# Analysis of Tidal Accelerations in the Solar System and in Extrasolar Planetary Systems
## 4 Discussion
Detailed and thorough analyses have to be performed for large \(R\) when trying to transfer the boundaries for expected volcanism given above from the solar to extrasolar systems. The older and the less enriched in radioactive metals the extrasolar system is, and the smaller the exoplanets(/-moons) are, the more reliable this transfer via our approach may be. The dashed line in Figures 6 and 7 shows via empirical findings in our solar system the division line for tidal-dominated and radioactive decay/stored accretion-energy-dominated objects. Again, the transfer of this division to extrasolar systems has to be performed cautiously due to the issues outlined above. This division line remains blurred and should not be considered too certain. As a first interpretation, this may be performed for the extrasolar planetary system TRAPPIST-1. The host star TRAPPIST-1 has a metallicity close to our Sun [12]. The age of this system might be older than our solar system [49]. This might favor a dominant influence by tidal heating in the present phase of this system, as the other possible energy sources might have dwindled further. Planets in the TRAPPIST-1 system have been taken to test and verify but also to show the limits and borders of this model. The objects are already quite big in comparison with considered objects in the solar system, but they are until now the only set of exoplanets well-characterized enough by other models to serve as check-up for our model. Planets of TRAPPIST-1 should experience strong heating by remaining accretion heat, radioactive heating, and tidal heating all together, as they appear close to the dashed line in Figure 6. Hence, planets of TRAPPIST-1 appear to be very hot worlds. This is in concordance with the conclusions from other simulations [43; 50; 51]. Future investigations might try to apply this simulation approach to depict perturbations regarding \(\Delta A\). It may be an aim to make long-term predictions about the stability and resonances of multi-body systems, since the mutual perturbations of the objects in an energetically relaxed state are visible (energy included in eccentricities dissipated to zero). Furthermore, simulations without the central object might be desirable to investigate only the mutual tidal influences of the orbiting objects. As already mentioned, this will show that also other objects orbiting the central object can provide the leading important tidal influence (see, e.g., the bottom panel of Figure 9 for Umbriel). This may justify our complex multi-body approach. Some new objects of interest were found and may justify further investigations. The testing of how strong the values change when some parameters are missing yields stable/similar results in the solar system. This encourages the application in extrasolar planetary system to evaluate less well-known objects. The transfer to the extrasolar planetary system TRAPPIST-1 also results in assumptions of the planets being in concordance with known simulations [43; 50; 51]. This confirms our choice of TRAPPIST-1 for verification that our model is applicable to extrasolar planetary systems. It might be encouraging to use this approach on further extrasolar systems. Only few sub-Earth-sized exoplanets with accurately measured physical and orbital parameters are known today. Among others, an outstanding example for such an extrasolar system of terrestrial and sub-Earth-sized planets is Kepler-444, an old triple-star system with five planets orbiting around the main star (K type) [52]. Nevertheless, not for all planets, and only few parameters are known in this system. We are eagerly waiting for the first observations by the upcoming James Webb Space Telescope, which should provide new and more accurate measurements of physical and orbital parameters of extrasolar planetary systems, in particular, as well for sub-Earth-sized exoplanets. Many \"super-Earth\" systems were found already, e.g., HD 10180 [53], LHS 1140 [54], and many others.