Indeed.. as you probably know..
Here it is..
Assuming that the painting was fulfilled on 25 Sept. 1888, we realize that the Big Dipper was represented as visible around 10:30 pm. We have the sensation, however, that it was not painted within few minutes.
In fact, the two rear stars indicate a direction which is in agreement with a time following that suggested by the eastern part of the Dipper: the Alkaid-Megrez line is almost horizontal, while the Dubhe-Merak direction points to the bottom right.
This direction is even in disagreement with the Alkaid-Dubhe direction, the latter being in accordance with the position of the eastern stars.
Van Gogh reported all the seven brighter stars, however slightly modifying their positions. In particular, Alioth is too close to Megrez, also resulting not aligned with the Mizar-Megrez direction. We've found Phecda quite out-of-place: the rear part of the Big Dipper should be almost rectangular, while in the painting it shows a clear trapezoidal shape.
A possible explanation, suggested by the time gap mentioned above, is that Merak was placed on the canvas about 40 minutes later than the others, followed by Phecda, probably placed looking at Dubhe and Merak, as the Dubhe-Merak-Phecda angle is correct (but Merak and Phecda are too close).
The elevation above the horizon of the Big Dipper, evaluated looking at its dimensions, is in good agreement with the latitude of Arles (43.66° N), so van Gogh in this case has correctly evaluated the angular distances involved.