%%==================================================================%% %% %% %% Find below the Tables 3 to 8 of the paper entitled : %% %% %% %% %% %% THEORY OF MOTION AND EPHEMERIDES OF HYPERION %% %% %% %% by DURIEZ \& VIENNE, to appear in Astron. Astrophys 1997. %% %% %% %% e-mail: duriez@gat.univ-lille1.fr and vienne@gat.univ-lille1.fr %% %% %% %% %% %% %% %% These Tables contain the full series of the representation %% %% of the Hyperion's motion, with terms larger than 1 km for the %% %% long-period part and than 5 km for the short-period part. %% %% %% %%==================================================================%% % %%==================================================================%% %% %% %% %% %% %% %% text in Plain TeX %% %% %% %% %% %%==================================================================%% \baselineskip10.5pt % \def\eps{\varepsilon} \def\crs{\cr\noalign{\smallskip}} \def\crm{\cr\noalign{\medskip}} % % \def\sst{\scriptscriptstyle} \def\st{\scriptstyle} \def\Sp{\vphantom0^{\prime\prime}\!\!.} \def\sqi{\sqrt{\st-1}\,} \def\Day{{\hbox{$^{\rm \,d}$\ }}} \def\Ud{$\,${\hbox{\rm d\ }}} \def\Uy{$\,${\hbox{\rm y\ }}} \def\Deg{\hbox{$^\circ$}} \def\Dp{\hbox{$\vphantom0^{\circ}\!\!.$}} \def\abs#1{\vert#1\vert} \def\tenp#1{\,\hbox{$\st10^{\st#1}$}} \def\f{\hfill} \def\pho{\phantom{0}} \font\katorz=cmr10 at 14pt \null \centerline{\bf \katorz Theory of motion and ephemerides of Hyperion} \bigskip \bigskip \centerline{\bf L. Duriez and A. Vienne } \bigskip \centerline{ Universit\'e des Sciences et Technologies de Lille} \centerline{ Laboratoire d'Astronomie} \centerline{ 1 Impasse de l'Observatoire} \centerline{ F-59000 Lille, France} \centerline{ e-mail: duriez@gat.univ-lille1.fr and vienne@gat.univ-lille1.fr} \bigskip \bigskip \noindent {\bf Abstract.} In this paper, we present a new theory of motion for Hyperion, defined like in TASS1.6 for the other Saturn's satellites (Vienne \& Duriez 1995, =1995A\&A...297..588V), by the osculating saturnicentric orbital elements referred to the equatorial plane of Saturn and to the node of this plane in the mean ecliptic for J2000.0. These elements are expressed as semi-numerical trigonometric series in which the argument of each term is given as an integer combination of 7 natural fundamental arguments (Table 3). These series (Tables 4 to 7) collect all the perturbations caused by Titan on the orbital elements of Hyperion, whose amplitudes are larger than 1~km in the long-period terms and than 5~km in the short-period ones. Taking also account of the perturbations from other satellites and Sun (Table 8), these series have been fitted to 8136 Earth-based observations of Hyperion in the interval [1874-1985]. The resulting series allows to produce new ephemerides for Hyperion, which have been compared to those previously given by Taylor (1992) (=1992A\&A...265..825T): Using the same set of observations and the same way to weight them, the root mean square (o-c) residual of the present theory is 0.156 arcseconds while the ephemerides of Taylor gives 0.203 arcseconds. \bigskip \bigskip \noindent Find below the Tables 3 to 8 of the paper of DURIEZ \& VIENNE, to appear in Astron. Astrophys 1997. These tables contain the full series of the representation of the Hyperion's motion, with terms larger than 1 km for the long-period part and than 5 km for the short-period part. These series have been adjusted to observations over one century, as explained in the paper cited above. \noindent (ask for an offprint to duriez@gat.univ-lille1.fr). \bigskip \bigskip % Fundamental arguments % \bigskip \noindent{\bf Table 3.} Fundamental arguments of the Titan-Hyperion interaction. Each one is in the form : $\omega^*_k t+\varphi^*_k$ where $t=(\hbox{Julian Date)}-2\,451\,545.0$. The columns $\eps(T^*_k)$ and $\eps(\varphi^*_k)$ give the estimated error on each period and on each phase, issued from the fit of the theory to observations \smallskip \halign{ $\ #$\hfil&\quad\hfil$#$\hfil &\quad\hfil$#$\quad&\quad\hfil$#$\hfil\quad &\quad\hfil$#$\quad&\quad\hfil$#$\quad& \quad\hfil$#$\cr \noalign{\hrule\medskip} k&\hfill\hbox{argument}\hfill &\hfill\hbox{$\omega^*_k$ (rad$/$d)}\hfill &\hfill\hbox{$\varphi^*_k$ (rad)}\hfill &\hfill\hbox{period (d)}\hfill &\hfill\hbox{$\eps(T^*_k)$ (d)}\hfill &\hfill\hbox{$\eps(\varphi^*_k)$ (rad)}\cr \noalign{\medskip\hrule\medskip} 1&\psi & 0.098733765027& 1.379026808& 63.6377& 0.00008& 0.00011\cr 2&\tau & 0.009810539955& 1.803677249& 640.4525& 0.03454& 0.00100\cr 3&\varpi^*_7& -0.000892481124& 3.382691058& -7040.1324& 3.98970& 0.00038\cr 4&\varpi^*_6& 0.000024646231& 2.860542690& 254934.9313& 0.00504& 0.00063\cr 5&\Omega^*_7& -0.000113616050& 3.864510578& -55301.9163& 15.97624& 0.00537\cr 6&\Omega^*_6& -0.000024636367& 6.141812995& -255037.0101& 0.01695& 0.00915\cr 7&\Omega_0 & 0.000000000000& 3.221557438&&& 0.00001\cr \noalign{\medskip\hrule} } \vfil\eject \bigskip \def\PS{\psi} \def\TO{\tau} \def\PH{\varpi^*_7} \def\PT{\varpi^*_6} \def\NH{\Omega^*_7} \def\NT{\Omega^*_6} \def\NO{\Omega_0} \def\A{\rlap{\ *}} \def\qhfil{\quad\hfil} \def\Cdots{\noalign{\vskip-1.3mm}\cdots\cr\noalign{\vskip-1.3mm}} % series p : \noindent{\bf Table 4.} Series for $p_7$ : Each term is in the form $\alpha \cos(\omega t+\varphi)$ with $t=(\hbox{Julian Date)}-2\,451\,545.0$. Each argument is also identified as an integer combination of the seven fundamental arguments given in Table 3; the values of $\omega $ and $\varphi$ are in fact computed from these combinations. The osculating semi-major axis is then $a_7=A_7(1+p_7)^{-2/3} $ where $A_7$ is a kind of mean value of $a_7$, computed from the third Kepler's law : $A_7=(k^2(M_s+m_7)/N_7^2)^{1/3}$ with $k$ the gaussian constant, with $M_s= M_\odot/3498.790 $ (from Campbell \& Anderson 1989) $m_7=3\ 10^{-8}\ M_s$ (from Burns 1986) and with the mean mean motion $N_7= 0.2953088139$~rad/d. The amplitudes in km represent $-(2/3)A_7p_7$ with $A_7= 1482333.4$~km. The estimated error $\varepsilon(\alpha)$ on each amplitude comes from the fit of the theory to observations \medskip \halign{ $#$\hfil&\qhfil$#$&\qhfil$#$&\qhfil$#$&\qhfil$#$& \quad\quad$#$\hfil &\quad\qhfil$#$&\qhfil$#$\cr \noalign{\hrule\medskip} \hbox{n\Deg} &\hfill\hbox{amplitude $\alpha $}\hfill &\hfill\hbox{phase $\varphi$}\hfill &\hfill\hbox{frequency $\omega $}\hfill &\hfill\hbox{period}\hfill &\hfill\hbox{argument}\hfill &\hfill\hbox{amplitude}\hfill &\hfill\hbox{$\varepsilon(\alpha)$}\hfill \cr &\hfill\hbox{(rad)}\hfill &\hfill\hbox{(deg)}\hfill &\hfill\hbox{(rad/d)}\hfill &\hfill\hbox{(d)}\hfill & &\hfill\hbox{(km)}\hfill &\hfill\hbox{(km)}\hfill \cr \noalign{\medskip\hrule\medskip} 0& -0.0015747& 0.000& 0.0000000000&&& 1556.14& 0.53\cr 1& 0.0052692& 103.343& 0.0098105400& 640.45&\TO & -5207.14& 5.30\cr 2& -0.0009448& 79.012& 0.0987337650& 63.64&\PS & 933.67& 0.26\cr 3& -0.0006016& 335.669& 0.0889232251& 70.66&\PS-\TO & 594.52& 0.61\cr 4& 0.0005148& 182.356& 0.1085443050& 57.89&\PS+\TO & -508.75& 0.52\cr 5& -0.0001310& 73.426& 0.0107276673& 585.70&\TO-\PH+\PT & 129.44& 0.23\cr 6& 0.0001186& 133.260& 0.0088934126& 706.50&\TO+\PH-\PT & -117.21& 0.21\cr 7& -0.0000759& 232.326& 0.0791126851& 79.42&\PS -2\TO & 74.98& 0.15\cr 8& -0.0000439& 285.699& 0.1183548449& 53.09&\PS+ 2\TO & 