Yes - there are ways of determining it. What you are looking for is hindcasting a overpass prediction for either the Terra or the Aqua satellite. While it is possible, it is usually not really a suitable thing, unless you are working on a large programmetical solution to a given problem.
If you choose to go for it, you'll need to look at ephemeris data for the satellites, and potentially get some dedicated software for the calculations.
If you specifically want the data, in a less automated fashion, I'd suggest using the available L1-browsers - such as http://oceancolor.gsfc.nasa.gov/cgi/browse.pl?sen=am