# Global climate by Rossby number in the Solar system planets

## TL;DR

This study investigates the relationship between planetary Rossby number and a scaled height parameter across Solar system planets, revealing a positive correlation that could inform the search for life on exoplanets.

## Contribution

It introduces a simplified model linking Rossby number to a scaled height parameter and explores its correlation across Solar system planets using observational wind data.

## Key findings

- Found a power-law correlation between Rossby number and height parameter with an exponent around 0.5.
- Identified Earth's height parameter as mainly influenced by lunar tides.
- Suggests exoplanet-moon systems as promising targets for life detection.

## Abstract

On the largest scales, planetary climates can be described by their Rossby number (\textit{Ro}). \textit{Ro} is in response to $Gr/Re^2$ , where Gr is the Grashof number and Re is the Reynolds number. We here simplify $Gr/Re^2$ as h, where $h=H/H_{Earth}$ with $H=gP/(2\pi V_e)$ for a planet with surface gravity \textit{g}, rotation period \textit{P} and equatorial velocity V\textsubscript{e}. Unlike \textit{h}, \textit{Ro} is difficult to obtain because of a large diversity in observation. We perform on an in-depth literature search on average (av) and maximum (mx) wind velocity for each planet in the Solar system by various observational methods and by altitude. We explore a correlation between \textit{Ro} and \textit{h} expressed as a power law with index $\alpha$ based on wind velocities of planets in the Solar system. We obtain a correlation between \textit{Ro} and \textit{h} with $\alpha=0.56$ (av) and $\alpha=0.52$ (mx). Earth's $H=H_{Earth}$ ($h=1$) is primarily due to lunar tidal interaction, given our relatively distant habitable zone (HZ) to the Sun. Our positive correlation, therefore, suggests exoplanet-moon systems as the `go-to-place' in our searches for potentially advanced life in exosolar system.