computing the apparent place of a star

[Giuseppe Donnini]

Since I have no knowledge of, nor interest in, the HP Prime calculator, I can only try to answer this question on purely astronomical grounds.

ΔT is an empirical quantity depending on Earth’s rotation, so you probably have to supply it yourself:

• For present-day observations you may simply use the current value – which is 69.2045 seconds as per NASA’s Earth Observing System Data and Information System (EOSDIS) – and keep it updated every month or so.
   
• For dates between February 1973 (first recorded data) and today, you may simply fetch the appropriate value from a table, either by hand or programmatically.
   
• For dates before February 1973, as well as for dates several years – or even centuries – in the future, you should translate the current state-of-the-art prediction models into a runnable HP Prime program.