43.42& 0.09\cr 9& -0.0000299& 310.029& 0.0294316199& 213.48& 3\TO & 29.51& 0.09\cr 10& 0.0000242& 206.686& 0.0196210799& 320.23& 2\TO & -23.94& 0.05\cr 11& 0.0000172& 5.586& 0.0880060977& 71.39&\PS-\TO+\PH-\PT & -17.01& 0.03\cr 12& -0.0000134& 305.752& 0.0898403524& 69.94&\PS-\TO-\PH+\PT & 13.23& 0.02\cr 13& -0.0000130& 152.439& 0.1094614323& 57.40&\PS+\TO-\PH+\PT & 12.88& 0.02\cr 14& 0.0000129& 66.505& 0.0099241560& 633.12&\TO-\NH+\NO & -12.75& 0.09\cr 15& -0.0000128& 140.182& 0.0096969239& 647.96&\TO+\NH-\NO & 12.61& 0.09\cr 16& -0.0000121& 108.929& 0.0978166377& 64.23&\PS+\PH-\PT & 11.92& 0.01\cr 17& 0.0000101& 212.272& 0.1076271776& 58.38&\PS+\TO+\PH-\PT & -10.01& 0.02\cr 18& -0.0000096& 330.083& 0.0009171274& 6850.94&-\PH+\PT & 9.48& 0.01\cr 19& 0.0000077& 128.983& 0.0693021452& 90.66&\PS -3\TO & -7.63& 0.02\cr 20& -0.0000050& 29.042& 0.1281653849& 49.02&\PS+ 3\TO & 4.97& 0.01\cr 21& -0.0000047& 158.556& 0.0113682701& 552.69&\TO -2\PH+ 2\NH & 4.67& 0.06\cr 22& -0.0000045& 233.823& 0.0098995196& 634.70&\TO-\NH+\NT & 4.44& 0.05\cr 23& 0.0000044& 332.863& 0.0097215603& 646.31&\TO+\NH-\NT & -4.39& 0.05\cr 24& 0.0000039& 48.131& 0.0082528098& 761.34&\TO+ 2\PH -2\NH & -3.88& 0.05\cr 25& 0.0000038& 262.243& 0.0781955578& 80.35&\PS -2\TO+\PH-\PT & -3.80& 0.01\cr 26& -0.0000035& 202.409& 0.0800298125& 78.51&\PS -2\TO-\PH+\PT & 3.46& 0.01\cr 27& 0.0000028& 43.509& 0.0116447947& 539.57&\TO -2\PH+ 2\PT & -2.78& 0.01\cr 28& 0.0000026& 49.096& 0.0996508924& 63.05&\PS-\PH+\PT & -2.59& 0.00\cr 29& 0.0000022& 280.112& 0.0303487472& 207.03& 3\TO-\PH+\PT & -2.14& 0.01\cr 30& 0.0000022& 255.782& 0.1192719723& 52.68&\PS+ 2\TO-\PH+\PT & -2.16& 0.01\cr 31& -0.0000022& 339.946& 0.0285144925& 220.35& 3\TO+\PH-\PT & 2.15& 0.01\cr 32& -0.0000021& 315.616& 0.1174377176& 53.50&\PS+ 2\TO+\PH-\PT & 2.06& 0.01\cr 33& 0.0000018& 296.025& 0.0098351763& 638.85&\TO-\NT+\NO & -1.74& 0.02\cr 34& -0.0000017& 270.661& 0.0097859036& 642.06&\TO+\NT-\NO & 1.71& 0.02\cr 35& 0.0000016& 25.640& 0.0594916052& 105.61&\PS -4\TO & -1.61& 0.01\cr 36& -0.0000014& 12.508& 0.0888096090& 70.75&\PS-\TO+\NH-\NO & 1.41& 0.01\cr 37& 0.0000014& 298.831& 0.0890368411& 70.57&\PS-\TO-\NH+\NO & -1.37& 0.01\cr 38& 0.0000014& 145.517& 0.1086579210& 57.83&\PS+\TO-\NH+\NO & -1.36& 0.01\cr 39& -0.0000013& 219.194& 0.1084306889& 57.95&\PS+\TO+\NH-\NO & 1.33& 0.01\crs 40& 0.0009846& 158.025& 0.1974675301& 31.82& 2\PS & -972.98& 0.20\cr 41& 0.0005722& 237.037& 0.2962012951& 21.21& 3\PS & -565.48& 0.15\cr 42& 0.0003064& 316.050& 0.3949350601& 15.91& 4\PS & -302.81& 0.12\cr 43& 0.0002329& 35.062& 0.4936688251& 12.73& 5\PS & -230.13& 0.07\cr 44& 0.0001830& 114.074& 0.5924025902& 10.61& 6\PS & -180.87& 0.05\cr 45& 0.0001428& 193.087& 0.6911363552& 9.09& 7\PS & -141.13& 0.04\cr 46& 0.0001031& 272.099& 0.7898701202& 7.95& 8\PS & -101.85& 0.04\cr 47& 0.0000916& 133.694& 0.2863907551& 21.94& 3\PS-\TO & -90.54& 0.10\cr 48& 0.0000842& 212.707& 0.3851245202& 16.31& 4\PS-\TO & -83.21& 0.10\cr 49& 0.0000748& 351.112& 0.8886038852& 7.07& 9\PS & -73.90& 0.03\cr 50& 0.0000625& 291.719& 0.4838582852& 12.99& 5\PS-\TO & -61.72& 0.07\cr 51& -0.0000593& 340.380& 0.3060118350& 20.53& 3\PS+\TO & 58.55& 0.07\cr 52& -0.0000587& 187.942& 0.1965504027& 31.97& 2\PS+\PH-\PT & 57.97& 0.03\cr 53& -0.0000584& 59.393& 0.4047456001& 15.52& 4\PS+\TO & 57.70& 0.07\cr 54& 0.0000552& 70.124& 0.9873376503& 6.36& 10\PS & -54.52& 0.03\cr 55& 0.0000529& 10.731& 0.5825920502& 10.78& 6\PS-\TO & -52.29& 0.06\cr 56& 0.0000479& 89.744& 0.6813258152& 9.22& 7\PS-\TO & -47.29& 0.05\cr 57& 0.0000465& 54.682& 0.1876569901& 33.48& 2\PS-\TO & -45.94& 0.05\cr 58& -0.0000451& 138.405& 0.5034793651& 12.48& 5\PS+\TO & 44.57& 0.05\cr 59& 0.0000439& 168.756& 0.7800595803& 8.05& 8\PS-\TO & -43.41& 0.05\cr 60& 0.0000427& 64.979& 0.4927516978& 12.75& 5\PS+\PH-\PT & -42.23& 0.03\cr 61& 0.0000415& 149.137& 1.0860714153& 5.79& 11\PS & -41.05& 0.02\cr 62& -0.0000406& 217.418& 0.6022131301& 10.43& 6\PS+\TO & 40.09& 0.05\cr 63& -0.0000386& 296.430& 0.7009468951& 8.96& 7\PS+\TO & 38.12& 0.04\cr 64& 0.0000382& 247.769& 0.8787933453& 7.15& 9\PS-\TO & -37.70& 0.04\cr 65& -0.0000362& 311.339& 0.1778464501& 35.33& 2\PS -2\TO & 35.73& 0.07\cr 66& -0.0000362& 15.442& 0.7996806602& 7.86& 8\PS+\TO & 35.77& 0.04\cr 67& 0.0000321& 326.781& 0.9775271103& 6.43& 10\PS-\TO & -31.73& 0.03\cr 68& -0.0000319& 94.455& 0.8984144252& 6.99& 9\PS+\TO & 31.54& 0.03\cr 69& 0.0000311& 228.149& 1.1848051803& 5.30& 12\PS & -30.70& 0.02\cr 70& -0.0000280& 4.711& 0.2170886100& 28.94& 2\PS+ 2\TO & 27.64& 0.06\cr 71& -0.0000272& 173.467& 0.9971481902& 6.30& 10\PS+\TO & 26.91& 0.03\cr 72& 0.0000267& 45.793& 1.0762608753& 5.84& 11\PS-\TO & -26.39& 0.02\cr 73& -0.0000230& 252.480& 1.0958819553& 5.73& 11\PS+\TO & 22.70& 0.02\cr 74& 0.0000230& 307.161& 1.2835389454& 4.90& 13\PS & -22.73& 0.02\cr 75& 0.0000223& 124.806& 1.1749946404& 5.35& 12\PS-\TO & -22.06& 0.02\cr 76& -0.0000194& 331.492& 1.1946157203& 5.26& 12\PS+\TO & 19.18& 0.02\cr 77& 0.0000186& 203.818& 1.2737284054& 4.93& 13\PS-\TO & -18.40& 0.01\cr 78& 0.0000168& 26.174& 1.3822727104& 4.55& 14\PS & -16.64& 0.02\cr 79& -0.0000164& 50.505& 1.2933494853& 4.86& 13\PS+\TO & 16.17& 0.01\cr 80& 0.0000154& 282.831& 1.3724621704& 4.58& 14\PS-\TO & -15.26& 0.01\cr 81& -0.0000137& 129.517& 1.3920832503& 4.51& 14\PS+\TO & 13.51& 0.01\cr 82& -0.0000134& 83.723& 0.3158223750& 19.89& 3\PS+ 2\TO & 13.21& 0.03\cr 83& -0.0000132& 30.351& 0.2765802152& 22.72& 3\PS -2\TO & 13.05& 0.03\cr 84& 0.0000127& 1.843& 1.4711959355& 4.27& 15\PS-\TO & -12.56& 0.01\cr 85& 0.0000122& 105.186& 1.4810064754& 4.24& 15\PS & -12.10& 0.02\cr 86& -0.0000113& 208.529& 1.4908170154& 4.21& 15\PS+\TO & 11.18& 0.01\cr 87& -0.0000109& 266.954& 0.2952841677& 21.28& 3\PS+\PH-\PT & 10.77& 0.01\cr 88& 0.0000104& 80.856& 1.5699297005& 4.00& 16\PS-\TO & -10.27& 0.01\cr 89& -0.0000093& 287.542& 1.5895507804& 3.95& 16\PS+\TO & 9.19& 0.01\cr 90& 0.0000088& 184.199& 1.5797402404& 3.98& 16\PS & -8.74& 0.01\cr 91& 0.0000085& 159.868& 1.6686634655& 3.77& 17\PS-\TO & -8.36& 0.00\cr 92& -0.0000079& 261.368& 0.2072780700& 30.31& 2\PS+\TO & 7.81& 0.02\cr 93& -0.0000076& 6.554& 1.6882845454& 3.72& 17\PS+\TO & 7.52& 0.00\cr 94& 0.0000074& 223.438& 0.9677165704& 6.49& 10\PS -2\TO & -7.34& 0.02\cr 95& 0.0000074& 144.426& 0.8689828053& 7.23& 9\PS -2\TO & -7.27& 0.02\cr 96& 0.0000072& 302.450& 1.0664503354& 5.89& 11\PS -2\TO & -7.08& 0.01\cr 97& 0.0000070& 65.413& 0.7702490403& 8.16& 8\PS -2\TO & -6.87& 0.01\cr 98& 0.0000069& 238.880& 1.7673972305& 3.56& 18\PS-\TO & -6.80& 0.00\cr 99& 0.0000066& 346.401& 0.6715152753& 9.36& 7\PS -2\TO & -6.54& 0.01\cr 100& 0.0000063& 263.211& 1.6784740055& 3.74& 17\PS & -6.26& 0.01\cr 101& -0.0000062& 85.567& 1.7870183104& 3.52& 18\PS+\TO & 6.11& 0.00\cr 102& 0.0000061& 100.475& 1.2639178654& 4.97& 13\PS -2\TO & -6.06& 0.01\cr 103& 0.0000056& 179.488& 1.3626516305& 4.61& 14\PS -2\TO & -5.52& 0.01\cr 104& 0.0000055& 317.893& 1.8661309956& 3.37& 19\PS-\TO & -5.47& 0.00\cr \noalign{\medskip\hrule} } \vfill\eject % series q : \bigskip \noindent{\bf Table 5.