David Terrazas, age 11, of Tucson, Arizona, for his question:

What is the earth moon mass system?

Actually, David's question was: Where is the center of the earth moon mass system? That sounds a bit complicated and might scare off an average reader, and one purpose of the column is to share our curiosities. However, his words are quite precise and accurate and Andy apologizes for changing them. The fascinating topic relates to what the moon does in our sky. David's question pinpoints one reason why it does what it does, which is something we also want to know.

We learn about the motions of the moon in easy stages. At first we picture a two dimensional diagram to compare its size with the earth and grasp the distance between them. Later, we may cope with a three dimensional model and shift the pieces to see how the moon orbits the earth while both of them orbit the sun. We get the basic idea, but it is pitifully over simplified. It ignores a whole package of variations in the moon's path. It does not explain that the earth moon system works as a unit, or how the two are linked together.

The key word is mass, which is weight with a college degree. Mass is the amount of matter, or material, packed into a given space, or volume. The mass of a heavenly body has a center around which all the matter is equally distributed. The earth's mass center is almost 4,000 miles below the global surface. The moon's is 1,080 miles below its surface. Astronomers figure distances between the mass centers of two bodies. This adds 5,043 miles to earth lunar surface landings, but we need it to figure their gravitational linkage.

Gravity is related to mass. Its force extends outward from the center and gets weaker with distance at a set ratio. The earth and moon pull at each other but this force is offset by the spin of rotation. The pattern of their system is related to mass, motion and distance. It somewhat resembles a seesaw that also makes circles.

Identical twins can balance an ordinary seesaw when each is the same distance from the pivot. If one is replaced by big brother, he tips down his end of the board. He may restore balance by moving closer to the center. The earth moon balancing system is related to their distance and their combined masses. Suppose their masses were identical. They could offset their gravitational pulls by orbiting around a mass center midway between them, like two balls on a dumbbell.

But big brother earth is 81.56 times more massive than the moon. We can find that pivot point by dividing the distance between them by 81.56. This places the mass center of the earth moon system about 2,900 miles from the earth's center, or some 1,100 miles below the surface.

Around this point, the earth and moon swing like a pair of partners at a hoedown. But since the earth has such a short end of the line, its motions are too slight to notice. The moon, way out there at the far end of the line, has much farther to go. Its orbit around the mutual mass center is so obvious that we assume it circles the earth while the earth stays perfectly still.