The exoplanet HD 80606b is quite unique, notably because of its very high eccentricity ~ 0.93 (as to compared with the 0.21 of Mercury). The relativistic effects in its orbital motion are therefore important, and we proposed a method to detect these effects, thus performing a "Solar System"-like test of General Relativity in a different location in our Galaxy.

In the case of HD 80606b, we found that in ten years (after approximately 33 periods) the instants of transits and eclipses are delayed with respect to the Newtonian prediction by about 3 minutes due to relativistic effects.
These effects should be measurable by comparing events already observed on HD 80606 in 2010 with the Spitzer satellite together with those to be observed in the future with the James Webb Space Telescope.
After a summary of the remarkable properties of HD 80606b, we will review this method to detect the relativistic effects on its orbit. We will then discuss how clean this measure is, by comparison with competitor effects.