With a new theory on the 1PN celestial mechanics recently developed by
Damour, Soffel and Xu (1991,1992,1993,1994), definitions and expressi
ons of the 1PN spin angular momentum are investigated and analysed. Th
e total spin angular momentum of a system of extended bodies such as t
he solar system is calculated and expressed as the function of local p
arameters and observables under reasonable assumptions, which would fi
nd its application in the evolution and dynamics of systems of celesti
al bodies.