"It is unclear whether the Dwarvish constellation Durin's Crown, seen in the reflection of Mirrormere, is the Valacirca."[edit source]
Why is it unclear? In the Lord of the Rings index it says:
Durin I, ‘the Deathless’ 315–17, 547, 1071, 1074, 1079;
This entry also states Valacirca is identified as the Big Dipper. Since Plough and Big Dipper are the same constellation, Durin's Crown and Valacrirca are also the same constellation.