Space methods - Physical Geodesy - page 282

or

( Γ + Γ T ) / 2= M + ΩΩ , (7-59)

which concludes our proof.
Since we have determined ˙ Ω in (7-57), we can get Ω by integration:
Ω ( t )= Ω ( t 0 )+ t
t 0

˙ Ω dt ,

(7-60)

where the initial orientation Ω ( t 0 ) is obtained from the star trackers. Squar-
ing the result for Ω ( t ) yields ΩΩ , which is needed in (7-59) so that we
find

M =( Γ + Γ T ) / 2 − ΩΩ (7-61)

as final result for the desired Marussi tensor M . Many more details may be
found in Rummel (1986).