. Carnegie Institution of Washington publication. 38 THE TIDAL PROBLEM. from a to & will lose velocity—and hence kinetic energy—and gain potential energy. At the point b it will have the minimum of motion and the maxi- mum of potential energy. From 6 to c it will fall back toward the center, a portion of its potential energy being converted into kinetic, and its veloc- ity being increased and reaching a second maximum at c. In the second half of its orbit, cda, similar exchanges of kinetic and poten- tial energy will take place. If p is affected by no friction or obstruction in its course,
. Carnegie Institution of Washington publication. 38 THE TIDAL PROBLEM. from a to & will lose velocity—and hence kinetic energy—and gain potential energy. At the point b it will have the minimum of motion and the maxi- mum of potential energy. From 6 to c it will fall back toward the center, a portion of its potential energy being converted into kinetic, and its veloc- ity being increased and reaching a second maximum at c. In the second half of its orbit, cda, similar exchanges of kinetic and poten- tial energy will take place. If p is affected by no friction or obstruction in its course, these exchanges of kinetic and potential energy will be com- pensatory and maybe continued indefinitely without affecting the rotation of E. The case is that of an inner satellite or an inner planet when all the bodies involved are considered as rigid bodies or massive points. But if now friction be introduced at any point in the orbit of p, heat will be developed and dissipated, and energy lost to the system. Looked at in detail, it would seem that the retardation of p by friction on E in some phases of its orbit would be accelerative to E's rotation, and in other portions, retardative, for in some por- tions p's angular motion ia greater than E's, and in others less, but traced out in its full history it appears that what is seemingly accelerative in one phase is retardative in another and that the ulterior effect is precisely measured by the loss of mechanical energy by con- version into radiant energy and dissipation. For example, fric- tion between p and the normal periphery of E as represented by A BCD, at or in the vicinity of c, will be accelerative in its immediate phase because p in this part of its orbit is moving faster than the contact portion of E, but the retardation of p in this portion will reduce the rise of p in the section at and near d which is retardative in its immediate phase because in this position p is moving more slowly than the normal. Please n
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