} Series for $q_7$ : Each term is in the form $\alpha \sin(\omega t+\varphi)$ with $t=(\hbox{Julian Date)}-2\,451\,545.0$. Each argument is also identified as an integer combination of the seven fundamental arguments given in Table 3; $\omega $ and $\varphi$ are in fact computed from these combinations. The mean longitude is then $\lambda _7= ( 4.3486836\pm 0.0001432)+( 0.2953088139\pm 0.0000001286) \,t + q_7$. The amplitudes in km represent $A_7q_7$ with $A_7= 1482333.4$~km. % The probable error (p.e.) on % each amplitude comes from the fit of the theory % to observations \medskip \halign{ $#$\hfil&\qhfil$#$&\qhfil$#$&\qhfil$#$&\qhfil$#$& \quad\quad$#$\hfil &\qhfil$#$&\qhfil$#$\cr \noalign{\hrule\medskip} \hbox{n\Deg} &\hfill\hbox{amplitude $\alpha $}\hfill &\hfill\hbox{phase $\varphi$}\hfill &\hfill\hbox{frequency $\omega $}\hfill &\hfill\hbox{period}\hfill &\hfill\hbox{argument}\hfill &\hfill\hbox{amplitude}\hfill &\hfill\hbox{$\varepsilon(\alpha)$}\hfill \cr &\hfill\hbox{(rad)}\hfill &\hfill\hbox{(deg)}\hfill &\hfill\hbox{(rad/d)}\hfill &\hfill\hbox{(d)}\hfill & &\hfill\hbox{(km)}\hfill &\hfill\hbox{(km)}\hfill \cr \noalign{\medskip\hrule\medskip} 1& 0.1591300& 103.343& 0.0098105400& 640.45&\TO & 235883.78& 229.13\cr 2& 0.0040425& 133.260& 0.0088934126& 706.50&\TO+\PH-\PT & 5992.32& 10.19\cr 3& -0.0036745& 73.426& 0.0107276673& 585.70&\TO-\PH+\PT & -5446.77& 9.42\cr 4& 0.0018763& 79.012& 0.0987337650& 63.64&\PS & 2781.35& 1.52\cr 5& -0.0015590& 335.669& 0.0889232251& 70.66&\PS-\TO & -2311.02& 2.38\cr 6& 0.0015341& 330.083& 0.0009171274& 6850.94&-\PH+\PT & 2274.02& 2.53\cr 7& 0.0011322& 182.356& 0.1085443050& 57.89&\PS+\TO & 1678.35& 1.72\cr 8& -0.0003899& 140.182& 0.0096969239& 647.96&\TO+\NH-\NO & -577.96& 3.88\cr 9& 0.0003851& 66.505& 0.0099241560& 633.12&\TO-\NH+\NO & 570.90& 3.83\cr 10& -0.0003603& 323.161& 0.0001136161& 55301.92&-\NH+\NO & -534.05& 3.23\cr 11& -0.0003109& 232.326& 0.0791126851& 79.42&\PS -2\TO & -460.84& 0.96\cr 12& -0.0003037& 310.029& 0.0294316199& 213.48& 3\TO & -450.16& 1.33\cr 13& -0.0001967& 192.682& 0.0000246364& 255037.01&-\NT+\NO & -291.58& 2.57\cr 14& 0.0001585& 206.686& 0.0196210799& 320.23& 2\TO & 234.91& 0.46\cr 15& 0.0001444& 48.131& 0.0082528098& 761.34&\TO+ 2\PH -2\NH & 214.01& 2.70\cr 16& -0.0001337& 285.699& 0.1183548449& 53.09&\PS+ 2\TO & -198.12& 0.41\cr 17& 0.0001354& 332.863& 0.0097215603& 646.31&\TO+\NH-\NT & 200.76& 2.25\cr 18& -0.0001344& 233.823& 0.0098995196& 634.70&\TO-\NH+\NT & -199.26& 2.23\cr 19& -0.0001248& 158.556& 0.0113682701& 552.69&\TO -2\PH+ 2\NH & -185.04& 2.33\cr 20& -0.0000934& 55.212& 0.0015577301& 4033.55& -2\PH+ 2\NH & -138.50& 1.71\cr 21& 0.0000856& 130.480& 0.0000889797& 70613.71&-\NH+\NT & 126.87& 1.33\cr 22& 0.0000722& 43.509& 0.0116447947& 539.57&\TO -2\PH+ 2\PT & 107.09& 0.25\cr 23& 0.0000530& 296.025& 0.0098351763& 638.85&\TO-\NT+\NO & 78.52& 0.77\cr 24& -0.0000525& 270.661& 0.0097859036& 642.06&\TO+\NT-\NO & -77.79& 0.76\cr 25& 0.0000419& 49.096& 0.0996508924& 63.05&\PS-\PH+\PT & 62.10& 0.04\cr 26& 0.0000410& 5.586& 0.0880060977& 71.39&\PS-\TO+\PH-\PT & 60.76& 0.11\cr 27& 0.0000376& 300.166& 0.0018342547& 3425.47& -2\PH+ 2\PT & 55.80& 0.08\cr 28& -0.0000353& 152.439& 0.1094614323& 57.40&\PS+\TO-\PH+\PT & -52.35& 0.09\cr 29& -0.0000295& 84.969& 0.0081391938& 771.97&\TO+ 2\PH-\NH-\NO & -43.70& 0.30\cr 30& 0.0000284& 212.272& 0.1076271776& 58.38&\PS+\TO+\PH-\PT & 42.11& 0.07\cr 31& 0.0000268& 128.983& 0.0693021452& 90.66&\PS -3\TO & 39.68& 0.12\cr 32& 0.0000247& 121.717& 0.0114818862& 547.23&\TO -2\PH+\NH+\NO & 36.54& 0.24\cr 33& 0.0000238& 18.374& 0.0016713462& 3759.36& -2\PH+\NH+\NO & 35.33& 0.22\cr 34& -0.0000236& 305.752& 0.0898403524& 69.94&\PS-\TO-\PH+\PT & -34.96& 0.07\cr 35& -0.0000231& 339.946& 0.0285144925& 220.35& 3\TO+\PH-\PT & -34.22& 0.12\cr 36& 0.0000217& 280.112& 0.0303487472& 207.03& 3\TO-\PH+\PT & 32.22& 0.11\cr 37& 0.0000164& 163.177& 0.0079762852& 787.73&\TO+ 2\PH -2\PT & 24.35& 0.11\cr 38& 0.0000155& 262.243& 0.0781955578& 80.35&\PS -2\TO+\PH-\PT & 23.03& 0.06\cr 39& -0.0000134& 202.409& 0.0800298125& 78.51&\PS -2\TO-\PH+\PT & -19.83& 0.05\cr 40& -0.0000113& 36.588& 0.0108412834& 579.56&\TO-\PH+\PT-\NH+\NO & -16.79& 0.13\cr 41& 0.0000109& 110.265& 0.0106140513& 591.97&\TO-\PH+\PT+\NH-\NO & 16.14& 0.12\cr 42& -0.0000100& 29.042& 0.1281653849& 49.02&\PS+ 3\TO & -14.84& 0.05\cr 43& 0.0000088& 25.640& 0.0594916052& 105.61&\PS -4\TO & 13.04& 0.05\cr 44& 0.0000082& 277.651& 0.0081638301& 769.64&\TO+ 2\PH-\NH-\NT & 12.16& 0.15\cr 45& 0.0000077& 96.421& 0.0090070287& 697.59&\TO+\PH-\PT-\NH+\NO & 11.45& 0.09\cr 46& -0.0000072& 170.098& 0.0087797965& 715.64&\TO+\PH-\PT+\NH-\NO & -10.70& 0.08\cr 47& -0.0000070& 188.472& 0.0104511427& 601.20&\TO-\PH-\PT+ 2\NH & -10.35& 0.13\cr 48& -0.0000069& 289.035& 0.0114572498& 548.40&\TO -2\PH+\NH+\NT & -10.20& 0.12\cr 49& 0.0000067& 255.782& 0.1192719723& 52.68&\PS+ 2\TO-\PH+\PT & 9.86& 0.02\cr 50& -0.0000063& 315.616& 0.1174377176& 53.50&\PS+ 2\TO+\PH-\PT & -9.33& 0.02\cr 51& 0.0000061& 108.929& 0.0978166377& 64.23&\PS+\PH-\PT & 9.06& 0.02\cr 52& 0.0000060& 85.129& 0.0006406028& 9808.24&-\PH-\PT+ 2\NH & 8.92& 0.11\cr 53& 0.0000054& 128.639& 0.0122853975& 511.44&\TO -3\PH+\PT+ 2\NH & 8.07& 0.10\cr 54& -0.0000056& 185.692& 0.0016467098& 3815.60& -2\PH+\NH+\NT & -8.24& 0.09\cr 55& -0.0000040& 151.474& 0.0180633498& 347.84& 2\TO+ 2\PH -2\NH & -5.87& 0.08\cr 56& 0.0000039& 203.906& 0.0108166470& 580.88&\TO-\PH+\PT-\NH+\NT & 5.84& 0.07\cr 57& -0.0000038& 302.946& 0.0106386876& 590.60&\TO-\PH+\PT+\NH-\NT & -5.60& 0.07\cr 58& -0.0000036& 12.508& 0.0888096090& 70.75&\PS-\TO+\NH-\NO & -5.36& 0.04\cr 59& 0.0000035& 298.831& 0.0890368411& 70.57&\PS-\TO-\NH+\NO & 5.20& 0.04\cr 60& 0.0000030& 145.517& 0.1086579210& 57.83&\PS+\TO-\NH+\NO & 4.39& 0.03\cr 61& -0.0000029& 219.194& 0.1084306889& 57.95&\PS+\TO+\NH-\NO & -4.26& 0.03\cr 62& -0.0000027& 263.740& 0.0089823923& 699.50&\TO+\PH-\PT-\NH+\NT & -3.98& 0.05\cr 63& 0.0000025& 2.780& 0.0088044329& 713.64&\TO+\PH-\PT+\NH-\NT & 3.75& 0.05\cr 64& -0.0000022& 273.191& 0.0295452359& 212.66& 3\TO-\NH+\NO & -3.30& 0.03\cr 65& 0.0000022& 346.868& 0.0293180038& 214.31& 3\TO+\NH-\NO & 3.27& 0.03\cr 66& 0.0000021& 156.715& 0.0490526998& 128.09& 5\TO & 3.09& 0.02\cr 67& -0.0000021& 158.900& 0.0683850178& 91.88&\PS -3\TO+\PH-\PT & -3.08& 0.01\cr 68& 0.0000021& 25.296& 0.0024748575& 2538.81& -3\PH+\PT+ 2\NH & 3.04& 0.04\cr 69& 0.0000019& 99.066& 0.0702192725& 89.48&\PS -3\TO-\PH+\PT & 2.86& 0.01\cr 70& 0.0000019& 266.520& 0.0177868252& 353.25& 2\TO+ 2\PH -2\PT & 2.77& 0.01\cr 71& 0.0000018& 280.457& 0.0873654949& 71.92&\PS-\TO+ 2\PH -2\NH & 2.66& 0.03\cr 72& 0.0000017& 132.385& 0.1379759248& 45.54&\PS+ 4\TO & 2.56& 0.01\cr 73& 0.0000017& 261.899& 0.0211788101& 296.67& 2\TO -2\PH+ 2\NH & 2.49& 0.03\cr 74& 0.0000015& 121.808& 0.0080255777& 782.90&\TO+ 2\PH -2\NO & 2.28& 0.00\cr 75& -0.0000015& 269.165& 0.0789990691& 79.53&\PS -2\TO+\NH-\NO & -2.26& 0.02\cr 76& -0.0000015& 341.535& 0.0017849622& 3520.07& -2\PH+ 2\NO & -2.22& 0.00\cr 77& -0.0000015& 266.108& 0.0107523037& 584.36&\TO-\PH+\PT-\NT+\NO & -2.26& 0.03\cr 78& 0.0000015& 195.488& 0.0792263012& 79.31&\PS -2\TO-\NH+\NO & 2.19& 0.02\cr 79& 0.0000015& 151.634& 0.0105647588& 594.73&\TO-\PH-\PT+\NH+\NO & 2.15& 0.02\cr 80& 0.0000015& 240.745& 0.0107030309& 587.05&\TO-\PH+\PT+\NT-\NO & 2.20& 0.02\cr 81& -0.0000012& 84.879& 0.0115955022& 541.86&\TO -2\PH+ 2\NO & -1.84& 0.00\cr 82& -0.0000012& 13.592& 0.0125619220& 500.18&\TO -3\PH+ 3\PT & -1.81& 0.00\cr 83& 0.0000012& 