# Analysis of Tidal Accelerations in the Solar System and in Extrasolar Planetary Systems
## 4 Discussion  
As a \"gold standard\" system, the simulation approach for tidal accelerations presented here using a minimalistic set of parameters was applied to all objects in our solar system known and correlated to cryo- or even siliceous volcanism. For celestial bodies known to show signs of strong tidal influence, the resulting values for \(\{A_{total}\cdot(\Delta A_{total}/\Delta t)\}_{max}\) are \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Object** & \(\mathbf{a}\) & \(\mathbf{n}\) & \(\mathbf{R}\) & \(\mathbf{M}\) & \(\{\mathbf{A_{total}}\cdot(\Delta A_{total}/\Delta t)\}_{max}\) \\  & [**km**] & \(\mathbf{e}\) & [**rad/day**] & [**km**] & [**kg**] & [**m\({}^{2}\)/s\({}^{4}\)**d**] \\ \hline TRAPPIST-1b & \(1.73\times 10^{6}\) & 0.0062 & 4.1586 & 7149.85 & \(6.08\times 10^{24}\) & \(9.36\times 10^{-3}\) \\ TRAPPIST-1c & \(2.37\times 10^{6}\) & 0.0065 & 2.5944 & 6984.02 & \(6.91\times 10^{24}\) & \(8.50\times 10^{-4}\) \\ (J1) Io & \(4.22\times 10^{5}\) & 0.0041 & 3.5516 & 1821.60 & \(8.93\times 10^{22}\) & \(2.43\times 10^{-4}\) \\ TRAPPIST-1d & \(3.33\times 10^{6}\) & 0.0084 & 1.5514 & 5000.43 & \(1.77\times 10^{24}\) & \(3.36\times 10^{-5}\) \\ TRAPPIST-1e & \(4.38\times 10^{6}\) & 0.0051 & 1.0302 & 5804.07 & \(4.61\times 10^{24}\) & \(5.70\times 10^{-6}\) \\ TRAPPIST-1f & \(5.76\times 10^{6}\) & 0.0101 & 0.6825 & 6671.49 & \(5.58\times 10^{24}\) & \(9.98\times 10^{-7}\) \\ Ganymede & \(1.07\times 10^{6}\) & 0.0013 & 0.8782 & 2631.20 & \(1.48\times 10^{23}\) & \(5.24\times 10^{-7}\) \\ TRAPPIST-1g & \(7.01\times 10^{6}\) & 0.0021 & 0.5086 & 7322.06 & \(6.86\times 10^{24}\) & \(2.62\times 10^{-7}\) \\ TRAPPIST-1h & \(9.27\times 10^{6}\) & 0.0057 & 0.3348 & 4930.27 & \(1.98\times 10^{24}\) & \(1.50\times 10^{-8}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of values of \(\{A_{total}\cdot(\Delta A_{total}/\Delta t)\}_{max}\) for all planets in the TRAPPIST-1 system and for (J1) Io and Ganymede. Figure 10: Tidal accelerations acting on exoplanet TRAPPIST-1b using the version of the simulation with full orbital elements (without the longitude of the ascending node \(\Omega\), the argument of periapsis \(\omega\), and the mean anomaly at a given epoch \(M_{0}\), since no data is available); \(\Delta t\) = 0.05 days. \(A\) denotes the individual tidal accelerations caused by other objects. The ordering of the legend is the same as in the uppermost plot with the strongest contribution at the top and the weakest at the bottom. \(A_{total}\) denotes the norm of the vector addition of all individual contributions. \(\Delta A_{total}\) denotes the norm of the vector difference of \(A_{total}\) for two consecutive time steps. among the largest occurring in this simulation. Furthermore, additional objects were suggested, which have not been subjects of research for tidal heating up to now. The identification of new candidates can also reveal conclusions about the composition and evolution of other properties not related to tidal heating, e.g., the inner Neptunian moon Despina shows the highest tidal acceleration value of all objects included in the simulation of the solar system (see Figures 5 and 6). According to [45], the composition of Despina and the other inner Neptunian moons should be structured like a rubble pile, i.e., a loose aggregation of small rocky pieces. Considering the strong tidal forces presumably associated with the relatively high tidal accelerations acting on Despina, it may be interesting to investigate whether or even how rubble piles exposed to such relative strong tidal forces are stable over the long history of the solar system. Therefore, this could lead to new insights into the stability of rubble piles or motivate new ideas about the inner composition of these objects. As may have been noticed in Figure 5, the Earth shows siliceous volcanism, although the tidal accelerations are quite low compared to (J1) Io, the only other object in the solar system for which this persistent characteristic is confirmed.