Why would the Catholic church need an observatory?

To study planets and stars. The observatory has its headquarters at the papal summer residence in Castel Gandolfo, Italy, outside Rome.

Its independent research center, the Vatican Observatory Research Group, is hosted by Steward Observatory at the University of Arizona, Tucson, USA. In the southeast portion of that state is the Vatican Observatory Research Group, which operates the 1.8m Alice P. Lennon Telescope, a superb instrument.

Thus the administrative facility is in Italy, while the eyeball is the southwest US.

Contrary to the popular notion that the Catholic Church has ignored or has no interest in material scientific matters, the church has actually, and very quietly, been engaged at the cutting edge in many fields. Among its more recognized talents is George Coyne, noted astronomer, who has contributed to the research of Seyfert galaxies, and very skillfully managed the intellectual challenges of Atheist poster boy Richard Dawkins.

Likewise, Catholics have contributed to new understanding of biological and genetic processes. Kevin Fitzgerald studies angiogenesis and abnormal gene regulation, and is as an associate research professor at Georgetown University.

I hope that helps.

To "observe" perhaps?

Perhaps to prove the point that the Catholic Church isn't nearly as anti-science as some people would like to believe.

To gaze upon the glory of God's creation and marvel at His goodness and fuel our love for and worship of Him.

To keep up with science behind closed doors and behind their limited teachings.

their head is stuck up there pretty far

So they can look for God.

I dunno, maybe to look at the stars?