How many scenes are there for ASTER per year ?
From what I understand is that the temporal is every 16 days. So, some month it will have 2 and some months it will have one.
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The ground track repeat cycle for ASTER is 16 days, which means every 16 days the pattern of orbit is repeated. So, each year a ground track is repeated (365/16) approximately 23 times. Therefore, you can acquire images of the same area 23 times per year.
The orbit period is approx. 98 minutes. Therefore, each year there are (365*25*60 = 547500/98), give or take, 5587 orbits per year.
The circumference of the earth is approx. 40,075km. For a scene size of 150km, that means (40,075/150) 267 150km scenes per orbit.
267*5587 = 1,491,729 scenes per year or 124,310 per month.
There are many assumptions built in here (e.g. the satellite is always capturing data, scene size is approximated), but that's a literal approach to the question you asked - is this actually what you were looking for or did you just want the repeat cycle?
I don't think it is possible to answer this question with a single number. ASTER does not provide a fixed number of scenes per month or per year.
@Radar answer is innacurate because the OP asked specifically about ASTER. ASTER is orbiting in the Terra satellite, which in fact has a repeat cycle of 16 days. But ASTER only collects on scheduled missions, that is, it is not ON all the time. Perhaps the main reason for this is that there are other four instruments in Terra and there is a bandwidth restriction, where MODIS most likely takes the largest share.
If you really want to know the number of scenes in a given year or month, you can look at the list of ASTER paths (2001 and scheduled up to 2020) provided by the ASTER Ground Data System:
Note: some of the links in the above page seem to be outdated, you need to replace the domain with http://www.aster.jspacesystems.or.jp