We present the results of detailed simulations of the RV and astrometric signals expected from the Sun, when taking into account its activity (spots, plages, convection). To do so, we considered all structures (2,000,000) identified on the Sun surface over a full cycle. We show that the Sun activity would prevent the detection of the Earth in the Habitable Zone with RV technics with today or future forthcoming instruments, mainly because of inhomogeneous convection. We also show that the activity-induced signal would be comparatively easier for the astrometric detection of the Earth of similar planets.