The detection of low-mass extra-solar planets through radial-velocity searches is currently limited by the intrinsic magnetic activity of the host stars. The correlated noise that arises from their natural radial-velocity variability can easily mimic or conceal the orbital signals of super-Earth and Earth-mass extra-solar planets. I developed an intuitive and robust data analysis framework in which the activity-induced variations are modelled with a Gaussian process that has the frequency structure of the photometric variations of the star, thus allowing me to determine precise and reliable planetary masses. I applied this technique to three recently discovered planetary systems: CoRoT-7, Kepler-78 and Kepler-10. I determined the masses of the transiting super-Earth CoRoT-7b and the small Neptune CoRoT-7c to be 4.73 ± 0.95 M⊕ and 13.56 ± 1.08 M⊕, respectively. The density of CoRoT-7b is 6.61 ± 1.72 g.cm⁻³, which is compatible with a rocky composition. I carried out Bayesian model selection to assess the nature of a previously identified signal at 9 days, and found that it is best interpreted as stellar activity. Despite the high levels of activity of its host star, I determined the mass of the Earth-sized planet Kepler-78b to be 1.76 ± 0.18 M⊕. With a density of 6.2(+1.8:-1.4) g.cm⁻³, it is also a rocky planet. I found the masses of Kepler-10b and Kepler-10c to be 3.31 ± 0.32 M⊕ and 16.25 ± 3.66 M⊕, respectively. Their densities, of 6.4(+1.1:-0.7) g.cm⁻³ and 8.1 ± 1.8 g.cm⁻³, imply that they are both of rocky composition – even the 2 Earth-radius planet Kepler-10c! In parallel, I deepened our understanding of the physical origin of stellar radial-velocity variability through the study of the Sun, which is the only star whose surface can be imaged at high resolution. I found that the full-disc magnetic flux is an excellent proxy for activity-induced radial-velocity variations; this result may become key to breaking the activity barrier in coming years. I also found that in the case of CoRoT-7, the suppression of convective blueshift leads to radial-velocity variations with an rms of 1.82 m.s⁻¹, while the modulation induced by the presence of dark spots on the rotating stellar disc has an rms of 0.46 m.s⁻¹. For the Sun, I found these contributions to be 2.22 m.s⁻¹ and 0.14 m.s⁻¹, respectively. These results suggest that for slowly rotating stars, the suppression of convective blueshift is the dominant contributor to the activity-modulated radial-velocity signal, rather than the rotational Doppler shift of the flux blocked by starspots.

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