The effects of the spin and quadrupole moment of SgrA* on the orbits of S stars

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Table 1.

Comparing the various maximal secular shifts of the star S2.

$Δ X_{S 2}^{2 PN}$ $Mathematical equation: $ \Delta X^{\mathrm{2PN}}_{\mathrm{S2}} $$	\|max(ΔX)\|	$\frac{\| max (Δ X) \|}{Δ ϖ_{Sch}}$ $Mathematical equation: $ \dfrac{\|\max(\Delta X)\|}{\Delta\varpi_{\mathrm{Sch}}} $$	θ	ω − β
Δϖ_Sch	732 ″/rev	100%	–	–
Δϖ_LT	13.3 ″/rev	1.81%	0	–
ΔΘ_LT	6.63 ″/rev	0.91%	π/2	π/2
ΔΞ_LT	6.63 ″/rev	0.91%	π/2	0
Δϖ_Q	0.0675 ″/rev	0.01%	0	–
ΔΘ_Q	0.0338 ″/rev	0.005%	π/4	π/2
ΔΞ_Q	0.0338 ″/rev	0.005%	π/4	0

Notes. We use a single set of orbital parameters for all shifts, the osculating one at apocenter. We recall the values with (mod π) of θ and ψ that maximize each effect.

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