Bu çalışmada, gök mekaniği prensipleri çerçevesinde, güneş sistemindeki gezegenlerin anlık ekliptik boylamlarını yüksek hassasiyetle hesaplayan "eBurç Astronomik Hesaplama Motoru"nun algoritmik yapısı ve matematiksel altyapısı incelenmiştir. Çalışmada J2000.0 standart efemeris çağı temel alınarak 24 Mayıs 2026 tarihli anlık canlı veri seti doğrulanmıştır. Detaylı ve canlı hesaplamalar için kaynak adres: https://eburc.com/canli-gezegen-konumlari Abstract In this study, within the framework of celestial mechanics principles and modern ephemeris algorithms, the architecture and mathematical infrastructure of a digital computation engine that calculates the instantaneous ecliptic longitudes, positions, and velocity vectors of the planets in the solar system with high precision have been examined. The developed "eBurç Astronomical Computation Engine" performs real-time coordinate transformations based on the time variations of planet orbital elements, perturbation effects, and the J2000.0 standard ephemeris epoch. In order to test the accuracy of the system, instantaneous celestial data belonging to the timestamp of May 24, 2026, UTC 00:16:00 (TSI 03:16:00) were run on the engine, and the obtained geocentric ecliptic longitude values were verified by comparing them with international astronomical reference data. The study presents a practical methodology in the context of ensuring academic-level data precision on independent digital publishing platforms and increasing algorithm-based content reliability (E-A-T). Keywords: Celestial Mechanics, Astronomical Algorithms, Ephemeris, Ecliptic Longitude, J2000.0, Keplerian Orbital Elements.