7 is about 1/6. Your weight on the Moon would then be 1/6 of the one you measure on the Earth. 

At this point you know that the Moon is a spherical body, as large as about 1/4 of the Earth, and that it contains about 1/100 of the mass of the Earth. But what is the Moon made of? What is its composition?