The paper discusses an assessment study about the impact of the distortions on the astrometric observations with the Extremely Large Telescope originated from the optics positioning errors and telescope instabilities .
Optical simulations combined with Monte Carlo approach reproducing typical inferred opto-mechanical and dynamical instabilities , show RMS distortions between \sim 0.1-5 mas over 1 arcmin field of view .
Over minutes timescales the plate scale variations from ELT-M2 caused by wind disturbances and gravity flexures and the field rotation from ELT-M4-M5 induce distortions and PSF jitter at the edge of 1 arcmin FoV ( radius 35 arcsec ) up to \sim 5 mas comparable to the diffraction-limited PSF size FWHM _ { H } = 8.5 mas .
The RMS distortions inherent to the ELT design are confined to the 1 ^ { st } -3 ^ { rd } order and reduce to an astrometric RMS residual post fit of \sim 10-20 \mu as for higher order terms .
In this paper , we study which calibration effort has to be undertaken to reach an astrometric stability close to this level of higher order residuals .
The amplitude and timescales of the assumed telescope tolerances indicate the need for frequent on-sky calibrations and MCAO stabilization of the plate scale to enable astrometric observations with ELT at the level of \leq 50 \mu as , which is one of the core science missions for the ELT / MICADO instrument .