= A chosen stellar-orbit mass estimate
Choose $D=7.5\,\mathrm{kpc}$, $\alpha=0.110$ <arcseconds>, $P=18$ years, $e=0.70$ and $i=55$ degrees. The small-angle conversion gives \b[$a=825\,\mathrm{AU}$]. Taking one model year as $365.25$ <days> gives $\mu\simeq2.30\times10^{26}\,\mathrm{m^3s^{-2}}$ and $K\simeq1566\,\mathrm{km/s}$.
Dividing by the <nominal solar mass parameter>, $(GM)_\odot^{\rm N}=1.3271244\times10^{20}\,\mathrm{m^3s^{-2}}$, gives \b[$1.73\times10^6$ nominal solar masses]. The nominal parameter is an exact conversion convention, rather than an assertion that the <Sun>'s measured <mass> is exact.<Resolution B3 on recommended nominal conversion constants for selected solar and planetary properties by International Astronomical Union>[PDF pp.2–3, exact nominal solar mass parameter and conversion recommendation]{ref}
The chosen <periapsis> radius is $r_p=a(1-e)=247.5\,\mathrm{AU}$. Its corresponding <Schwarzschild radius>, $r_s=2\mu/c^2$, is about $0.0342\,\mathrm{AU}$. Thus this illustrative orbit remains roughly $7200$ Schwarzschild radii from the centre at closest approach. Inferring a very concentrated mass from such an orbit is different from directly resolving its <event horizon>. Every number here follows from the chosen orbit, not from a fit to the actual Galactic-centre measurements.
Back to article page
