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Ideally, an object which is the result of letting the mass approach the limiting value of infinity. In practice, an object whose mass so far exceeds those of any others in the system that its mass may, for practical purposes, be taken as that limiting case. |
Of course, no infinitely massive objects exist, but they are the natural extrapolation of physical syatems in which the mass of one object so far exceeds another that it is absurd to consider the consequences of the relative motion of the larger mass. For instance, when treating problems in which an object moves under the earth's gravitational field, the motion of the Earth itself relatuive to the object is so small that one is justified in ignoring the earth's motion, and in assuming that the object moves relative to a fixed surface under a constant acceleration. Similarly, the center of mass of a system consisting of a pebble and the earth will be effectively at the center of the earth, and will negligibly affected by the position of the pebble.