From Tolkien Gateway

"It is unclear whether the Dwarvish constellation Durin's Crown, seen in the reflection of Mirrormere,[7] is the Valacirca."

Why is it unclear? In the Lord of the Rings index it says:

Durin I, ‘the Deathless’ 315–17, 547, 1071, 1074, 1079;

emblem of [seven stars above a crown and anvil, had eight rays, represented the Plough] Colonelviied (talk) 21:20, 15 July 2023 (UTC)Reply[reply]

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.