Unlocking the Secrets of Satellite Speed. A Novel Perturbed Orbital Velocity Formula

Research Paper (postgraduate) from the year 2026 in the subject Physics - Astronomy, grade: B, , language: English, abstract: Satellite orbital velocities form the backbone of space mission design, traditionally captured by the Keplerian expression v = sqrt(GM/r) for circular orbits. This research introduces an innovative extension: v(r) = sqrt(GM/r) * [1 + A sin^2 (pi ln(r/r0)/ln eta0)]^(1/2), blending classical gravity with a logarithmic-periodic perturbation to model real-world deviations from ideal motion. Parameters A (amplitude), r0 (reference radius), and eta0 (>1, period control) enable flexible capture of effects like atmospheric drag, J2 oblateness, and radiation pressure. Through detailed derivations, numerical examples for Earth low Earth orbit (LEO) and Mars trajectories, sensitivity analyses, and comparisons to standard models, we demonstrate 0.1-2% corrections aligning with observational data. This semi-analytic tool offers astrodynamicists a balance of precision and simplicity, paving the way for applications in CubeSat constellations, interplanetary transfers, and exoplanet dynamics.