there maybe a wrong orbit extrapolation about celestial body

[BlackBreezeCastle]

when i try to make a orbit calculator to design lunar polar transfer orbit, I used krpc to check the correctness about position extrapolation and velocity extrapolation ,and it works well without rss. but when load rss the extrapolation of celestial body's position is wrong and extrapolation about vessel is till right.
I've checked and found that when the true anomly is same the result is same but same time caused a different extrapolation( extrapolation about vessel or is still right). then I get the semi majo axis length ,gravitational parameter and period in celestial body‘s orbit but it turn out to be not match to physics formula T=2π√(a^3/GM)
so I wonder how the celestial body move so that I can make a right orbit extrapolation about celestial body to lead my vessel into a right transfer orbit.

[BlackBreezeCastle]

On closer inspection ，it seems when the mean anomaly is same the extrapolation is same, so only the calculation of period does not match.

[Kerbas-ad-astra]

RSS has Kopernicus "finalize" the orbit of the Moon to take account of the fact that the Moon's mass is large enough to have a slightly different orbital period than if it had zero mass. (Well, RSS has Kopernicus do this for all celestial bodies, but the Moon happens to be one where this matters.)

[BlackBreezeCastle]

thanks