The file BMAN20 contains the periodic and Poisson terms of the rigid Mars nutation series BMAN20. the file BMAN20RS contains the periodic terms of the rigid Mars nutation series BMAN20RS. Computational procedure explained in (Baland et al. 2020) %------------------------------------------------------------------------------------------------------------------------- Truncation criterion: prograde and/or retrograde amplitude larger than 0.025 mas. Solution computed with HD=0.00538017, so that the total longitude variation rate is -7608.3 mas/year (Konopliv et al. 2016). The solution can be rescaled to any value of HD. %------------------------------------------------------------------------------------------------------------------------- Columns signification: - j is the item number. - Ma, Ju, Sa, Te, Ve are the mean longitudes of Mars, Jupiter, Saturn, the Earth and of Venus. - phi is the rotation angle of Mars. - NPh and NDe are the mean longitudes of the nodes of Phobos and Deimos, respectively. - Periods are given in Earth solar days. - psiC and psiS (mas) are the cosine and sine amplitudes of the nutation in longitude of the angular momentum axis. - epsC and epsS (mas) are the cosine and sine amplitudes of the nutation in obliquity of the angular momentum axis. - P and R (mas) are the prograde and retrograde amplitudes of the nutation of the angular momentum axis. - pi and rho (deg) are the phases to be added to the phase of the prograde and retrograde terms, respectively. - alphaC and alphaS (mas) are the cosine and sine amplitudes of the nutation in right ascension of the angular momentum axis. - deltaC and deltaS (mas) are the cosine and sine amplitudes of the nutation in declination of the angular momentum axis. %------------------------------------------------------------------------------------------------------------------------- The rotation axis can be assimilated to the angular momentum axis. The figure axis CANNOT be assimilated to the angular momentum axis. %------------------------------------------------------------------------------------------------------------------------- The values of the arguments are (Moisson and Bretagnon 2000: VSOP2000) (Jacobson and Lainey 2014: Phobos and Deimos ephemerides) Sa = 0.87401678345 + 213.2990797783 T Ju = 0.59954667809 + 529.6909721118 T Ma = 6.20349959869 + 3340.6124347175 T Te = 1.75346994632 + 6283.0758504457 T Ve = 3.17613445715 + 10213.2855473855 T NPh= 2.13055663363 - 2779.4193805084 T NDe= 0.20283841509 - 114.7466716724 T phi= 3.63666363337 + 2236871.5151256 T where T is the dynamical time measured in thousand of years since J2000.0 %------------------------------------------------------------------------------------------------------------------------- For BMAN20, the waves in the time domain are obtained the following way: Delta psi = T^alpha ( psiC Cos(varphi) + psiS Sin(varphi) ) Delta eps = T^alpha ( epsC Cos(varphi) + epsS Sin(varphi) ) Delta alpha = T^alpha ( alphaC Cos(varphi) + alphaS Sin(varphi) ) Delta delta = T^alpha ( deltaC Cos(phvarphii) + deltaS Sin(varphi) ) with varphi = f t + varphi0, a linear combination of the arguments Sa, Ju, Ma, Te, Ve, NPh, NDe, and phi. f is positive. delta x = T^alpha ( P Cos(f t + pi) + R Cos (-f t - rho) ) delta y = T^alpha ( P Sin(f t + pi) + R Sin (-f t - rho) ) alpha in T^alpha is an integer in-between 0 and 1 (not the right ascension) Times series can be found in the file bman20_TimesSeries.dat %------------------------------------------------------------------------------------------------------------------------- For BMAN20RS, the waves in the time domain are obtained the following way: Delta psi = ( psiC Cos(varphi) + psiS Sin(varphi) ) Delta eps = ( epsC Cos(varphi) + epsS Sin(varphi) ) Delta alpha = ( alphaC Cos(varphi) + alphaS Sin(varphi) ) Delta delta = ( deltaC Cos(varphi) + deltaS Sin(varphi) ) with varphi = f t + varphi0, a linear combination of the arguments Ma, NPh, and NDe. f is positive. delta x = ( P Cos(f t + pi) + R Cos (-f t - rho) ) delta y = ( P Sin(f t + pi) + R Sin (-f t - rho) ) An alternative representation is also provided, for which Delta psi = ( psiC Cos(f t) + psiS Sin(f t) ) Delta eps = ( epsC Cos(f t) + epsS Sin(f t) ) Delta alpha = ( alphaC Cos(f t) + alphaS Sin(f t) ) Delta delta = ( deltaC Cos(f t) + deltaS Sin(f t) ) Times series can be found in the file bman20rs_TimesSeries.dat %------------------------------------------------------------------------------------------------------------------------- The J2000 epoch values are (in degrees) psi0 = 35.4975258 eps0 = 25.1918197 alpha0 = 317.6811155 delta0 = 52.8863525 %------------------------------------------------------------------------------------------------------------------------- The secular and quadratic terms of the BMAN20 solution are (in mas): (-7.61428E06 T - 14353.7 T^2) in longitude for the Solar torque (+6754 T) in longitude (geodetic precession) (-235 T) in longitude for Phobos torque (-201 T) in longitude for Deimos torque (-342 T) in longitude for Planet torque (-2.42138 T + 2007.5 T^2) in obliquity for the Solar torque ( 0 ) in obliquity for Phobos torque ( 0 ) in obliquity for Deimos torque (-3 T) in obliquity for Planet torque (-3.91248E06 T - 5096.0 T^2) in right ascension for the Solar torque (-121 T) in right ascension for Phobos torque (-103 T) in right ascension for Deimos torque (-179 T) in right ascension for Planet torque (-2.22056E06 T - 5648.2 T^2) in declination for the Solar torque (-69 T) in declination for Phobos torque (-59 T) in declination for Deimos torque (-98 T) in declination for Planet torque %------------------------------------------------------------------------------------------------------------------------- The secular and quadratic terms of the BMAN20RS solution are (in mas): (-7.6083E06 T - 14353.7 T^2) in longitude (2007.5 T^2) in obliquity (-3.90940E06 T - 5096.0 T^2) in right ascension (-2.21882E06 T - 5648.2 T^2) in declination %------------------------------------------------------------------------------------------------------------------------- Any comments or request could be send to Baland Rose-Marie at the following e-mail address: Rose-Marie.Baland@oma.be Last revision: 28/05/20.