Table 5.
Open in new tab

Results of our |$\chi ^2$|-fitting.|$^*$|

|$\chi _{\rm red.min}^2$| and parameters|$\chi _{\rm red.min}^2$||$M_{\rm SgrA}$||$R_{\rm GC}$||$V_{\rm O.ra}$|
determined by |$\chi ^2$|-fitting[no dim.][|$10^6\, M_\odot$|][kpc][mas|$\:$|yr|$^{-1}$|]
GR-best-fit1.1903|$4.232\pm 0.066$||$8.098\pm 0.066$||$-0.162\pm 28.782$|
NG-best-fit1.2134|$4.274\pm 0.067$||$8.114\pm 0.067$||$-0.168\pm 29.056$|
NG-art-best-fit0.0754|$4.352\pm 0.020$||$8.207\pm 0.018$||$-0.128\pm 0.002$|
Parameters|$V_{\rm O.dec}$||$V_{\rm O.Z}$||$I_{\rm S}$||$\Omega _{\rm S}$|
[mas|$\:$|yr|$^{-1}$|][km|$\:$|s|$^{-1}$|][|$^{\circ }$|][|$^{\circ }$|]
GR-best-fit|$0.174\pm 28.787$||$-8.345\pm 3.213$||$134.239\pm 0.217$||$227.766\pm 0.242$|
NG-best-fit|$0.166\pm 29.061$||$5.261\pm 3.196$||$134.063\pm 0.214$||$227.518\pm 0.245$|
NG-art-best-fit|$0.191\pm 0.001$||$9.307\pm 1.070$||$134.306\pm 0.056$||$226.974\pm 0.066$|
Parameters|$\omega _{\rm S}$||$e_{\rm S}$||$T_{\rm S}$||$t_{\rm S.apo}$|
[|$^{\circ }$|][no dim.][yr][AD]
GR-best-fit|$66.204\pm 0.333$||$0.8903\pm 0.0007$||$16.0504\pm 0.0023$||$2010.3383\pm 0.0015$|
NG-best-fit|$66.049\pm 0.340$||$0.8911\pm 0.0007$||$16.0468\pm 0.0022$||$2010.3432\pm 0.0014$|
NG-art-best-fit|$65.521\pm 0.062$||$0.8899\pm 0.0002$||$16.0489\pm 0.0003$||$2010.3410\pm 0.0003$|
Parameters|$\Delta {\rm RA}_{\rm K.apo}$||$\Delta {\rm DEC}_{\rm K.apo}$||$V_{\rm K.ra}$||$V_{\rm K.dec}$|
[mas][mas][mas|$\:$|yr|$^{-1}$|][mas|$\:$|yr|$^{-1}$|]
GR-best-fit|$0.576\pm 0.611$||$-1.796\pm 0.611$||$0.262\pm 28.790$||$-0.708\pm 28.790$|
NG-best-fit|$0.689\pm 0.620$||$-1.725\pm 0.620$||$0.309\pm 29.063$||$-0.692\pm 29.063$|
Parameters|$\Delta {\rm RA}_{\rm V.apo}$||$\Delta {\rm DEC}_{\rm V.apo}$||$V_{\rm V.ra}$||$V_{\rm V.dec}$|
[mas][mas][mas|$\:$|yr|$^{-1}$|][mas|$\:$|yr|$^{-1}$|]
GR-best-fit|$-1.061\pm 0.611$||$2.152\pm 0.611$||$0.154\pm 28.790$||$-0.220\pm 28.790$|
NG-best-fit|$-0.964\pm 0.620$||$2.223\pm 0.620$||$0.200\pm 29.063$||$-0.199\pm 29.063$|
|$\chi _{\rm red.min}^2$| and parameters|$\chi _{\rm red.min}^2$||$M_{\rm SgrA}$||$R_{\rm GC}$||$V_{\rm O.ra}$|
determined by |$\chi ^2$|-fitting[no dim.][|$10^6\, M_\odot$|][kpc][mas|$\:$|yr|$^{-1}$|]
GR-best-fit1.1903|$4.232\pm 0.066$||$8.098\pm 0.066$||$-0.162\pm 28.782$|
NG-best-fit1.2134|$4.274\pm 0.067$||$8.114\pm 0.067$||$-0.168\pm 29.056$|
NG-art-best-fit0.0754|$4.352\pm 0.020$||$8.207\pm 0.018$||$-0.128\pm 0.002$|
Parameters|$V_{\rm O.dec}$||$V_{\rm O.Z}$||$I_{\rm S}$||$\Omega _{\rm S}$|
[mas|$\:$|yr|$^{-1}$|][km|$\:$|s|$^{-1}$|][|$^{\circ }$|][|$^{\circ }$|]
GR-best-fit|$0.174\pm 28.787$||$-8.345\pm 3.213$||$134.239\pm 0.217$||$227.766\pm 0.242$|
NG-best-fit|$0.166\pm 29.061$||$5.261\pm 3.196$||$134.063\pm 0.214$||$227.518\pm 0.245$|
NG-art-best-fit|$0.191\pm 0.001$||$9.307\pm 1.070$||$134.306\pm 0.056$||$226.974\pm 0.066$|
Parameters|$\omega _{\rm S}$||$e_{\rm S}$||$T_{\rm S}$||$t_{\rm S.apo}$|
[|$^{\circ }$|][no dim.][yr][AD]
GR-best-fit|$66.204\pm 0.333$||$0.8903\pm 0.0007$||$16.0504\pm 0.0023$||$2010.3383\pm 0.0015$|
NG-best-fit|$66.049\pm 0.340$||$0.8911\pm 0.0007$||$16.0468\pm 0.0022$||$2010.3432\pm 0.0014$|
NG-art-best-fit|$65.521\pm 0.062$||$0.8899\pm 0.0002$||$16.0489\pm 0.0003$||$2010.3410\pm 0.0003$|
Parameters|$\Delta {\rm RA}_{\rm K.apo}$||$\Delta {\rm DEC}_{\rm K.apo}$||$V_{\rm K.ra}$||$V_{\rm K.dec}$|
[mas][mas][mas|$\:$|yr|$^{-1}$|][mas|$\:$|yr|$^{-1}$|]
GR-best-fit|$0.576\pm 0.611$||$-1.796\pm 0.611$||$0.262\pm 28.790$||$-0.708\pm 28.790$|
NG-best-fit|$0.689\pm 0.620$||$-1.725\pm 0.620$||$0.309\pm 29.063$||$-0.692\pm 29.063$|
Parameters|$\Delta {\rm RA}_{\rm V.apo}$||$\Delta {\rm DEC}_{\rm V.apo}$||$V_{\rm V.ra}$||$V_{\rm V.dec}$|
[mas][mas][mas|$\:$|yr|$^{-1}$|][mas|$\:$|yr|$^{-1}$|]
GR-best-fit|$-1.061\pm 0.611$||$2.152\pm 0.611$||$0.154\pm 28.790$||$-0.220\pm 28.790$|
NG-best-fit|$-0.964\pm 0.620$||$2.223\pm 0.620$||$0.200\pm 29.063$||$-0.199\pm 29.063$|

