On the use of analytical theories in the calculation of precession-nutation |
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| Authors: | P Bretagnon |
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| Institution: | (1) Bureau des longitudes, 77, avenue Denfert-Rochereau, 75014 Paris, France |
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| Abstract: | We present the use of the analytical solutions of the planets and of the Moon's motion in the determination of the quantities which relate the barycentric and the geocentric coordinate systems and of the expressions of precession-nutation. The computation of the precession and nutation quantities are built with the analytical theories of the motion of the Moon, the Sun and the planets of the Bureau des longitudes. We take into account the influence of the Moon, the Sun and all the planets on the potential of the Earth limited to C
j,0 for j from 2 to 5, C
2,2, S
2,2, C
3,
S
3, , for from 1 to 3 and C
4,1, S
4,1. We determine the 3 Euler angles  ,  , and  2 calculating the components of the torque of the external forces with respect to the geocenrer in the case of the rigid Earth. The equations are solved by iterations and so are taken into account the nutations-on-the-nutations effects. We have determined the analytical variations of the angles and w fixing the equator with respect to the ecliptic J2000. We find, in w, a secular term of –26.5026 mas per century. The analytical solution of the precession-nutation has been compared to a numerical integration over the time span 1900–2050. The differences do not exceed 16 µas for and 12 µas for . |
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| Keywords: | precession nutation analytical theory |
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