Tidal evolution in close binary systems.

Mathematical outline of the theory of tidal evolution in close binary systems of secularly constant total momentum. Following a general outline of the problem the basic expressions for the energy and momenta of close binaries consisting of components of arbitrary internal structure are established, and the maximum and minimum values of the energy (kinetic and potential) which such systems can attain for a given amount of total momentum are investigated. These results are compared with the actual facts encountered in binaries with components whose internal structure (and, therefore, rotational momenta) are known from evidence furnished by the observed rates of apsidal advance. The results show that all such systems whether of detached or semidetached type - disclose that more than 99% of their total momenta are stored in the orbital momentum. The sum of the rotational momenta of the constituent components amounts to less than 1% of the total -a situation characteristic of a state close to the minimum energy for given total momentum.