Table summarizing the dynamical fit solution. Parameter values as the MLE and HDI at 68.27 per cent equivalent. Dynamical parameters are computed at the epoch of reference BJD|$_\textrm{TDB}\, 2455088.212$|.
| Parameter . | Kepler-9b . | Kepler-9c . |
|---|---|---|
| Fitted dynamical model | ||
| Mp/M⋆ | |$0.000128_{-0.000002}^{+0.000001}$| | |$0.000088_{-0.000001}^{+0.000001}$| |
| Pp (day) | |$19.23891_{-0.00006}^{+0.00006}$| | |$38.9853_{-0.0003}^{+0.0003}$| |
| |$\sqrt{e}\cos (\omega _\mathrm{p})$| | |$0.24651_{-0.0027}^{+0.0021}$| | |$-0.2526_{-0.0003}^{+0.0003}$| |
| |$\sqrt{e}\sin (\omega _\mathrm{p})$| | |$-0.014_{-0.002}^{+0.002}$| | |$0.0559_{-0.0005}^{+0.0005}$| |
| i (°) | |$88.982_{-0.005}^{+0.007}$| | – |
| icos (Ωp) | – | |$-89.172_{-0.005}^{+0.002}$| |
| isin (Ωp) | – | |$1.7_{-0.5}^{+0.2}$| |
| λp (°)(a) | |$179.49_{-0.11}^{+0.15}$| | |$293.9_{-0.1}^{+0.3}$| |
| Derived dynamical model | ||
| Mp (M⊕) | |$43.4_{-2.0}^{+1.6}$| | |$29.9_{-1.3}^{+1.1}$| |
| ρp (g cm−3) | |$0.42_{-0.09}^{+0.06}$| | |$0.31_{-0.06}^{+0.05}$| |
| ep | |$0.0609_{-0.0013}^{+0.0010}$| | |$0.06691_{-0.00012}^{+0.00010}$| |
| ωp (°) | |$357.0_{-0.4}^{+0.5}$| | |$167.5_{-0.1}^{+0.1}$| |
| |$\mathcal {M}_\mathrm{p}$| (°) | |$2.6_{-0.6}^{+0.5}$| | |$307.4_{-0.1}^{+0.1}$| |
| i (°) | – | |$89.188_{-0.006}^{+0.005}$| |
| Ωp (°) | 180. (fixed) | |$179.0_{-0.1}^{+0.3}$| |
| dynamical model|$\chi ^2_\textrm{r}$| (dof = 230) | 1.16 | – |
| Parameter . | Kepler-9b . | Kepler-9c . |
|---|---|---|
| Fitted dynamical model | ||
| Mp/M⋆ | |$0.000128_{-0.000002}^{+0.000001}$| | |$0.000088_{-0.000001}^{+0.000001}$| |
| Pp (day) | |$19.23891_{-0.00006}^{+0.00006}$| | |$38.9853_{-0.0003}^{+0.0003}$| |
| |$\sqrt{e}\cos (\omega _\mathrm{p})$| | |$0.24651_{-0.0027}^{+0.0021}$| | |$-0.2526_{-0.0003}^{+0.0003}$| |
| |$\sqrt{e}\sin (\omega _\mathrm{p})$| | |$-0.014_{-0.002}^{+0.002}$| | |$0.0559_{-0.0005}^{+0.0005}$| |
| i (°) | |$88.982_{-0.005}^{+0.007}$| | – |
| icos (Ωp) | – | |$-89.172_{-0.005}^{+0.002}$| |
| isin (Ωp) | – | |$1.7_{-0.5}^{+0.2}$| |
| λp (°)(a) | |$179.49_{-0.11}^{+0.15}$| | |$293.9_{-0.1}^{+0.3}$| |
| Derived dynamical model | ||
| Mp (M⊕) | |$43.4_{-2.0}^{+1.6}$| | |$29.9_{-1.3}^{+1.1}$| |
| ρp (g cm−3) | |$0.42_{-0.09}^{+0.06}$| | |$0.31_{-0.06}^{+0.05}$| |
| ep | |$0.0609_{-0.0013}^{+0.0010}$| | |$0.06691_{-0.00012}^{+0.00010}$| |
| ωp (°) | |$357.0_{-0.4}^{+0.5}$| | |$167.5_{-0.1}^{+0.1}$| |
| |$\mathcal {M}_\mathrm{p}$| (°) | |$2.6_{-0.6}^{+0.5}$| | |$307.4_{-0.1}^{+0.1}$| |
| i (°) | – | |$89.188_{-0.006}^{+0.005}$| |
| Ωp (°) | 180. (fixed) | |$179.0_{-0.1}^{+0.3}$| |
| dynamical model|$\chi ^2_\textrm{r}$| (dof = 230) | 1.16 | – |
Note. (a)λp is the mean longitude of the planet, defined as |$\lambda _\mathrm{p}= \Omega _\mathrm{p}+ \omega _\mathrm{p}+ \mathcal {M}_\mathrm{p}$|.
