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In Section 5.11, the Kepler problem in planetary motion was studied for the special case of one of the masses being very large. From the discussion in Sections 6.6 and 6.7, it follows that the result can now be generalized to the case of any two masses m and M provided that the mass m in Section 5.11 is replaced by the reduced mass of the system

                                                          \( m_ \text{r} = {mM \over m + M} \)

The angular momentum L = r × m_rv is now the total angular momentum of the two-body system.

It is important to note that the two-body problem is unique in that it can be solved analytically as in Section 6.7. For three-body, four-body, ... etc. problems, the physicist has to resort to approximation techniques or to computerised numerical solutions.

The angular momentum of many-body systems is of considerable importance in astrophysics, for example in the dynamics of solar systems or galaxies.

Another important application is in the behaviour of rigid bodies which will be discussed in Chapter 7.