Note on the perihelion/periastron advance due to cosmological constant

We will comment on the perihelion/periastron advance of celestial bodies due to the cosmological constant $Λ$. It is well known that the cosmological constant $Λ$ causes the perihelion/periastron shift; however, there seems to still exist a discrepancy among the various derived precession formulae. We will point out that the expression $Δω_Λ = (πc^2 Λa^3/(GM))\sqrt{1 - e^2}$ is the general formula for any orbital eccentricity $e$ and the expression $Δω_Λ = (πc^2 Λa^3/(GM))(1 - e^2)^3$ comes from the nearly circular ($e \ll 1$) approximation.

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