Broadcasting one bit per day isotropically requires using the sidereal day, not the solar day, making things more complicated. (More precisely, not the sidereal day but the sidereal rotation period because the misnamed former drifts due to the precession of the equinoxes.) We must rely on astronomers to keep a sidereal clock in sync with the apparent motion of the stars.
Most astronomical sidereal clocks only provide the time elapsed within a sidereal day. However, in order to know which bit to transmit, we need to keep track of the number sidereal days elapsed. Unlike the Julian day number which uses solar days, there does not seem to be a standard epoch from which to count sidereal days.
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