*GR-best-fit is the result of fitting the real observational data with the S0-2 motion at the 1PN|$\, +\,$|0PM approximation of GR. NG-best-fit is the result of fitting the real observational data with the S0-2 motion in the Newtonian gravity. NG-art-best-fit is the result of fitting the artificial accurate data with the S0-2 motion in the Newtonian gravity, where the artificial data are created from the GR-best-fit. The error in |$\chi ^2$|-fitting is given by definition (18).

Table 5.
Open in new tab

Results of our |$\chi ^2$|-fitting.|$^*$|

|$\chi _{\rm red.min}^2$| and parameters|$\chi _{\rm red.min}^2$||$M_{\rm SgrA}$||$R_{\rm GC}$||$V_{\rm O.ra}$|
determined by |$\chi ^2$|-fitting[no dim.][|$10^6\, M_\odot$|][kpc][mas|$\:$|yr|$^{-1}$|]
GR-best-fit1.1903|$4.232\pm 0.066$||$8.098\pm 0.066$||$-0.162\pm 28.782$|
NG-best-fit1.2134|$4.274\pm 0.067$||$8.114\pm 0.067$||$-0.168\pm 29.056$|
NG-art-best-fit0.0754|$4.352\pm 0.020$||$8.207\pm 0.018$||$-0.128\pm 0.002$|
Parameters|$V_{\rm O.dec}$||$V_{\rm O.Z}$||$I_{\rm S}$||$\Omega _{\rm S}$|
[mas|$\:$|yr|$^{-1}$|][km|$\:$|s|$^{-1}$|][|$^{\circ }$|][|$^{\circ }$|]
GR-best-fit|$0.174\pm 28.787$||$-8.345\pm 3.213$||$134.239\pm 0.217$||$227.766\pm 0.242$|
NG-best-fit|$0.166\pm 29.061$||$5.261\pm 3.196$||$134.063\pm 0.214$||$227.518\pm 0.245$|
NG-art-best-fit|$0.191\pm 0.001$||$9.307\pm 1.070$||$134.306\pm 0.056$||$226.974\pm 0.066$|
Parameters|$\omega _{\rm S}$||$e_{\rm S}$||$T_{\rm S}$||$t_{\rm S.apo}$|
[|$^{\circ }$|][no dim.][yr][AD]
GR-best-fit|$66.204\pm 0.333$||$0.8903\pm 0.0007$||$16.0504\pm 0.0023$||$2010.3383\pm 0.0015$|
NG-best-fit|$66.049\pm 0.340$||$0.8911\pm 0.0007$||$16.0468\pm 0.0022$||$2010.3432\pm 0.0014$|
NG-art-best-fit|$65.521\pm 0.062$||$0.8899\pm 0.0002$||$16.0489\pm 0.0003$||$2010.3410\pm 0.0003$|
Parameters|$\Delta {\rm RA}_{\rm K.apo}$||$\Delta {\rm DEC}_{\rm K.apo}$||$V_{\rm K.ra}$||$V_{\rm K.dec}$|
[mas][mas][mas|$\:$|yr|$^{-1}$|][mas|$\:$|yr|$^{-1}$|]
GR-best-fit|$0.576\pm 0.611$||$-1.796\pm 0.611$||$0.262\pm 28.790$||$-0.708\pm 28.790$|
NG-best-fit|$0.689\pm 0.620$||$-1.725\pm 0.620$||$0.309\pm 29.063$||$-0.692\pm 29.063$|
Parameters|$\Delta {\rm RA}_{\rm V.apo}$||$\Delta {\rm DEC}_{\rm V.apo}$||$V_{\rm V.ra}$||$V_{\rm V.dec}$|
[mas][mas][mas|$\:$|yr|$^{-1}$|][mas|$\:$|yr|$^{-1}$|]
GR-best-fit|$-1.061\pm 0.611$||$2.152\pm 0.611$||$0.154\pm 28.790$||$-0.220\pm 28.790$|
NG-best-fit|$-0.964\pm 0.620$||$2.223\pm 0.620$||$0.200\pm 29.063$||$-0.199\pm 29.063$|
