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Magnetic fields play an important role in the evolution of molecular cloudsand star formation. Using the Velocity Gradient Technique (VGT) model, wemeasured the magnetic field in Orion A using the 12CO, 13CO, and C18O (1-0)emission lines at a scale of 0.07 pc. The measured B-field shows an east-westorientation that is perpendicular to the integral shaped filament of Orion A atlarge scale. The VGT magnetic fields obtained from 13CO and C18O are inagreement with the B-field that is measured from the Planck 353 GHz dustpolarization at a scale of 0.55 pc. Removal of density effects by using aVelocity Decomposition Algorithm can significantly improve the accuracy of theVGT in tracing magnetic fields with the 12CO (1-0) line. The magnetic fieldstrength of seven sub-clouds, OMC-1, OMC-2, OMC-3, OMC-4, OMC-5, L 1641-N, andNGC 1999 has also been estimated with the Davis-Chandrasekhar-Fermi (DCF) andMM2 technique, and these are found to be in agreement with previous resultsobtained from dust polarization at far-infrared and sub-millimeter wavelengths.At smaller scales, the VGT proves a good method to measure magnetic fields.

Magnetic Field of Molecular Gas Measured with the Velocity Gradient Technique I. Orion A