Abstract. We present here a new solution for the astronomical computation of the insolation quantities on Earth spanning from −250 Myr to 250 Myr. This solution has been improved with respect to La93 (Laskar et al. 1993) by using a direct integration of the gravitational equations for the orbital motion, and by improving the dissipative contributions, in particular in the evolution of the Earth-Moon System. The orbital solution has been used for the calibration of the Neogene period (Lourens et al. 2004), and is expected to be used for age calibrations of paleoclimatic data over 40 to 50 Myr, eventually over the full Palaeogene period (65 Myr) with caution. Beyond this time span, the chaotic evolution of the orbits prevents a precise determination of the Earth's motion. However, the most regular components of the orbital solution could still be used over a much longer time span, which is why we provide here the solution over 250 Myr. Over this time interval, the most striking feature of the obliquity solution, apart from a secular global increase due to tidal dissipation, is a strong decrease of about 0.38 degree in the next few millions of years, due to the crossing of the s 6 + g 5 − g 6 resonance (Laskar et al. 1993). For the calibration of the Mesozoic time scale (about 65 to 250 Myr), we propose to use the term of largest amplitude in the eccentricity, related to g 2 − g 5 , with a fixed frequency of 3.200 /yr, corresponding to a period of 405 000 yr. The uncertainty of this time scale over 100 Myr should be about 0.1%, and 0.2% over the full Mesozoic era.

Context. Ultra-short period planets undergo strong tidal interactions with their host star which lead to planet deformation and orbital tidal decay. Aims. WASP-103b is the exoplanet with the highest expected deformation signature in its transit light curve and one of the shortest expected spiral-in times. Measuring the tidal deformation of the planet would allow us to estimate the second degree fluid Love number and gain insight into the planet’s internal structure. Moreover, measuring the tidal decay timescale would allow us to estimate the stellar tidal quality factor, which is key to constraining stellar physics. Methods. We obtained 12 transit light curves of WASP-103b with the CHaracterising ExOplanet Satellite (CHEOPS) to estimate the tidal deformation and tidal decay of this extreme system. We modelled the high-precision CHEOPS transit light curves together with systematic instrumental noise using multi-dimensional Gaussian process regression informed by a set of instrumental parameters. To model the tidal deformation, we used a parametrisation model which allowed us to determine the second degree fluid Love number of the planet. We combined our light curves with previously observed transits of WASP-103b with the Hubble Space Telescope (HST) and Spitzer to increase the signal-to-noise of the light curve and better distinguish the minute signal expected from the planetary deformation. Results. We estimate the radial Love number of WASP-103b to be hf = 1.59−0.53+0.45. This is the first time that the tidal deformation is directly detected (at 3 σ) from the transit light curve of an exoplanet. Combining the transit times derived from CHEOPS, HST, and Spitzer light curves with the other transit times available in the literature, we find no significant orbital period variation for WASP-103b. However, the data show a hint of an orbital period increase instead of a decrease, as is expected for tidal decay. This could be either due to a visual companion star if this star is bound, the Applegate effect, or a statistical artefact. Conclusions. The estimated Love number of WASP-103b is similar to Jupiter’s. This will allow us to constrain the internal structure and composition of WASP-103b, which could provide clues on the inflation of hot Jupiters. Future observations with James Webb Space Telescope can better constrain the radial Love number of WASP-103b due to their high signal-to-noise and the smaller signature of limb darkening in the infrared. A longer time baseline is needed to constrain the tidal decay in this system.

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