|$\chi _{\rm red.min}^2$| and parameters|$\chi _{\rm red.min}^2$||$M_{\rm SgrA}$||$R_{\rm GC}$||$V_{\rm O.ra}$|
determined by |$\chi ^2$|-fitting[no dim.][|$10^6\, M_\odot$|][kpc][mas|$\:$|yr|$^{-1}$|]
GR-best-fit1.1903|$4.232\pm 0.066$||$8.098\pm 0.066$||$-0.162\pm 28.782$|
NG-best-fit1.2134|$4.274\pm 0.067$||$8.114\pm 0.067$||$-0.168\pm 29.056$|
NG-art-best-fit0.0754|$4.352\pm 0.020$||$8.207\pm 0.018$||$-0.128\pm 0.002$|
Parameters|$V_{\rm O.dec}$||$V_{\rm O.Z}$||$I_{\rm S}$||$\Omega _{\rm S}$|
[mas|$\:$|yr|$^{-1}$|][km|$\:$|s|$^{-1}$|][|$^{\circ }$|][|$^{\circ }$|]
GR-best-fit|$0.174\pm 28.787$||$-8.345\pm 3.213$||$134.239\pm 0.217$||$227.766\pm 0.242$|
NG-best-fit|$0.166\pm 29.061$||$5.261\pm 3.196$||$134.063\pm 0.214$||$227.518\pm 0.245$|
NG-art-best-fit|$0.191\pm 0.001$||$9.307\pm 1.070$||$134.306\pm 0.056$||$226.974\pm 0.066$|
Parameters|$\omega _{\rm S}$||$e_{\rm S}$||$T_{\rm S}$||$t_{\rm S.apo}$|
[|$^{\circ }$|][no dim.][yr][AD]
GR-best-fit|$66.204\pm 0.333$||$0.8903\pm 0.0007$||$16.0504\pm 0.0023$||$2010.3383\pm 0.0015$|
NG-best-fit|$66.049\pm 0.340$||$0.8911\pm 0.0007$||$16.0468\pm 0.0022$||$2010.3432\pm 0.0014$|
NG-art-best-fit|$65.521\pm 0.062$||$0.8899\pm 0.0002$||$16.0489\pm 0.0003$||$2010.3410\pm 0.0003$|
Parameters|$\Delta {\rm RA}_{\rm K.apo}$||$\Delta {\rm DEC}_{\rm K.apo}$||$V_{\rm K.ra}$||$V_{\rm K.dec}$|
[mas][mas][mas|$\:$|yr|$^{-1}$|][mas|$\:$|yr|$^{-1}$|]
GR-best-fit|$0.576\pm 0.611$||$-1.796\pm 0.611$||$0.262\pm 28.790$||$-0.708\pm 28.790$|
NG-best-fit|$0.689\pm 0.620$||$-1.725\pm 0.620$||$0.309\pm 29.063$||$-0.692\pm 29.063$|
Parameters|$\Delta {\rm RA}_{\rm V.apo}$||$\Delta {\rm DEC}_{\rm V.apo}$||$V_{\rm V.ra}$||$V_{\rm V.dec}$|
[mas][mas][mas|$\:$|yr|$^{-1}$|][mas|$\:$|yr|$^{-1}$|]
GR-best-fit|$-1.061\pm 0.611$||$2.152\pm 0.611$||$0.154\pm 28.790$||$-0.220\pm 28.790$|
NG-best-fit|$-0.964\pm 0.620$||$2.223\pm 0.620$||$0.200\pm 29.063$||$-0.199\pm 29.063$|

*GR-best-fit is the result of fitting the real observational data with the S0-2 motion at the 1PN|$\, +\,$|0PM approximation of GR. NG-best-fit is the result of fitting the real observational data with the S0-2 motion in the Newtonian gravity. NG-art-best-fit is the result of fitting the artificial accurate data with the S0-2 motion in the Newtonian gravity, where the artificial data are created from the GR-best-fit. The error in |$\chi ^2$|-fitting is given by definition (18).

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