We aim at studying the gamma-ray burst GRB 081008 environment by analysing the spectra of its optical afterglow .
UVES/VLT high resolution spectroscopy of GRB 081008 was secured \sim 5 hr after the Swift -BAT trigger .
Our dataset comprises also three VLT/FORS2 nearly simultaneous spectra of the same source .
The availability of nearly simultaneous high and low resolution spectra for a GRB afterglow is an extremely rare event .
The GRB-Damped Lyman Alpha system at z = 1.9683 shows that the interstellar medium ( ISM ) of the host galaxy is constituted by at least three components which contribute to the line profiles .
Component I is the redmost one , and is 20 km/s and 78 km/s redward component II and III , respectively .
We detect several ground state and excited absorption features in components I and II .
These features have been used to compute the distances between the GRB and the absorbers .
Component I is found to be 52 \pm 6 pc away from the GRB , while component II presents few excited transitions and its distance is 200 ^ { +60 } _ { -80 } pc .
Component III only features a few , low ionization and saturated lines suggesting that it is even farther from the GRB .
Component I represents the closest absorber ever detected near a GRB .
This ( relatively ) low distance can possibly be a consequence of a dense GRB environment , which prevents the GRB prompt/afterglow emission to strongly affect the ISM up to higher distances .
The hydrogen column density associated to GRB 081008 is \log N _ { H } / { cm } ^ { -2 } = 21.11 \pm 0.10 , and the metallicity of the host galaxy is in the range [ X/H ] = -1.29 to -0.52 .
In particular , we found [ Fe/H ] = -1.19 \pm 0.11 and [ Zn/H ] = -0.52 \pm 0.11 with respect to solar values .
This discrepancy can be explained by the presence of dust in the GRB ISM , given the opposite refractory properties of iron and zinc .
By deriving the depletion pattern for GRB 081008 , we find the optical extinction in the visual band to be A _ { V } \sim 0.19 mag .
The Curve of Growth analysis applied to the FORS2 spectra brings column densities consistent at the 3 \sigma level to that evaluated from the UVES data using the line fitting procedure .
This reflects the low saturation of the detected GRB 081008 absorption features .