What does coelum empireum mean in Latin?

coelum empireum, a noun, means “coelum empireum (outermost part of the cosmos in the Ptolemaic system)”.

What is the genitive of coelum empireum?

The genitive singular is coelī empireī. coelum empireum is second declension.

nounsecond declension

coelum empireum n (genitive coelī empireī)

neuterobsoletecoelum empireum (outermost part of the cosmos in the Ptolemaic system)
Quis enim locus cœlo empireo sanctior?For which place is more holy than the coelum empireum?c. 1190, Alexander Neckam, De Naturis Rerum, 1863 edition, Longman, Green, Longman, Roberts, and Green, page 21:
Ergo & corpora ſanctorum, mouebuntur, ſcilicet aſcendendo de terra in cœlum empireum.Therefore also the bodies of the saints will be moved, to wit by ascending from the Earth to the coelum empireum.1585, Hieronymus Theutonicus, Summa Theologiæ D. Th. Aquinatis, Doct. Angelici. iuxta præcipuas illius concluſiones in compendium redactæ, Tomus Primus, Damiano Zenario, page 471:

From coelum (alternative form of caelum) + empireus (from πῦρ (pûr)).