Table summarizing the dynamical fit solution. Parameter values as the MLE and HDI at 68.27 per cent equivalent. Dynamical parameters are computed at the epoch of reference BJD|$_\textrm{TDB}\, 2455088.212$|.
| Parameter . | Kepler-9b . | Kepler-9c . |
|---|---|---|
| Fitted dynamical model | ||
| Mp/M⋆ | |$0.000128_{-0.000002}^{+0.000001}$| | |$0.000088_{-0.000001}^{+0.000001}$| |
| Pp (day) | |$19.23891_{-0.00006}^{+0.00006}$| | |$38.9853_{-0.0003}^{+0.0003}$| |
| |$\sqrt{e}\cos (\omega _\mathrm{p})$| | |$0.24651_{-0.0027}^{+0.0021}$| | |$-0.2526_{-0.0003}^{+0.0003}$| |
| |$\sqrt{e}\sin (\omega _\mathrm{p})$| | |$-0.014_{-0.002}^{+0.002}$| | |$0.0559_{-0.0005}^{+0.0005}$| |
| i (°) | |$88.982_{-0.005}^{+0.007}$| | – |
| icos (Ωp) | – | |$-89.172_{-0.005}^{+0.002}$| |
| isin (Ωp) | – | |$1.7_{-0.5}^{+0.2}$| |
| λp (°)(a) | |$179.49_{-0.11}^{+0.15}$| | |$293.9_{-0.1}^{+0.3}$| |
| Derived dynamical model | ||
| Mp (M⊕) | |$43.4_{-2.0}^{+1.6}$| | |$29.9_{-1.3}^{+1.1}$| |
| ρp (g cm−3) | |$0.42_{-0.09}^{+0.06}$| | |$0.31_{-0.06}^{+0.05}$| |
| ep | |$0.0609_{-0.0013}^{+0.0010}$| | |$0.06691_{-0.00012}^{+0.00010}$| |
| ωp (°) | |$357.0_{-0.4}^{+0.5}$| | |$167.5_{-0.1}^{+0.1}$| |
| |$\mathcal {M}_\mathrm{p}$| (°) | |$2.6_{-0.6}^{+0.5}$| | |$307.4_{-0.1}^{+0.1}$| |
| i (°) | – | |$89.188_{-0.006}^{+0.005}$| |
| Ωp (°) | 180. (fixed) | |$179.0_{-0.1}^{+0.3}$| |
| dynamical model|$\chi ^2_\textrm{r}$| (dof = 230) | 1.16 | – |
| Parameter . | Kepler-9b . | Kepler-9c . |
|---|---|---|
| Fitted dynamical model | ||
| Mp/M⋆ | |$0.000128_{-0.000002}^{+0.000001}$| | |$0.000088_{-0.000001}^{+0.000001}$| |
| Pp (day) | |$19.23891_{-0.00006}^{+0.00006}$| | |$38.9853_{-0.0003}^{+0.0003}$| |
| |$\sqrt{e}\cos (\omega _\mathrm{p})$| | |$0.24651_{-0.0027}^{+0.0021}$| | |$-0.2526_{-0.0003}^{+0.0003}$| |
| |$\sqrt{e}\sin (\omega _\mathrm{p})$| | |$-0.014_{-0.002}^{+0.002}$| | |$0.0559_{-0.0005}^{+0.0005}$| |
| i (°) | |$88.982_{-0.005}^{+0.007}$| | – |
| icos (Ωp) | – | |$-89.172_{-0.005}^{+0.002}$| |
| isin (Ωp) | – | |$1.7_{-0.5}^{+0.2}$| |
| λp (°)(a) | |$179.49_{-0.11}^{+0.15}$| | |$293.9_{-0.1}^{+0.3}$| |
| Derived dynamical model | ||
| Mp (M⊕) | |$43.4_{-2.0}^{+1.6}$| | |$29.9_{-1.3}^{+1.1}$| |
| ρp (g cm−3) | |$0.42_{-0.09}^{+0.06}$| | |$0.31_{-0.06}^{+0.05}$| |
| ep | |$0.0609_{-0.0013}^{+0.0010}$| | |$0.06691_{-0.00012}^{+0.00010}$| |
| ωp (°) | |$357.0_{-0.4}^{+0.5}$| | |$167.5_{-0.1}^{+0.1}$| |
| |$\mathcal {M}_\mathrm{p}$| (°) | |$2.6_{-0.6}^{+0.5}$| | |$307.4_{-0.1}^{+0.1}$| |
| i (°) | – | |$89.188_{-0.006}^{+0.005}$| |
| Ωp (°) | 180. (fixed) | |$179.0_{-0.1}^{+0.3}$| |
| dynamical model|$\chi ^2_\textrm{r}$| (dof = 230) | 1.16 | – |
Note. (a)λp is the mean longitude of the planet, defined as |$\lambda _\mathrm{p}= \Omega _\mathrm{p}+ \omega _\mathrm{p}+ \mathcal {M}_\mathrm{p}$|.
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