205.190& 0.0888342454& 70.73&\PS-\TO+\NH-\NT & 1.84& 0.02\cr 84& -0.0000012& 106.149& 0.0890122048& 70.59&\PS-\TO-\NH+\NT & -1.81& 0.02\cr 85& -0.0000012& 146.852& 0.0214553346& 292.85& 2\TO -2\PH+ 2\PT & -1.76& 0.01\cr 86& -0.0000012& 237.568& 0.1101020351& 57.07&\PS+\TO -2\PH+ 2\NH & -1.78& 0.02\cr 87& -0.0000011& 35.503& 0.0870889704& 72.15&\PS-\TO+ 2\PH -2\PT & -1.67& 0.00\cr 88& -0.0000011& 91.800& 0.0123990135& 506.75&\TO -3\PH+\PT+\NH+\NO & -1.63& 0.01\cr 89& 0.0000010& 325.942& 0.0089180490& 704.55&\TO+\PH-\PT-\NT+\NO & 1.52& 0.02\cr 90& -0.0000010& 312.835& 0.1086332847& 57.84&\PS+\TO-\NH+\NT & -1.51& 0.02\cr 91& -0.0000010& 300.578& 0.0088687762& 708.46&\TO+\PH-\PT+\NT-\NO & -1.50& 0.02\cr 92& 0.0000010& 51.876& 0.1084553253& 57.93&\PS+\TO+\NH-\NT & 1.48& 0.02\cr 93& -0.0000011& 282.297& 0.0496810653& 126.47&\PS -5\TO & -1.57& 0.02\cr 94& 0.0000009& 188.312& 0.0179497337& 350.04& 2\TO+ 2\PH-\NH-\NO & 1.40& 0.01\cr 95& -0.0000009& 250.195& 0.0312658746& 200.96& 3\TO -2\PH+ 2\PT & -1.37& 0.01\cr 96& -0.0000009& 55.557& 0.0585744779& 107.27&\PS -4\TO+\PH-\PT & -1.32& 0.01\cr 97& -0.0000009& 254.817& 0.0278738897& 225.41& 3\TO+ 2\PH -2\NH & -1.27& 0.02\cr 98& 0.0000008& 169.848& 0.0197346960& 318.38& 2\TO-\NH+\NO & 1.25& 0.01\cr 99& -0.0000009& 314.489& 0.0080502141& 780.50&\TO+ 2\PH-\NT-\NO & -1.27& 0.01\cr 100& -0.0000008& 30.882& 0.0904809552& 69.44&\PS-\TO -2\PH+ 2\NH & -1.22& 0.02\cr 101& 0.0000008& 18.214& 0.0091699372& 685.19&\TO+\PH+\PT -2\NH & 1.19& 0.02\cr 102& -0.0000008& 58.959& 0.1272482575& 49.38&\PS+ 3\TO+\PH-\PT & -1.16& 0.00\cr 103& 0.0000008& 355.723& 0.0604087326& 104.01&\PS -4\TO-\PH+\PT & 1.17& 0.00\cr 104& 0.0000008& 5.242& 0.0309893500& 202.75& 3\TO -2\PH+ 2\NH & 1.18& 0.02\cr 105& 0.0000008& 122.522& 0.1103785597& 56.92&\PS+\TO -2\PH+ 2\PT & 1.13& 0.00\cr 106& 0.0000008& 127.143& 0.1069865748& 58.73&\PS+\TO+ 2\PH -2\NH & 1.12& 0.01\cr 107& 0.0000008& 80.509& 0.0295205995& 212.84& 3\TO-\NH+\NT & 1.15& 0.01\cr 108& -0.0000008& 179.549& 0.0293426402& 214.13& 3\TO+\NH-\NT & -1.13& 0.01\cr 109& -0.0000007& 243.525& 0.0195074639& 322.09& 2\TO+\NH-\NO & -1.08& 0.01\cr 110& 0.0000007& 48.291& 0.0007542188& 8330.72&-\PH-\PT+\NH+\NO & 1.04& 0.01\cr 111& -0.0000007& 248.860& 0.1184684610& 53.04&\PS+ 2\TO-\NH+\NO & -1.02& 0.01\crs 112& 0.0024777& 158.025& 0.1974675301& 31.82& 2\PS & 3672.78& 0.85\cr 113& 0.0011774& 237.037& 0.2962012951& 21.21& 3\PS & 1745.35& 0.43\cr 114& 0.0007098& 316.050& 0.3949350601& 15.91& 4\PS & 1052.09& 0.23\cr 115& 0.0004277& 35.062& 0.4936688251& 12.73& 5\PS & 633.97& 0.17\cr 116& 0.0002883& 114.074& 0.5924025902& 10.61& 6\PS & 427.37& 0.12\cr 117& 0.0002445& 54.682& 0.1876569901& 33.48& 2\PS-\TO & 362.46& 0.40\cr 118& 0.0002080& 133.694& 0.2863907551& 21.94& 3\PS-\TO & 308.27& 0.35\cr 119& 0.0001998& 193.087& 0.6911363552& 9.09& 7\PS & 296.12& 0.10\cr 120& 0.0001532& 212.707& 0.3851245202& 16.31& 4\PS-\TO & 227.10& 0.26\cr 121& 0.0001392& 272.099& 0.7898701202& 7.95& 8\PS & 206.31& 0.08\cr 122& -0.0001347& 340.380& 0.3060118350& 20.53& 3\PS+\TO & -199.68& 0.23\cr 123& -0.0001169& 261.368& 0.2072780700& 30.31& 2\PS+\TO & -173.23& 0.18\cr 124& 0.0001158& 291.719& 0.4838582852& 12.99& 5\PS-\TO & 171.71& 0.19\cr 125& -0.0001110& 59.393& 0.4047456001& 15.52& 4\PS+\TO & -164.57& 0.19\cr 126& 0.0000988& 351.112& 0.8886038852& 7.07& 9\PS & 146.40& 0.06\cr 127& 0.0000936& 10.731& 0.5825920502& 10.78& 6\PS-\TO & 138.76& 0.15\cr 128& -0.0000879& 138.405& 0.5034793651& 12.48& 5\PS+\TO & -130.26& 0.15\cr 129& 0.0000763& 89.744& 0.6813258152& 9.22& 7\PS-\TO & 113.05& 0.12\cr 130& -0.0000742& 217.418& 0.6022131301& 10.43& 6\PS+\TO & -110.04& 0.12\cr 131& 0.0000707& 70.124& 0.9873376503& 6.36& 10\PS & 104.78& 0.05\cr 132& -0.0000695& 187.942& 0.1965504027& 31.97& 2\PS+\PH-\PT & -102.98& 0.06\cr 133& -0.0000651& 311.339& 0.1778464501& 35.33& 2\PS -2\TO & -96.57& 0.20\cr 134& -0.0000625& 296.430& 0.7009468951& 8.96& 7\PS+\TO & -92.58& 0.10\cr 135& 0.0000624& 168.756& 0.7800595803& 8.05& 8\PS-\TO & 92.44& 0.09\cr 136& -0.0000521& 15.442& 0.7996806602& 7.86& 8\PS+\TO & -77.26& 0.08\cr 137& 0.0000509& 149.137& 1.0860714153& 5.79& 11\PS & 75.41& 0.04\cr 138& 0.0000506& 247.769& 0.8787933453& 7.15& 9\PS-\TO & 74.99& 0.07\cr 139& -0.0000481& 4.711& 0.2170886100& 28.94& 2\PS+ 2\TO & -71.35& 0.15\cr 140& -0.0000430& 94.455& 0.8984144252& 6.99& 9\PS+\TO & -63.76& 0.06\cr 141& 0.0000410& 326.781& 0.9775271103& 6.43& 10\PS-\TO & 60.84& 0.06\cr 142& 0.0000367& 228.149& 1.1848051803& 5.30& 12\PS & 54.33& 0.04\cr 143& -0.0000354& 173.467& 0.9971481902& 6.30& 10\PS+\TO & -52.45& 0.05\cr 144& 0.0000333& 45.793& 1.0762608753& 5.84& 11\PS-\TO & 49.31& 0.04\cr 145& -0.0000290& 252.480& 1.0958819553& 5.73& 11\PS+\TO & -43.02& 0.04\cr 146& 0.0000269& 124.806& 1.1749946404& 5.35& 12\PS-\TO & 39.93& 0.03\cr 147& 0.0000267& 345.967& 0.3940179328& 15.95& 4\PS+\PH-\PT & 39.56& 0.02\cr 148& 0.0000264& 307.161& 1.2835389454& 4.90& 13\PS & 39.14& 0.04\cr 149& -0.0000237& 331.492& 1.1946157203& 5.26& 12\PS+\TO & -35.19& 0.03\cr 150& 0.0000218& 203.818& 1.2737284054& 4.93& 13\PS-\TO & 32.26& 0.03\cr 151& -0.0000193& 50.505& 1.2933494853& 4.86& 13\PS+\TO & -28.68& 0.02\cr 152& 0.0000190& 26.174& 1.3822727104& 4.55& 14\PS & 28.13& 0.03\cr 153& 0.0000175& 282.831& 1.3724621704& 4.58& 14\PS-\TO & 26.01& 0.02\cr 154& 0.0000157& 128.108& 0.1983846574& 31.67& 2\PS-\PH+\PT & 23.31& 0.02\cr 155& -0.0000157& 129.517& 1.3920832503& 4.51& 14\PS+\TO & -23.30& 0.02\cr 156& -0.0000154& 83.723& 0.3158223750& 19.89& 3\PS+ 2\TO & -22.83& 0.05\cr 157& 0.0000141& 1.843& 1.4711959355& 4.27& 15\PS-\TO & 20.91& 0.01\cr 158& 0.0000136& 105.186& 1.4810064754& 4.24& 15\PS & 20.12& 0.03\cr 159& -0.0000127& 208.529& 1.4908170154& 4.21& 15\PS+\TO & -18.88& 0.01\cr 160& 0.0000116& 346.401& 0.6715152753& 9.36& 7\PS -2\TO & 17.25& 0.04\cr 161& 0.0000114& 267.388& 0.5727815103& 10.97& 6\PS -2\TO & 16.89& 0.04\cr 162& 0.0000114& 65.413& 0.7702490403& 8.16& 8\PS -2\TO & 16.89& 0.04\cr 163& 0.0000114& 266.954& 0.2952841677& 21.28& 3\PS+\PH-\PT & 16.83& 0.01\cr 164& 0.0000113& 80.856& 1.5699297005& 4.00& 16\PS-\TO & 16.77& 0.01\cr 165& 0.0000109& 144.426& 0.8689828053& 7.23& 9\PS -2\TO & 16.09& 0.03\cr 166& -0.0000106& 30.351& 0.2765802152& 22.72& 3\PS -2\TO & -15.67& 0.03\cr 167& 0.0000104& 188.376& 0.4740477452& 13.25& 5\PS -2\TO & 15.37& 0.04\cr 168& -0.0000103& 287.542& 1.5895507804& 3.95& 16\PS+\TO & -15.23& 0.01\cr 169& 0.0000103& 24.765& 0.1885741175& 33.32& 2\PS-\TO-\PH+\PT & 15.23& 0.03\cr 170& 0.0000101& 223.438& 0.9677165704& 6.49& 10\PS -2\TO & 14.92& 0.03\cr 171& 0.0000096& 184.199& 1.5797402404& 3.98& 16\PS & 14.28& 0.02\cr 172& 0.0000092& 302.450& 1.0664503354& 5.89& 11\PS -2\TO & 13.60& 0.03\cr 173& 0.0000091& 159.868& 1.6686634655& 3.77& 17\PS-\TO & 13.44& 0.01\cr 174& 0.0000089& 207.120& 0.2971184224& 21.15& 3\PS-\PH+\PT & 13.12& 0.01\cr 175& 0.0000083& 21.463& 1.1651841004& 5.39& 12\PS -2\TO & 12.23& 0.03\cr 176& -0.0000083& 6.554& 1.6882845454& 3.72& 17\PS+\TO & -12.24& 0.01\cr 177& 0.0000079& 103.777& 0.2873078825& 21.87& 3\PS-\TO-\PH+\PT & 11.72& 0.02\cr 178& -0.0000079& 291.285& 0.2063609427& 30.45& 2\PS+\TO+\PH-\PT & -11.64& 0.02\cr 179& 0.0000073& 100.475& 1.2639178654& 4.97& 13\PS -2\TO & 10.88& 0.02\cr 180& 0.0000072& 238.880& 1.7673972305& 