2023ApJ...954..219I

The maximal values of the general relativistic Lense-Thirring (LT) orbital shifts ΔI^LT, ΔΩ^LT, and Δω^LT of the inclination I, the longitude of the ascending node Ω, and the perinigricon ω, respectively, of the recently discovered star S4716, which has the shortest orbital period $\left({P}_{{\rm{b}}}=4.02\,\mathrm{yr}\right)$ of all the S stars that orbit the supermassive black hole (SMBH) in Sgr A*, are of the order of ≃5-16 arcseconds per revolution $\left({}^{{\prime\prime} }\,{\mathrm{rev}}^{-1}\right)$. Given the current error σ_ω = 0.°02 in determining ω, which is the most accurate orbital parameter of S4716 among all those affected by the SMBH's gravitomagnetic field through its angular momentum J_•, about 48 yr would be needed to reduce σ_ω to ≃10% of the cumulative LT perinigricon shift over the same time span. Measuring ΔI^LT and ΔΩ^LT to the same level of accuracy would take much longer. Instead, after just 16 yr, a percent measurement of the larger gravitoelectric (GE) Schwarzschild-like perinigricon shift Δω^GE, which depends only on the SMBH's mass M_•, would be possible. On the other hand, the uncertainties in the physical and orbital parameters entering Δω^GE would cause a huge systematic bias of Δω^LT itself. The SMBH's quadrupole mass moment ${Q}_{2}^{\bullet }$ induces orbital shifts as little as ≃0.01-0.05″ rev^–1.