\begin{table}%t8 \par \caption {\label{Tab:orbits}An extensive list of orbital elements for (non-symbiotic) M~giants. } { %\tabcolsep 2 pt \begin{tabular}{rrrcrlllclrrrl} \noalign{\bf New orbits}\\ \hline\hline HD & Sp. & $N$ & $\sigma$(O$-$C) & $\Delta t$ & \multicolumn{1}{c}{$P$} & \multicolumn{1}{c}{$e$} & \multicolumn{1}{c}{$f(M)$} & \multicolumn{1}{c}{$T_0$} & \multicolumn{1}{c}{$\omega$} & \multicolumn{1}{c}{$K_1$} & \multicolumn{1}{c}{$V_0$} & \multicolumn{1}{c}{$a_1 \sin i$} & \\ & & & \multicolumn{1}{c}{(\kms)} & (d) & \multicolumn{1}{c}{(d)} & & \multicolumn{1}{c}{(\Msun)} & \multicolumn{1}{c}{(JD $-$2\ts400\ts000)} & \multicolumn{1}{c}{($^\circ$)} & \multicolumn{1}{c}{(\kms)} & \multicolumn{1}{c}{(\kms)} & ($10^6$~km)\\ \hline 83~069 & M2III & 9 & 0.11 & 4450 & $4768\pm175$ & $0.36\pm0.12$ & 0.0076 & $53\ts344\pm106$ & $132\pm15$ & $2.7\pm 0.2$ & $-17.9\pm0.1$ & 163.3 \\ 108~907 & M4III & 15 & 0.60 & 6821 & $1714\pm4$ & $0.20\pm0.03$ & 0.0094 & $53\ts239\pm40$ & $278\pm9$ & $3.8\pm0.2$&$-15.6\pm0.1$ & 88.6 & (1)\\ && 71 & 0.90 & 24~830 & $1703\pm3$ & $0.30\pm0.05$ & 0.0076& $42\ts868\pm40$ & $244\pm9$ & $3.7\pm0.2$&$-14.3\pm0.1$ & 82.0 & (2) \\ && 72 & 1.02 & 9451 & $1703\pm3$ & $0.33\pm0.02$ & 0.0063& $53\ts204\pm19$ & $267\pm4$ & $3.5\pm0.1$&$-14.8\pm0.1$ & $77.1$ & (3)\\ 111~129& M2III & 10 & 0.18 & 3633 & $496.7\pm0.7$ & $0.14\pm0.01$ & 0.047& $50\ts630\pm17$ & $299\pm12$ & $9.8\pm0.3$ & $-15.9\pm0.1$ & 66.3 \\ 113~406 & M1III & 12 & 0.25 & 4324 & $1338\pm7$ & $0.30\pm0.03$ & 0.0065 & $50\ts865\pm18$ & $18\pm5$ & $3.8\pm0.3$ & $4.8\pm0.1$ & 66.4 \\ 137~853 & M1III & 11 & 0.12 & 3794 & $1373\pm15$ & $0.15\pm0.06$ & 0.0015 & $51\ts616\pm62$ & $119\pm17$ & $2.2\pm0.1$ & $-9.8\pm0.1$ & 41.7& \\ 159~608& M2III & 16 & 0.39 & 3981 & $599.3\pm0.4$ & $0.22\pm0.01$& 0.0751 & $52\ts731\pm5$ & $357\pm3$ & $10.9\pm0.2$ & $-59.9\pm0.1$ & 87.8 \\ 165~374& M2III & 37 & 0.41 & 7349 & $2741\pm13$ & $0.05\pm0.02$ & 0.0782& $51\ts058\pm128$ & $74\pm17$ & $6.5\pm0.1$ & $-32.0\pm0.1$ & 245.3 \\ 182~190& M1III & 40 & 0.30 & 5258 & $3856\pm22$& $0.57\pm0.01$ & 0.0155 & $53\ts053\pm11$ & $164\pm2$ & $4.1\pm0.1$ & $-24.4\pm0.1$ & 179.0 \\ 187~372& M1III & 16 & 0.36 & 5787 & $986\pm3$ & $0.24\pm0.03$ & 0.0034& $50\ts201\pm22 $ & $204\pm8$ & $3.3\pm0.2$ & $0.1\pm0.1$ & 43.8 \\ 199~871& M0III & 10 & 0.31 & 3964 & $840.2\pm0.7$ & $0.16\pm0.02$ & 0.203& $51\ts899\pm7$ & $17\pm3$ & $13.4\pm0.1$ & $-48.2\pm0.1$ & 153.1 \\ 212~009& M0III & 9 & 0.17 & 5008 & $791.8\pm1.1$ & $0.17\pm0.04$ & 0.0231& $53\ts529\pm15$ & $70\pm6$ & $6.6\pm0.2$ & $-17.7\pm0.2$ & 71.3 \\ 212~047& M4III & 12 & 0.24 & 3984 & $328.2\pm0.1$ & $0.016\pm0.012$& 0.0290& $49\ts315\pm47$ & $176\pm53$ & $9.4\pm0.1$ & $-7.5\pm0.1$ & 42.8 \\ 220~088& M0III & 37 & 0.13 & 5874 & $2516.6\pm1.5$ & $0.639\pm0.004$ & 0.0169 &$53\ts622.5\pm2.6$ & $259.5\pm1.1$ & $5.21\pm0.05$ & $-20.48\pm0.03$ & 138.9 \\ \hline\\ \end{tabular} } { \begin{tabular}{rlrcrlll} \noalign{ \bf Preliminary orbit } \smallskip\\ \hline\hline HD & Sp. & $N$ & $\sigma$(O$-$C) & $\Delta t$ & \multicolumn{1}{c}{$P$} & \multicolumn{1}{c}{$e$} & Rem.