The mass of beta Pictoris c from beta Pictoris b orbital motion

Aims. We aim to demonstrate that the presence and mass of an exoplanet can now be effectively derived from the astrometry of another exoplanet. Methods. We combined previous astrometry of beta Pictoris b with a new set of observations from the GRAVITY interferometer. The orbital motion of beta Pictoris b is fit using Markov chain Monte Carlo simulations in Jacobi coordinates. The inner planet, beta Pictoris c, was also reobserved at a separation of 96 mas, confirming the previous orbital estimations. Results. From the astrometry of planet b only, we can (i) detect the presence of beta Pictoris c and (ii) constrain its mass to 10.04(-3.10)(+4.53) M-Jup . If one adds the astrometry of beta Pictoris c, the mass is narrowed down to 9.15(-1.06)(+1.08) M-Jup. The inclusion of radial velocity measurements does not affect the orbital parameters significantly, but it does slightly decrease the mass estimate to 8.89(-0.75)(+0.75) M-Jup.With a semimajor axis of 2.68 +/- 0.02 au, a period of 1221 +/- 15 days, and an eccentricity of 0.32 +/- 0.02, the orbital parameters of beta Pictoris c are now constrained as precisely as those of beta Pictoris b. The orbital configuration is compatible with a high-order mean-motion resonance (7:1). The impact of the resonance on the planets' dynamics would then be negligible with respect to the secular perturbations, which might have played an important role in the eccentricity excitation of the outer planet.