2. In astronomy, a sidereal year is denoted as $E=365.256$ days, and the time it takes for the Moon to orbit the Earth once is called a sidereal month, represented as $T=27.322$ days. The cycle of the Moon's phases, from full moon to half moon, crescent moon, gibbous moon, new moon, and back to full moon, is called a "synodic month," and its duration is denoted by $S$. $E$, $T$, and $S$ satisfy the conjunction motion equation $\frac{1}{S}+\frac{1}{E}=\frac{1}{T}$. From this, we can derive that $S=$ $\qquad$ days (accurate to 0.001 days).
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