3.56& 18\PS-\TO & 10.72& 0.01\cr 181& 0.0000068& 263.211& 1.6784740055& 3.74& 17\PS & 10.03& 0.02\cr 182& -0.0000066& 85.567& 1.7870183104& 3.52& 18\PS+\TO & -9.81& 0.00\cr 183& 0.0000065& 197.798& 0.9082249652& 6.92& 9\PS+ 2\TO & 9.70& 0.02\cr 184& 0.0000065& 179.488& 1.3626516305& 4.61& 14\PS -2\TO & 9.59& 0.02\cr 185& 0.0000064& 276.810& 1.0069587302& 6.24& 10\PS+ 2\TO & 9.53& 0.02\cr 186& 0.0000063& 118.786& 0.8094912001& 7.76& 8\PS+ 2\TO & 9.38& 0.02\cr 187& -0.0000063& 163.611& 0.2854736278& 22.01& 3\PS-\TO+\PH-\PT & -9.40& 0.02\cr 188& 0.0000061& 355.823& 1.1056924952& 5.68& 11\PS+ 2\TO & 9.08& 0.02\cr 189& 0.0000057& 317.893& 1.8661309956& 3.37& 19\PS-\TO & 8.52& 0.00\cr 190& 0.0000057& 74.835& 1.2044262602& 5.22& 12\PS+ 2\TO & 8.46& 0.02\cr 191& 0.0000058& 182.790& 0.3860416475& 16.28& 4\PS-\TO-\PH+\PT & 8.53& 0.02\cr 192& 0.0000056& 39.773& 0.7107574351& 8.84& 7\PS+ 2\TO & 8.37& 0.02\cr 193& 0.0000056& 258.500& 1.4613853955& 4.30& 15\PS -2\TO & 8.37& 0.02\cr 194& 0.0000054& 109.363& 0.3753139802& 16.74& 4\PS -2\TO & 8.05& 0.02\cr 195& 0.0000054& 286.133& 0.3958521875& 15.87& 4\PS-\PH+\PT & 7.93& 0.01\cr 196& 0.0000053& 64.979& 0.4927516978& 12.75& 5\PS+\PH-\PT & 7.78& 0.01\cr 197& -0.0000053& 164.579& 1.8857520755& 3.33& 19\PS+\TO & -7.82& 0.00\cr 198& 0.0000052& 153.848& 1.3031600253& 4.82& 13\PS+ 2\TO & 7.75& 0.02\cr 199& 0.0000049& 337.512& 1.5601191605& 4.03& 16\PS -2\TO & 7.25& 0.02\cr 200& 0.0000047& 232.860& 1.4018937903& 4.48& 14\PS+ 2\TO & 7.00& 0.01\cr 201& 0.0000047& 342.223& 1.7772077705& 3.54& 18\PS & 6.96& 0.02\cr 202& 0.0000046& 36.905& 1.9648647606& 3.20& 20\PS-\TO & 6.76& 0.00\cr 203& -0.0000044& 287.008& 0.2667696752& 23.55& 3\PS -3\TO & -6.55& 0.02\cr 204& 0.0000043& 320.761& 0.6120236701& 10.27& 6\PS+ 2\TO & 6.43& 0.01\cr 205& -0.0000044& 207.996& 0.1680359102& 37.39& 2\PS -3\TO & -6.49& 0.02\cr 206& 0.0000043& 56.525& 1.6588529256& 3.79& 17\PS -2\TO & 6.32& 0.01\cr 207& 0.0000043& 261.802& 0.4847754125& 12.96& 5\PS-\TO-\PH+\PT & 6.36& 0.01\cr 208& 0.0000042& 311.872& 1.5006275553& 4.19& 15\PS+ 2\TO & 6.26& 0.01\cr 209& -0.0000042& 243.591& 1.9844858405& 3.17& 20\PS+\TO & -6.22& 0.00\cr 210& 0.0000037& 30.885& 1.5993613203& 3.93& 16\PS+ 2\TO & 5.53& 0.01\cr 211& 0.0000036& 115.918& 2.0635985256& 3.04& 21\PS-\TO & 5.39& 0.01\cr 212& 0.0000034& 5.145& 0.4945859525& 12.70& 5\PS-\PH+\PT & 5.05& 0.00\cr 213& -0.0000035& 242.623& 0.3842073928& 16.35& 4\PS-\TO+\PH-\PT & -5.19& 0.01\cr 214& 0.0000035& 340.815& 0.5835091776& 10.77& 6\PS-\TO-\PH+\PT & 5.12& 0.01\cr \noalign{\medskip\hrule} } % series z : \bigskip \noindent{\bf Table 6.} Series for $z_7= e_7\,\exp\sqi\varpi_7$ : Each term is in the form $\alpha\exp\sqi(\omega t+\varphi)$ with $t=(\hbox{Julian Date)}-2\,451\,545.0$. Each argument is also identified as an integer combination of the seven fundamental arguments given in Table 3; $\omega $ and $\varphi$ are in fact computed from these combinations. The amplitudes in km represent $A_7z_7$ with $A_7= 1482333.4$~km. \medskip \halign{ $#$\hfil&\qhfil$#$&\qhfil$#$&\qhfil$#$&\qhfil$#$& \quad\quad$#$\hfil &\qhfil$#$&\qhfil$#$\cr \noalign{\hrule\medskip} \hbox{n\Deg} &\hfill\hbox{amplitude $\alpha $}\hfill &\hfill\hbox{phase $\varphi$}\hfill &\hfill\hbox{frequency $\omega $}\hfill &\hfill\hbox{period}\hfill &\hfill\hbox{argument}\hfill &\hfill\hbox{amplitude}\hfill &\hfill\hbox{$\varepsilon(\alpha)$}\hfill \cr &\hfill\hbox{(rad)}\hfill &\hfill\hbox{(deg)}\hfill &\hfill\hbox{(rad/d)}\hfill &\hfill\hbox{(d)}\hfill & &\hfill\hbox{(km)}\hfill &\hfill\hbox{(km)}\hfill \cr \noalign{\medskip\hrule\medskip} 1& 0.1030661& 193.814& -0.0008924811& 7040.13&\PH & 152778.39& 46.77\cr 2& 0.0244818& 163.897& 0.0000246462& 254934.93&\PT & 36290.25& 20.63\cr 3& -0.0025006& 297.157& 0.0089180588& 704.55&\TO+\PH & -3706.74& 4.04\cr 4& -0.0016531& 90.471& -0.0107030211& 587.05&-\TO+\PH & -2450.48& 2.65\cr 5& -0.0011220& 272.826& 0.0978412839& 64.22&\PS+\PH & -1663.13& 0.38\cr 6& 0.0007518& 114.802& -0.0996262462& 63.07&-\PS+\PH & 1114.43& 0.39\cr 7& 0.0002580& 218.145& -0.0898157062& 69.96&-\PS+\TO+\PH & 382.46& 0.43\cr 8& -0.0001702& 11.458& -0.1094367861& 57.41&-\PS-\TO+\PH & -252.33& 0.28\cr 9& -0.0001630& 16.169& 0.1076518239& 58.37&\PS+\TO+\PH & -241.69& 0.27\cr 10& 0.0001502& 169.483& 0.0880307439& 71.37&\PS-\TO+\PH & 222.66& 0.25\cr 11& 0.0001081& 267.240& 0.0098351862& 638.85&\TO+\PT & 160.20& 0.25\cr 12& 0.0000856& 223.731& -0.0018096085& 3472.12& 2\PH-\PT & 126.94& 0.18\cr 13& -0.0000764& 327.074& 0.0080009315& 785.31&\TO+ 2\PH-\PT & -113.28& 0.18\cr 14& 0.0000641& 230.652& -0.0010060972& 6245.11&\PH+\NH-\NO & 95.02& 0.56\cr 15& -0.0000638& 156.975& -0.0007788651& 8067.10&\PH-\NH+\NO & -94.57& 0.56\cr 16& -0.0000374& 40.500& 0.0187285988& 335.49& 2\TO+\PH & -55.42& 0.13\cr 17& 0.0000318& 242.909& 0.0987584113& 63.62&\PS+\PT & 47.10& 0.03\cr 18& 0.0000307& 120.388& -0.0116201484& 540.71&-\TO+ 2\PH-\PT & 45.48& 0.08\cr 19& 0.0000273& 249.026& 0.0006652490& 9444.86&-\PH+ 2\NH & 40.51& 0.48\cr 20& 0.0000256& 321.488& -0.0800051662& 78.53&-\PS+ 2\TO+\PH & 37.94& 0.09\cr 21& 0.0000202& 66.140& 0.0782202040& 80.33&\PS -2\TO+\PH & 30.01& 0.06\cr 22& -0.0000202& 63.334& -0.0009814608& 6401.87&\PH+\NH-\NT & -29.93& 0.31\cr 23& 0.0000201& 324.294& -0.0008035014& 7819.76&\PH-\NH+\NT & 29.77& 0.31\cr 24& -0.0000181& 347.128& -0.0205135610& 306.29& -2\TO+\PH & -26.85& 0.05\cr 25& 0.0000124& 60.554& -0.0097858937& 642.07&-\TO+\PT & 18.32& 0.03\cr 26& 0.0000117& 143.843& 0.0285391387& 220.16& 3\TO+\PH & 17.29& 0.05\cr 27& 0.0000109& 243.785& -0.0303241010& 207.20& -3\TO+\PH & 16.11& 0.05\cr 28& -0.0000104& 188.228& -0.0888985788& 70.68&-\PS+\TO+\PT & -15.46& 0.02\cr 29& 0.0000082& 1.132& -0.0009171175& 6851.01&\PH+\NT-\NO & 12.22& 0.11\cr 30& -0.0000082& 26.496& -0.0008678448& 7239.99&\PH-\NT+\NO & -12.16& 0.11\cr 31& 0.0000080& 84.885& -0.0987091188& 63.65&-\PS+\PT & 11.86& 0.01\cr 32& 0.0000080& 119.513& 0.1174623638& 53.49&\PS+ 2\TO+\PH & 11.81& 0.02\cr 33& 0.0000072& 346.253& 0.1085689512& 57.87&\PS+\TO+\PT & 10.73& 0.02\cr 34& 0.0000073& 138.601& -0.0024502113& 2564.34& 3\PH -2\NH & 10.78& 0.13\cr 35& 0.0000067& 248.061& -0.0907328336& 69.25&-\PS+\TO+ 2\PH-\PT & 9.96& 0.02\cr 36& 0.0000067& 278.943& -0.0002518783& 24945.32&-\PT+ 2\NH & 9.99& 0.12\cr 37& 0.0000052& 268.115& -0.1192473261& 52.69&-\PS -2\TO+\PH & 7.71& 0.02\cr 38& -0.0000052& 212.188& 0.0007788651& 8067.10&-\PH+\NH+\NO & -7.72& 0.05\cr 39& 0.0000050& 53.632& -0.0105894050& 593.35&-\TO+\PH-\NH+\NO & 7.48& 0.05\cr 40& -0.0000050& 127.309& -0.0108166371& 580.88&-\TO+\PH+\NH-\NO & -7.46& 0.05\cr 41& -0.0000048& 46.086& 0.1067346965& 58.87&\PS+\TO+ 2\PH-\PT & -7.17& 0.01\cr 42& -0.0000046& 260.319& 0.0090316749& 695.68&\TO+\PH-\NH+\NO & -6.84& 0.05\cr 43& 0.0000044& 333.996& 0.0088044428& 713.64&\TO+\PH+\NH-\NO & 6.59& 0.04\cr 44& -0.0000042& 241.945& 0.0073603287& 853.66&\TO+ 3\PH -2\NH & -6.16& 0.08\cr 45& -0.0000039& 322.797& 0.0684096640& 91.85&\PS -3\TO+\PH & -5.75& 0.02\cr 46& 0.0000036& 41.375& -0.1103539135& 56.94&-\PS-\TO+ 2\PH-\PT & 5.35& 0.01\cr 47& -0.0000031& 64.831& -0.0701946263& 89.51&-\PS+ 3\TO+\PH & -4.61& 0.01\cr 48& -0.0000027& 199.400& 0.0871136166& 72.13&\PS-\TO+ 2\PH-\PT & -3.98& 0.01\cr 49& 0.0000025& 222.856& 0.1272729038& 49.37&\PS+ 3\TO+\PH & 3.77& 0.01\cr 50& -0.0000025& 302.743& 0.0969241565& 64.83&\PS+ 2\PH-\PT & -3.75& 0.00\cr 51& 0.0000025& 10.583& 0.0196457261& 319.82& 2\TO+\PT & 3.66& 0.01\cr 52& -0.0000024& 70.417& 0.0178114714& 352.76& 2\TO+ 2\PH-\PT & -3.55& 0.01\cr 53& 0.0000023& 164.772& -0.1290578660& 48.69&-\PS -3\TO+\PH & 3.44& 0.01\cr 54& -0.0000023& 237.323& 0.0107523135& 584.36&\TO-\PH+ 2\PT & -3.34& 0.01\cr 55& -0.0000020& 291.571& -0.0790880389& 79.45&-\PS+ 2\TO+\PT & -3.02& 0.01\cr 56& 0.0000020& 352.369& 0.0104757890& 599.78&\TO-\PH+ 2\NH & 2.93& 0.04\cr 57& -0.0000018& 175.440& -0.0025638273& 2450.71& 3\PH-\NH-\NO & -2.69& 0.02\cr 58& -0.0000018& 253.648& -0.0027267358& 2304.29& 3\PH -2\PT & -2.61& 0.00\cr 59& 0.0000017& 319.991& -0.0107920008& 582.21&-\TO+\PH+\NH-\NT & 2.53& 0.03\cr 60& -0.0000017& 220.951& -0.0106140414& 591.97&-\TO+\PH-\NH+\NT & -2.53& 0.03\cr 61& 0.0000016& 67.637& 0.0090070385& 697.59&\TO+\PH-\NH+\NT & 2.43& 0.03\cr 62& -0.0000015& 317.211& -0.0195964337& 320.63& -2\TO+\PT & -2.30& 0.01\cr 63& -0.0000016& 166.677& 0.0088290791& 711.65&\TO+\PH+\NH-\NT & -2.36& 0.03\cr 64& 0.0000015& 19.506& 0.0007542287& 8330.61&-\PH+\NH+\NT & 2.23& 0.02\cr 65& 0.0000014& 200.736& -0.0000889698& 70621.54&\PT+\NH-\NO & 2.06& 0.01\cr 66& -0.0000013& 145.683& -0.0091452909& 687.04&-\TO-\PH+ 2\NH & -1.98& 0.03\cr 67& 0.0000013& 351.405& -0.0809222936& 77.64&-\PS+ 2\TO+ 2\PH-\PT & 1.90& 0.01\cr 68& 0.0000013& 30.637& -0.0088687664& 708.46&-\TO-\PH+ 2\PT & 1.89& 0.00\cr 69& -0.0000011& 113.926& 0.0294562661& 213.31& 3\TO+\PT & -1.60& 0.01\cr 70& -0.0000011& 96.057& 0.0773030766& 81.28&\PS -2\TO+ 2\PH-\PT & -1.61& 0.00\cr 71& 0.0000011& 17.045& -0.0214306884& 293.19& -2\TO+ 2\PH-\PT & 1.59& 0.00\cr 72& -0.0000011& 242.105& -0.0001382623& 45443.96&-\PT+\NH+\NO & -1.57& 0.01\cr 73& -0.0000011& 108.685& -0.0015330839& 4098.40& 2\PH+\PT -2\NH & -1.56& 0.02\cr 74& 0.0000010& 144.718& -0.1005433735& 62.49&-\PS+ 2\PH-\PT & 1.51& 0.00\cr 75& 0.0000009& 278.783& 0.0072467126& 867.04&\TO+ 3\PH-\NH-\NO & 1.37& 0.01\cr 76& 0.0000009& 173.760& 0.0276220114& 227.47& 3\TO+ 2\PH-\PT & 1.26& 0.00\cr 77& -0.0000008& 273.702& -0.0312412283& 201.12& -3\TO+ 2\PH-\PT & -1.11& 0.00\cr 78& -0.0000007& 168.174& -0.0603840863& 104.05&-\PS+ 4\TO+\PH & -1.10& 0.01\cr 79& -0.0000007& 139.566& 0.0889478713& 70.64&\PS-\TO+\PT & -1.02& 0.00\crs 80& 0.0003778& 35.789& -0.1983600112& 31.68& -2\PS+\PH & 560.07& 0.17\cr 81& -0.0003775& 351.839& 0.1965750489& 31.96& 2\PS+\PH & -559.65& 0.16\cr 82& -0.0003598& 149.864& 0.3940425790& 15.95& 4\PS+\PH & -533.32& 0.05\cr 83& -0.0002928& 70.851& 0.2953088140& 21.28& 3\PS+\PH & -434.02& 0.09\cr 84& 0.0002217& 316.777& -0.2970937762& 21.15& -3\PS+\PH & 328.61& 0.10\cr 85& 0.0001404& 237.764& -0.3958275412& 15.87& -4\PS+\PH & 208.10& 0.08\cr 86& 0.0001283& 139.132& -0.1885494712& 33.32& -2\PS+\TO+\PH & 190.14& 0.21\cr 87& -0.0000984& 292.446& -0.2081705511& 30.18& -2\PS-\TO+\PH & -145.91& 0.16\cr 88& 0.0000930& 158.752& -0.4945613063& 12.70& -5\PS+\PH & 137.90& 0.06\cr 89& 0.0000861& 60.120& -0.2872832363& 21.87& -3\PS+\TO+\PH & 127.61& 0.13\cr 90& -0.0000698& 213.434& -0.3069043162& 20.47& -3\PS-\TO+\PH & -103.41& 0.11\cr 91& 0.0000639& 341.107& -0.3860170013& 16.28& -4\PS+\TO+\PH & 94.78& 0.10\cr 92& 0.0000639& 79.739& -0.5932950713& 10.59& -6\PS+\PH & 94.68& 0.05\cr 93& -0.0000534& 134.421& -0.4056380812& 15.49& -4\PS-\TO+\PH & -79.14& 0.08\cr 94& 0.0000491& 262.095& -0.4847507663& 12.96& -5\PS+\TO+\PH & 72.76& 0.07\cr 95& 0.0000481& 228.876& 0.4927763440& 12.75& 5\PS+\PH & 71.32& 0.02\cr 96& 0.0000449& 0.727& -0.6920288363& 9.08& -7\PS+\PH & 66.51& 0.04\cr 97& -0.0000418& 55.409& -0.5043718462& 12.46& -5\PS-\TO+\PH & -61.93& 0.06\cr 98& -0.0000388& 46.520& 0.3842320390& 16.35& 4\PS-\TO+\PH & -57.52& 0.06\cr 99& 0.0000382& 183.083& -0.5834845313& 10.77& -6\PS+\TO+\PH & 56.61& 0.05\cr 100& -0.0000355& 327.508& 0.2854982740& 22.01& 3\PS-\TO+\PH & -52.68& 0.05\cr 101& 0.0000342& 307.888& 0.5915101090& 10.62& 6\PS+\PH & 50.63& 0.01\cr 102& 0.0000334& 253.207& 0.4038531189& 15.56& 4\PS+\TO+\PH & 49.51& 0.05\cr 103& -0.0000330& 336.396& -0.6031056112& 10.42& -6\PS-\TO+\PH & -48.93& 0.05\cr 104& 0.0000318& 281.715& -0.7907626013& 7.95& -8\PS+\PH & 47.15& 0.04\cr 105& 0.0000300& 104.070& -0.6822182964& 9.21& -7\PS+\TO+\PH & 44.52& 0.04\cr 106& 0.0000273& 5.872& -0.1974428838& 31.82& -2\PS+\PT & 40.46& 0.02\cr 107& -0.0000263& 257.384& -0.7018393763& 8.95& -7\PS-\TO+\PH & -38.98& 0.03\cr 108& 0.0000247& 174.194& 0.3051193539& 20.59& 3\PS+\TO+\PH & 36.67& 0.04\cr 109& -0.0000242& 248.496& 0.1867645090& 33.64& 2\PS-\TO+\PH & -35.83& 0.03\cr 110& 0.0000238& 25.058& -0.7809520614& 8.05& -8\PS+\TO+\PH & 35.34& 0.03\cr 111& 0.0000226& 202.702& -0.8894963664& 7.06& -9\PS+\PH & 33.50& 0.03\cr 112& -0.0000211& 178.371& -0.8005731413& 7.85& -8\PS-\TO+\PH & -31.28& 0.03\cr 113& 0.0000190& 306.045& -0.8796858264& 7.14& -9\PS+\TO+\PH & 28.20& 0.02\cr 114& 0.0000171& 242.475& -0.1787389313& 35.15& -2\PS+ 2\TO+\PH & 25.29& 0.06\cr 115& -0.0000170& 99.359& -0.8993069063& 6.99& -9\PS-\TO+\PH & -25.17& 0.02\cr 116& 0.0000168& 145.153& 0.1769539690& 35.51& 2\PS -2\TO+\PH & 24.90& 0.05\cr 117& 0.0000160& 123.690& -0.9882301314& 6.36&-10\PS+\PH & 23.77& 0.03\cr 118& 0.0000152& 227.033& -0.9784195914& 6.42&-10\PS+\TO+\PH & 22.53& 0.02\cr 119& 0.0000138& 163.463& -0.2774726963& 22.64& -3\PS+ 2\TO+\PH & 20.45& 0.04\cr 120& -0.0000137& 20.347& -0.9980406714& 6.30&-10\PS-\TO+\PH & -20.26& 0.01\cr 121& 0.0000128& 263.938& 0.9864451691& 6.37& 10\PS+\PH & 18.96& 0.00\cr 122& 0.0000124& 198.525& 0.2161961288& 29.06& 2\PS+ 2\TO+\PH & 18.44& 0.04\cr 123& 0.0000123& 184.926& 0.8877114041& 7.08& 9\PS+\PH & 18.16& 0.00\cr 124& 0.0000123& 135.830& 0.7880605117& 7.97& 8\PS+ 2\PH-\PT & 18.17& 0.01\cr 125& -0.0000122& 125.533& 0.4829658041& 13.01& 5\PS-\TO+\PH & -18.11& 0.02\cr 126& 0.0000121& 148.020& -1.0771533565& 5.83&-11\PS+\TO+\PH & 17.98& 0.01\cr 127& 0.0000120& 84.450& -0.3762064613& 16.70& -4\PS+ 2\TO+\PH & 17.76& 0.04\cr 128& 0.0000114& 44.677& -1.0869638964& 5.78&-11\PS+\PH & 16.83& 0.02\cr 129& -0.0000110& 301.334& -1.0967744364& 5.73&-11\PS-\TO+\PH & -16.28& 0.01\cr 130& 0.0000107& 5.438& -0.4749402263& 13.23& -5\PS+ 2\TO+\PH & 15.85& 0.03\cr 131& 0.0000107& 332.219& 0.5025868840& 12.50& 5\PS+\TO+\PH & 15.82& 0.02\cr 132& 0.0000097& 342.950& 1.0851789342& 5.79& 11\PS+\PH & 14.37& 0.00\cr 133& 0.0000097& 69.008& -1.1758871215& 5.34&-12\PS+\TO+\PH & 14.35& 0.01\cr 134& 0.0000096& 286.426& -0.5736739914& 10.95& -6\PS+ 2\TO+\PH & 14.18& 0.03\cr 135& 0.0000095& 105.913& 0.7889776391& 7.96& 8\PS+\PH & 14.04& 0.01\cr 136& -0.0000088& 222.322& -1.1955082014& 5.26&-12\PS-\TO+\PH & -13.04& 0.01\cr 137& 0.0000086& 321.922& 0.1974921763& 31.81& 2\PS+\PT & 12.75& 0.01\cr 138& 0.0000085& 207.413& -0.6724077564& 9.34& -7\PS+ 2\TO+\PH & 12.58& 0.03\cr 139& 0.0000080& 325.665& -1.1856976614& 5.30&-12\PS+\PH & 11.85& 0.02\cr 140& 0.0000077& 349.996& -1.2746208865& 4.93&-13\PS+\TO+\PH & 11.42& 0.00\cr 141& 0.0000075& 128.401& -0.7711415214& 8.15& -8\PS+ 2\TO+\PH & 11.08& 0.02\cr 142& 0.0000074& 224.165& 0.2756877340& 22.79& 3\PS -2\TO+\PH & 10.95& 0.02\cr 143& 0.0000071& 61.963& 1.1839126992& 5.31& 12\PS+\PH & 10.59& 0.00\cr 144& -0.0000070& 143.309& -1.2942419664& 4.85&-13\PS-\TO+\PH & -10.44& 0.01\cr 145& 0.0000068& 110.090& -0.3167148561& 19.84& -3\PS -2\TO+\PH & 10.05& 0.02\cr 146& 0.0000068& 31.078& -0.4154486211& 15.12& -4\PS -2\TO+\PH & 10.01& 0.02\cr 147& 0.0000067& 189.103& -0.2179810911& 28.82& -2\PS -2\TO+\PH & 9.86& 0.02\cr 148& 0.0000066& 312.066& -0.5141823862& 12.22& -5\PS -2\TO+\PH & 9.74& 0.02\cr 149& 0.0000066& 49.388& -0.8698752865& 7.22& -9\PS+ 2\TO+\PH & 9.71& 0.02\cr 150& 0.0000064& 277.537& 0.3149298939& 19.95& 3\PS+ 2\TO+\PH & 9.55& 0.02\cr 151& 0.0000062& 233.053& -0.6129161512& 10.25& -6\PS -2\TO+\PH & 9.22& 0.02\cr 152& -0.0000062& 258.793& 0.4918592167& 12.77& 5\PS+ 2\PH-\PT & -9.21& 0.01\cr 153& 0.0000061& 270.983& -1.3733546515& 4.58&-14\PS+\TO+\PH & 9.08& 0.00\cr 154& 0.0000058& 154.041& -0.7116499162& 8.83& -7\PS -2\TO+\PH & 8.53& 0.02\cr 155& 0.0000057& 330.376& -0.9686090515& 6.49&-10\PS+ 2\TO+\PH & 8.48& 0.02\cr 156& 0.0000057& 283.558& 0.6804333341& 9.23& 7\PS-\TO+\PH & 8.46& 0.01\cr 157& -0.0000056& 64.297& -1.3929757315& 4.51&-14\PS-\TO+\PH & -8.33& 0.00\cr 158& 0.0000056& 246.653& -1.2844314265& 4.89&-13\PS+\PH & 8.28& 0.02\cr 159& 0.0000055& 140.975& 1.2826464642& 4.90& 13\PS+\PH & 8.09& 0.00\cr 160& 0.0000052& 75.028& -0.8103836813& 7.75& -8\PS -2\TO+\PH & 7.76& 0.02\cr 161& 0.0000050& 251.364& -1.0673428165& 5.89&-11\PS+ 2\TO+\PH & 7.38& 0.01\cr 162& 0.0000050& 95.182& 0.2063855889& 30.44& 2\PS+\TO+\PH & 7.34& 0.02\cr 163& -0.0000050& 262.529& -0.2072534238& 30.32& -2\PS-\TO+\PT & -7.34& 0.01\cr 164& 0.0000049& 191.971& -1.4720884166& 4.27&-15\PS+\TO+\PH & 7.21& 0.00\cr 165& 0.0000047& 356.016& -0.9091174463& 6.91& -9\PS -2\TO+\PH & 6.98& 0.01\cr 166& 0.0000046& 286.860& -0.2961766489& 21.21& -3\PS+\PT & 6.89& 0.00\cr 167& -0.0000045& 345.285& -1.4917094965& 4.21&-15\PS-\TO+\PH & -6.62& 0.00\cr 168& 0.0000044& 219.988& 1.3813802293& 4.55& 14\PS+\PH & 6.56& 0.00\cr 169& 0.0000043& 172.351& -1.1660765815& 5.39&-12\PS+ 2\TO+\PH & 6.37& 0.01\cr 170& 0.0000042& 277.004& -1.0078512113& 6.23&-10\PS -2\TO+\PH & 6.23& 0.01\cr 171& -0.0000041& 130.244& 0.7000544140& 8.98& 7\PS+\TO+\PH & -6.07& 0.01\cr 172& 0.0000039& 26.901& 0.6902438741& 9.10& 7\PS+\PH & 5.77& 0.02\cr 173& 0.0000038& 112.958& -1.5708221816& 4.00&-16\PS+\TO+\PH & 5.70& 0.00\cr 174& 0.0000038& 167.640& -1.3831651915& 4.54&-14\PS+\PH & 5.70& 0.01\cr 175& 0.0000037& 197.991& -1.1065849763& 5.68&-11\PS -2\TO+\PH & 5.52& 0.01\cr 176& 0.0000037& 93.339& -1.2648103466& 4.97&-13\PS+ 2\TO+\PH & 5.48& 0.01\cr 177& -0.0000035& 266.272& -1.5904432615& 3.95&-16\PS-\TO+\PH & -5.25& 0.00\cr 178& 0.0000035& 299.000& 1.4801139943& 4.25& 15\PS+\PH & 5.23& 0.00\cr 179& 0.0000034& 40.934& 0.2962259413& 21.21& 3\PS+\PT & 5.04& 0.01\cr \noalign{\medskip\hrule} } \vfill\eject % series zt : \bigskip \noindent{\bf Table 7.} Series for $\zeta_7= \sin(i_7/2)\exp\sqi\Omega_7$ : Each term is in the form $\alpha\exp\sqi(\omega t+\varphi)$ with $t=(\hbox{Julian Date)}-2\,451\,545.0$. Each argument is also identified as an integer combination of the seven fundamental arguments given in Table 3; $\omega $ and $\varphi$ are in fact computed from these combinations. The amplitudes in km represent $2A_7\zeta_7$ with $A_7= 1482333.4$~km. \medskip \halign{ $#$\hfil&\qhfil$#$&\qhfil$#$&\qhfil$#$&\qhfil$#$& \quad\quad$#$\hfil &\qhfil$#$&\qhfil$#$\cr \noalign{\hrule\medskip} \hbox{n\Deg} &\hfill\hbox{amplitude $\alpha $}\hfill &\hfill\hbox{phase $\varphi$}\hfill &\hfill\hbox{frequency $\omega $}\hfill &\hfill\hbox{period}\hfill &\hfill\hbox{argument}\hfill &\hfill\hbox{amplitude}\hfill &\hfill\hbox{$\varepsilon(\alpha)$}\hfill \cr &\hfill\hbox{(rad)}\hfill &\hfill\hbox{(deg)}\hfill &\hfill\hbox{(rad/d)}\hfill &\hfill\hbox{(d)}\hfill & &\hfill\hbox{(km)}\hfill &\hfill\hbox{(km)}\hfill \cr \noalign{\medskip\hrule\medskip} 0& 0.0049552& 184.582& 0.0000000000&& \NO & 14690.65& 0.59\cr 1& 0.0059485& 221.420& -0.0001136161& 55301.92&\NH & 17635.36& 102.71\cr 2& 0.0015359& 351.900& -0.0000246364& 255037.01&\NT & 4553.41& 40.15\cr 3& -0.0001497& 166.208& -0.0016713462& 3759.36& 2\PH-\NH & -443.91& 2.76\cr 4& -0.0000491& 136.291& -0.0007542188& 8330.72&\PH+\PT-\NH & -145.62& 0.95\cr 5& 0.0000219& 251.337& -0.0010307434& 6095.78&\PH-\PT+\NH & 64.90& 0.42\cr 6& 0.0000150& 203.046& -0.0017849622& 3520.07& 2\PH-\NO & 44.37& 0.04\cr 7& 0.0000140& 269.551& 0.0081391938& 771.97&\TO+ 2\PH-\NH & 41.63& 0.28\cr 8& -0.0000131& 191.503& 0.0008035113& 7819.66&-\PH+\PT+\NH & -38.96& 0.25\cr 9& 0.0000084& 62.865& -0.0114818862& 547.23&-\TO+ 2\PH-\NH & 24.87& 0.17\cr 10& 0.0000075& 106.374& 0.0001629085& 38568.80& 2\PT-\NH & 22.14& 0.15\cr 11& -0.0000049& 300.433& 0.0986201490& 63.71&\PS+\NH & -14.57& 0.09\cr 12& 0.0000045& 173.129& -0.0008678349& 7240.07&\PH+\PT-\NO & 13.37& 0.01\cr 13& -0.0000041& 35.728& -0.0017603259& 3569.33& 2\PH-\NT & -12.29& 0.12\cr 14& 0.0000038& 142.408& -0.0988473811& 63.56&-\PS+\NH & 11.38& 0.07\cr 15& 0.0000036& 118.077& -0.0099241560& 633.12&-\TO+\NH & 10.57& 0.07\cr 16& 0.0000030& 245.220& 0.0970624188& 64.73&\PS+ 2\PH-\NH & 8.98& 0.06\cr 17& -0.0000027& 214.499& -0.0009171274& 6850.94&\PH-\PT+\NO & -7.95& 0.01\cr 18& -0.0000020& 87.195& -0.1004051112& 62.58&-\PS+ 2\PH-\NH & -5.94& 0.04\cr 19& -0.0000016& 306.389& 0.0080255777& 782.90&\TO+ 2\PH-\NO & -4.63& 0.00\cr 20& -0.0000014& 143.212& 0.0000492925& 127467.47& 2\PT-\NO & -4.15& 0.01\cr 21& 0.0000013& 154.665& 0.0009171274& 6850.94&-\PH+\PT+\NO & 3.72& 0.00\cr 22& -0.0000013& 5.811& -0.0008431985& 7451.61&\PH+\PT-\NT & -3.77& 0.04\cr 23& 0.0000012& 12.894& 0.0179497337& 350.04& 2\TO+ 2\PH-\NH & 3.62& 0.03\cr 24& -0.0000012& 190.538& -0.0905945713& 69.35&-\PS+\TO+ 2\PH-\NH & -3.53& 0.02\cr 25& -0.0000011& 141.877& 0.0872518789& 72.01&\PS-\TO+ 2\PH-\NH & -3.33& 0.02\cr 26& 0.0000011& 348.563& 0.1068729588& 58.79&\PS+\TO+ 2\PH-\NH & 3.31& 0.02\cr 27& -0.0000009& 99.703& -0.0115955022& 541.86&-\TO+ 2\PH-\NO & -2.63& 0.00\cr 28& 0.0000008& 343.852& -0.1102156512& 57.01&-\PS-\TO+ 2\PH-\NH & 2.46& 0.02\cr 29& 0.0000008& 32.948& -0.0105647588& 594.73&-\TO+\PH+\PT-\NH & 2.46& 0.02\cr 30& 0.0000008& 258.259& -0.0002272321& 27650.96& 2\NH-\NO & 2.32& 0.03\cr 31& -0.0000008& 197.089& 0.0888096090& 70.75&\PS-\TO+\NH & -2.26& 0.02\cr 32& 0.0000007& 68.106& 0.0195074639& 322.09& 2\TO+\NH & 2.20& 0.02\cr 33& -0.0000007& 14.734& -0.0197346960& 318.38& -2\TO+\NH & -2.16& 0.02\cr 34& 0.0000007& 21.817& -0.0009417637& 6671.72&\PH-\PT+\NT & 2.12& 0.02\cr 35& 0.0000007& 239.634& 0.0090563211& 693.79&\TO+\PH+\PT-\NH & 2.05& 0.02\cr 36& 0.0000007& 196.125& -0.0025884736& 2427.37& 3\PH-\PT-\NH & 1.95& 0.01\cr 37& -0.0000006& 354.680& 0.0087797965& 715.64&\TO+\PH-\PT+\NH & -1.86& 0.01\cr 38& -0.0000006& 319.522& -0.0212924261& 295.09& -2\TO+ 2\PH-\NH & -1.65& 0.01\cr 39& 0.0000005& 263.594& 0.0987337650& 63.64&\PS+\NO & 1.61& 0.00\cr 40& -0.0000005& 147.994& -0.0108412834& 579.56&-\TO+\PH-\PT+\NH & -1.34& 0.01\cr 41& -0.0000004& 105.569& -0.0987337650& 63.64&-\PS+\NO & -1.26& 0.00\cr 42& 0.0000004& 215.303& 0.0979795462& 64.13&\PS+\PH+\PT-\NH & 1.25& 0.01\cr 43& 0.0000004& 139.071& 0.0080502141& 780.50&\TO+ 2\PH-\NT & 1.27& 0.01\cr 44& -0.0000004& 81.239& -0.0098105400& 640.45&-\TO+\NO & -1.22& 0.00\cr 45& 0.0000004& 88.160& -0.0090070287& 697.59&-\TO-\PH+\PT+\NH & 1.16& 0.01\cr 46& 0.0000004& 245.751& -0.0890368411& 70.57&-\PS+\TO+\NH & 1.06& 0.01\cr 47& -0.0000004& 321.983& 0.0008924910& 7040.05&-\PH+\PT+\NT & -1.04& 0.01\crs 48& 0.0000031& 63.395& -0.1975811461& 31.80& -2\PS+\NH & 9.33& 0.05\cr 49& -0.0000022& 19.445& 0.1973539140& 31.84& 2\PS+\NH & -6.43& 0.04\cr 50& 0.0000018& 324.233& 0.1957961839& 32.09& 2\PS+ 2\PH-\NH & 5.44& 0.03\cr 51& 0.0000018& 344.383& -0.2963149111& 21.20& -3\PS+\NH & 5.28& 0.03\cr \noalign{\medskip\hrule} } \def\L#1{\lambda_{o#1}} \def\PR#1{\varpi_{#1}^{*}} \def\ND#1{\Omega_{#1}^{*}} \def\LS{\lambda_{9}} \def\PRS{\varpi_{9}} \def\NDS{\Omega_{9}} \def\NDz{\Omega_{0}} \vfill\eject % solar perturbations : \bigskip \noindent{\bf Table 8.