One-Sidedness as a Speedometer: Bulk Velocity from Jet to Counterjet Brightness Ratios

This paper addresses a single accounting question in the physics of relativistic jets: what the absence or faintness of a counterjet, quantified as a brightness ratio, implies for the product of speed and viewing geometry in a two-sided outflow. Using published jet-to-counterjet brightness ratios from three to one thousand for five sources, with a spectral index of 0.8, the calculation derives new bounds and budgets from standard synchrotron and special-relativistic relations, with every number produced by the deposited compute script. The headline results are: most constrained = 0.844. M87: 0.389, Centaurus A: 0.194, 3C 273: 0.844, Cygnus A: 0.676, NGC 6251: 0.489. The nearby, modest-ratio sources require only mildly relativistic motion on the measured scales, while the ratio of one thousand requires beta cos theta close to unity, demanding both high speed and favourable orientation on scales where the ratio was measured. The study is a computation from stated assumptions and published inputs; it is simulated, not measured, and its conclusions are stated at the precision those inputs support.