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Since you are using I2C, you could use something like the PCF85063A real-time-clock which has an alarm function. You set the alarm time and it pops up a pin. You can either do the sidereal to solar calculation or, since the osc uses the crystal in series resonance, pull it off frequency to run the clock at sidereal rate. The chip will keep time for years on a hearing aid battery.
Excellent project BTW.
Steve.
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