} Solar and short-period perturbations of Hyperion: These are expressed as $\alpha \cos(\omega t+\phi)$ for $p_7$, as $\alpha \sin(\omega t+\phi)$ for $q_7$ and as $\alpha \exp\sqi(\omega t+\phi)$ for $z_7$ and $\zeta_7$, with $t=(\hbox{Julian Date})-2\,451\,545.0$. We give also for each term, the combination of arguments from which the frequency and the phase are computed: $\lambda_9$, $\varpi_9$ and $\Omega_9$ concern the elements of the Sun in the saturnicentric Saturn-equatorial reference frame referred to the mean ecliptic for the J2000.0 epoch, $\L{i}$ refers to the linear part of the mean longitude of the satellite $i$ and other arguments to the fundamental arguments given in Table 3. Amplitudes in kilometres are computed like in Tables 4 to 7. \medskip \halign{ $#$\hfil&\qhfil$#$&\qhfil$#$&\qhfil$#$&\qhfil$#$& \quad\quad$#$\qhfil &\qhfil$#$\cr \noalign{\hrule\medskip} &\hfill\hbox{amplitude $\alpha $}\hfill &\hfill\hbox{phase $\varphi$}\hfill &\hfill\hbox{frequency $\omega $}\hfill &\hfill\hbox{period}\hfill &\hfill\hbox{argument}\hfill &\hfill\hbox{amplitude}\hfill \cr &\hfill\hbox{(rad)}\hfill &\hfill\hbox{(deg)}\hfill &\hfill\hbox{(rad/d)}\hfill &\hfill\hbox{(d)}\hfill & &\hfill\hbox{(km)}\hfill \cr \noalign{\medskip\hrule\medskip} % % perturbations of p_7 % p_7& -0.0000268& 123.098& 1.0955449042& 5.74& \L5-\L7 & 26.45\cr & -0.0000131& 247.802& 2.0004088347& 3.14& \L4-\L7 & 12.93\cr & -0.0000125& 55.315& 0.2962012606& 21.21& \L7-\PR7 & 12.35\cr & -0.0000088& 16.193& 0.5894496611& 10.66& 2\L7-2\LS & 8.68\cr & -0.0000030& 85.277& 0.2952841655& 21.28& \L7-\PR6 & 2.93\cr % % perturbations of q_7 % \noalign{\medskip\hrule\medskip} q_7& -0.0002989& 112.955& 0.0011679623& 5379.61& 2\LS-2\NDS & -443.05\cr & -0.0002231& 317.020& 0.0005839811& 10759.23& \LS-\PRS & -330.68\cr & -0.0000409& 69.976& 0.0017519434& 3586.41& 3\LS-2\NDS-\PRS & -60.67\cr & -0.0000233& 94.436& 0.0029528601& 2127.83& 2\LS-2\PR7 & -34.51\cr & 0.0000175& 155.935& 0.0005839811& 10759.23& \LS+\PRS-2\NDS & 26.00\cr & -0.0000160& 124.398& 0.0020357649& 3086.40& 2\LS-\PR7-\PR6 & -23.72\cr & -0.0000137& 274.041& 0.0011679623& 5379.61& 2\LS-2\PRS & -20.28\cr & 0.0000129& 76.654& 0.0012815784& 4902.69& 2\LS-\NDS-\ND7 & 19.10\cr & 0.0000118& 112.958& 0.0011679623& 5379.61& 2\LS-\NDS-\NDz & 17.56\cr & 0.0000037& 307.094& 0.0011925987& 5268.48& 2\LS-\NDS-\ND6 & 5.49\cr & -0.0000035& 154.360& 0.0011186698& 5616.66& 2\LS-2\PR6 & -5.11\cr & 0.0000146& 55.315& 0.2962012606& 21.21& \L7-\PR7 & 21.64\cr & 0.0000134& 123.098& 1.0955449042& 5.74& \L5-\L7 & 19.86\cr & -0.0000102& 16.193& 0.5894496611& 10.66& 2\L7-2\LS & -15.19\cr & 0.0000073& 247.802& 2.0004088347& 3.14& \L4-\L7 & 10.75\cr & 0.0000035& 85.277& 0.2952841655& 21.28& \L7-\PR6 & 5.13\cr %% % perturbations of z_7 %% \noalign{\medskip\hrule\medskip} z_7& 0.0001928& 288.280& 0.0020604112& 3049.48& 2\LS-\PR7 & 285.74\cr & 0.0000823& 318.242& 0.0011433161& 5495.58& 2\LS-\PR6 & 122.02\cr & 0.0000517& 306.799& 0.0002755134& 22805.37& 2\LS-2\NDS+\PR7 & 76.69\cr & 0.0000327& 245.300& 0.0026443923& 2376.04& 3\LS-\PRS-\PR7 & 48.46\cr & -0.0000163& 150.864& -0.0003084677& -20369.02& \LS-\PRS+\PR7 & -24.20\cr & 0.0000128& 218.304& 0.0003084677& 20369.02& -\LS+\PRS+2\NDS-\PR7 & 19.02\cr & 0.0000119& 275.262& 0.0017272972& 3637.58& 3\LS-\PRS-\PR6 & 17.58\cr & -0.0000084& 331.259& 0.0014764300& 4255.66& \LS+\PRS-\PR7 & -12.40\cr & -0.0000069& 80.888& -0.0020604112& -3049.48& -2\LS+2\NDS+\PR7 & -10.25\cr & -0.0000030& 50.926& -0.0011433161& -5495.58& -2\LS+2\NDS+\PR6 & -4.38\cr & 0.0000029& 120.902& 0.0006086274& 10323.53& \LS-\PRS+\PR6 & 4.28\cr & 0.0000028& 276.837& 0.0011926085& 5268.44& 2\LS-2\NDS+\PR6 & 4.20\cr & -0.0000015& 248.266& -0.0006086274& -10323.53& -\LS+\PRS+2\NDS-\PR6 & -2.28\cr & 0.0000404& 249.158& 0.2953088117& 21.28& \L7 & 59.92\cr & 0.0000111& 12.256& 1.3908537159& 4.52& \L5 & 16.43\cr & 0.0000088& 232.965& -0.2941408494& -21.36& 2\LS-\L7 & 13.05\cr %% % perturbations of \zeta_7 %% \noalign{\medskip\hrule\medskip} \zeta_7& -0.0001609& 297.539& 0.0011679623& 5379.61& 2\LS-\NDS & -477.05\cr & -0.0000247& 227.564& -0.0005839811& -10759.23& -\LS+\PRS+\NDS & -73.10\cr & 0.0000247& 141.604& 0.0005839811& 10759.23& \LS-\PRS+\NDS & 73.10\cr & -0.0000221& 254.560& 0.0017519434& 3586.41& 3\LS-\PRS-\NDS & -65.62\cr & 0.0000095& 340.519& 0.0005839811& 10759.23& \LS+\PRS-\NDS & 28.12\cr & -0.0000091& 71.629& -0.0011679623& -5379.61& -2\LS+3\NDS & -27.05\cr & 0.0000040& 261.238& 0.0012815784& 4902.69& 2\LS-\ND7 & 11.81\cr & 0.0000037& 297.541& 0.0011679623& 5379.61& 2\LS-\NDz & 10.85\cr & 0.0000011& 131.678& 0.0011925987& 5268.48& 2\LS-\ND6 & 3.39\cr \noalign{\medskip\hrule} } \bye We present here a new theory of motion for Hyperion, the seventh major satellite of Saturn. The Hyperion's motion is defined like in TASS1.6 for the other satellites (Vienne \& Duriez 1995), by the osculating saturnicentric orbital elements referred to the equatorial plane of Saturn and to the node of this plane in the mean ecliptic for J$2000.0$. These elements are expressed as semi-numerical trigonometric series in which the argument of each term is given as an integer combination of 7 natural fundamental arguments. These series collect all the perturbations caused by Titan on the orbital elements of Hyperion, whose amplitudes are larger than 1~km in the long-period terms and than 5~km in the short-period ones. However, the convergence of these series is so slow that, in spite of several hundreds of terms, their internal accuracy over one century is about 200~km only. These series have been constructed in such a way that the fundamental arguments and the amplitude of each term depend explicitly on 13 parameters (the twelve initial conditions of the motions of Titan and Hyperion and the mass of Titan). Taking also account of the perturbations from other satellites and Sun, we have fitted these series to 8136 Earth-based observations of Hyperion in the interval [1874-1985], giving a set of better values for these parameters. In particular the mass of Titan is found equal to $(237.399\pm0.005)\,10^{-6}$ (in units of the Saturn's mass) and we discuss this value in comparison with that [$(236.638\pm0.008)\ 10^{-6}$] obtained by Campbell \& Anderson from their analysis of the Voyager missions to Saturn. The resulting fitted series allows us to produce new ephemerides for Hyperion. Their comparison to those from Taylor (1992) shows that, with the same set of observations and the same way to weight them, we obtain a root mean square (o$-$c) residual of $0\Sp156$ while the ephemerides of Taylor gives $0\Sp203$.