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Eccentricity of wide binaries is difficult to measure due to their longorbital periods. With Gaia's high-precision astrometric measurements,eccentricity of a wide binary can be constrained by the angle between theseparation vector and the relative velocity vector (the $v$-$r$ angle). In thispaper, by using the $v$-$r$ angles of wide binaries in Gaia Early Data Release3, we develop a Bayesian approach to measure the eccentricity distribution as afunction of binary separations. Furthermore, we infer the eccentricities ofindividual wide binaries and make them publicly available. Our results showthat the eccentricity distribution of wide binaries at $10^2$ AU is close touniform and becomes superthermal at $>10^{3}$ AU, suggesting two formationmechanisms dominating at different separation regimes. The close binaryformation, most likely disk fragmentation, results in a uniform eccentricitydistribution at $<10^{2}$ AU. The wide binary formation that leads to highlyeccentric wide binaries at $>10^{3}$ AU may be turbulent fragmentation and/orthe dynamical unfolding of compact triples. With Gaia, measuring eccentricitiesis now possible for a large number of wide binaries, opening a new window tounderstanding binary formation and evolution.

The eccentricity distribution of wide binaries and their individual measurements