The MACRO underground detector at Gran Sasso has recorded about 30 million muon events in the period 1989-1995. We have analyzed these data to look for time variations and to study the pointing capabilities of the apparatus in the search for astrophysical point sources. We have observed a 3% seasonal variation of the high energy muon rate, due to atmospheric temperature variations, in agreement with theoretical predictions. We report also the detection of the moon shadowing effect with a statistical significance of 3.7 σ. The results obtained straighten the possibility that a "muon astronomy" using underground experiments is possible.