If Saruman was not performing astronomy and not necessarily astrology either, what was he doing? Was he looking at the stars of Varda and remembering his time in Valinor with longing? *squeals* Awww, Emo-Saruman!
A bit more seriously, it is indeed a good question what was he doing up there. Like
Gwath said, he probably knew a lot of the "scientific facts" about space, so he would not need to bother with that. And as to astronomy, can you really picture Saruman at his towers, musing: "So, Éowyn is a Virgo... hmmm... looking at the postion of Mercury, it looks like she'll develop a fatal crush on a Mysterious Stranger... "?