\\ & & & & (d) & \multicolumn{1}{c}{(d)} \\ \hline\\ 203~525& M0III & 10 & 0.12 & 4741 & 7290: & 0.4: \\ \hline\\ \end{tabular} \par \begin{tabular}{r@{}llllll} \noalign{ \bf Orbits from the literature } \smallskip\\ \hline\hline HD & & Sp. & $P$ & $e$ & $f(M)$ & Ref. \\ & & & (d) & & (\Msun)\\ \hline 9053 & & M0III & 193.8 & 0.0 & 0.083 & $\gamma$ Phe: \citet{Luyten-1936}\\ 41~511 & & M4III & $260.34\pm1.80$ & $0.024\pm0.005$ & $0.261\pm0.005$ & (4)\\ 42~995 & & M3III & 2983 & 0.53 & 0.13 & $\eta$ Gem: \citet{McLaughlin-1944}\\ 80~655 & & gM & 834 & 0.0 & 0.0074& \citet{Griffin-1983}\\ 89~758 & & M0III & $230.089\pm0.039$ & $0.061\pm0.022$ & 0.01 & $\mu$~UMa: \citet{Jackson-1957,Lucy-Sweeney-71}\\ 108~815 & & M & $4448\pm20$ & $0.73\pm0.03$ & $0.012\pm0.003$ & Griffin, priv. comm.\\ 111~307 & & M0 & $18000\pm3000$ & 0: & $0.10\pm0.04$ & Griffin, priv. comm.\\ 115~521 &Aa+b & M2III & $>$7000 & $>$0.5 & .. & Sect.~\ref{Sect:115521} \\ 115~521 &A+a & & $475.1\pm1.4$ & $0.15\pm0.06$ & $9.3\times 10^{-5}$ & (5), revised but orbital nature doubtful (Sect.~\ref{Sect:115521}) \\ 117~673 & & M0III & $1360.8\pm2.3$ & $0.26\pm0.02$ & 0.0095 & \citet{Griffin-2008}\\ 126~947 & & M3III & $2812.3\pm9.4$ & $0.432\pm0.021$ & 0.045 & \citet{Prieur-2006}\\ 132~813 & & M4.5III & 748.9 & 0.13 & 0.0043 & RR UMi (SRb, $P = 43.3$ d):\\ & & & & & & \citet{Dettmar-1983,Batten-1986}\\ 147~395 & & M2III & 335.5 & 0.24 & 0.154 & \citet{Carquillat-96}\\ 187~076 & & M2II+late B & $3704.2\pm3.2$ & $0.45\pm0.01$ & $0.135\pm0.005$ & Griffin, priv.comm.\\ & & & & & & $\delta$~Sge: A $\zeta$~Aur/VV~Cep-like system \citep{Reimers-Schroeder-1983}\\ 190~658 & & M2.5III & 198.7 & 0.05 & 0.045 & (6) \\ 192~867 & & M1III & 5929 & 0.64 & 0.032 & \citet{Griffin-1990}\\ 220~007 & & M3III & 1520 & 0.51 & 0.013 & \citet{Griffin-1979}\\ \hline\\ \end{tabular} } Remarks: (1) this work; (2) \citet{Reimers-1988}; (3) combined solution (see text); (4) SS Lep: M4III + accreting A1 star \citep{Welty-1995}. \citet{Verhoelst-2007} shows, from interferometric measurements of the M-giant radius, that the giant fills its Roche lobe (see also Paper~III); (5) possibly a triple system, formerly a radial-velocity standard star; \citet{Duquennoy-Mayor-91} found a preliminary 509~d period for the inner pair, but the orbital nature of the short-period variations is questionable (Sect.~\ref{Sect:115521}); (6) HD 190~658 = V1472 Aql = HIP~98~954: semiregular or most likely eclipsing or ellipsoidal variable with $P = 100.37$~d, almost exactly half the orbital period \citep{Samus-1997}. Orbital elements from \citet{Lucke-Mayor-1982}. A (physical?) companion is present at 2.3\arcsec\ \citep{Tokovinin-1997,Frankowski-2007}. \end{table}