Consider now two objects falling towards the Earth, but far from it, as shown in the first sketch in Figure 13.3. Both objects fall towards the center of the Earth — which is not quite the same direction for each object. Assuming the objects start at the same distance from the Earth, their paths will converge. Now, if they don't realize they are falling — by virtue of being in a large falling elevator, say — they will nevertheless notice that they are approaching each other. This is gravity!

Similarly, if, as shown in the second sketch, one object starts out above the other, it is slightly further from the Earth, and hence experiences a slightly weaker gravitational attraction. Thus, the lower object will always accelerate more then the upper one, and so the distance between the objects will increase.

                                                               
Figure 13.3: Two objects falling towards the Earth from far away either move closer together or further apart depending on their initial configuration.

This effect causes tides! To see this, imagine that the Earth is falling towards the Moon, as shown in Figure 13.4. The Earth itself can be regarded as a rigid body, falling toward the moon with the velocity given by the arrow at its center. But the water on the surface of the Earth falls toward the moon depending on its location, with velocities given by the four arrows shown. The relative motion of the water and the Earth is given by comparing the arrows: Both the nearest and furthest points from the Moon move away from the center, causing high tides, whereas the points on either side move toward the center, causing low tides. This explains why there are two, not one, high (and low) tides every day! A similar effect, but roughly half as strong, is caused by the Sun.

Figure 13.4: Tides are caused by the Earth falling towards the Moon!