Suspend the satsumas in cheesecloth above the grain alcohol in a vessel with an airtight seal; if it is not air tight, all of your alcohol will evaporate. Seal the vessel and put in a cool, dark place for 45 days. Remove the satsumas—they should be hard and fibrous inside—and discard. Strain the satsuma oil-infused alcohol, and measure remaining volume.
Combine the water and sugar in a saucepot and bring to a light simmer until the sugar dissolves. Remove from heat and cool completely. Combine one part alcohol with 2 parts simple syrup. (Add less syrup depending on the sweetness of the fruit). Bottle the mixture, and store 30 to 45 days before drinking. Chill the bottles before serving.