Is it possible to get the seconds for the Zmanim?»
Although this would be technically possible to compute the astronomical times for sunset, sunrise, and other related planetary events, up to the seconds, this would make little sense with regards to Halacha.
Our Sages in the Talmud discussed the times in terms of counting a walking distance, or distinguishing the color of the tzitziot. Later, the poskim fixed various methods to calculate the zmanim according to the position of the sun, which enabled the introduction of mathematical formulas.
In any case, the calculations are only approached values, whether by observing the actual position of the Sun in the sky, or by measuring the amount of ambient light or the inaccurate average walking pace — or by using simplified astronomical formulas.
Therefore, despite the importance of expressing an explicit halacha rule (such as “18 minutes after sunset”, or “the Sun at -8.333 degrees below the horizon”), the maths here involve an estimate of the Earth’ radius and Sun-Earth distance and of many more elements, including the actual position of the observer. It would have no real meaning to specify the Zmanim down to the second. A synagogue at one end of Paris will not have the same second-specific Havdala time as another synagogue at the other end of the city.
In addition, even if there was a consensus to find in the second-wise Zmanim, the accuracy of everyone’s wrist watch is not sufficient enough, nor properly synchronized.
In conclusion, the times are in general expressed by rounding up — or down, depending whether we’re talking about Shabbat’s end or begin time for example — to the nearest minute, which still leaves some room for the random inaccuracy of small approximations.
In CalJ for extra-safety, the “minimum” times are rounded up to the minute (earliest Shema’, end of Shabbat of fast, etc.) whereas “maximum” times are rounded down (beginning of Shabbat of fasts, latest time for Shema’, etc.).