## 2 Materials and Methods
### Hypotheses and Environmental Control Calculations  
The primary hypothesis of this study is based on the assumption of extremely low Reynolds numbers in the Martian atmosphere. This is attributed to its very low density atmosphere, coupled with the relatively low velocities of atmospheric flows and the high viscosity of the air. The Martian atmosphere is much thinner than Earth's, resulting in a small numerator in the Reynolds number formula (Equation (1)). This classification aligns with prior studies, which highlight the unique atmospheric dynamics on Mars. For instance, [PERSON] (2011) [13] discusses how mesoscale meteorological phenomena, including boundary layer convection, are significantly influenced by the low atmospheric density. Similarly, [PERSON] et al. (2017) [14] review the near-surface Martian climate and emphasize the impact of the atmosphere's thinness on fluid dynamics and heat transfer processes. Additionally, [PERSON] et al. (2008) [15] and [PERSON] (2004) [5] emphasize that at Reynolds numbers below \(10^{4}\), viscous forces dominate, leading to laminar wakes and weak turbulent structures. [PERSON] et al. (2020) [16] and [PERSON] (2010) [17] further analyzed aerodynamic performance at low Reynolds numbers relevant to Martian conditions, where thin atmospheres and reduced gravity amplify viscous effects and inhibit boundary layer separation recovery. These references support the designation of Reynolds numbers on the order of \(10^{3}\) as extremely low in the Martian context, as follows:  
\[\text{Re}=\frac{\rho\cdot v\cdot L}{\mu} \tag{1}\]  
Figure 3: MMRTG and mast on the experimental floor: the 200 mm spacing between the mast and the MMRTG can be seen. Figure 2: MMRTG cavity (**left**) in addition to the resistor housing and the presence of the ink holes. MMRTG’s shell (**right**) with \(30^{\circ}\) angled brackets. where  
* \(\rho\) is the fluid density (kg/m\({}^{3}\));
* \(v\) is the characteristic velocity of the fluid flow (m/s);
* \(L\) is the characteristic length (m), which is a relevant dimension of the object or flow system;
* \(\mu\) is the dynamic viscosity of the fluid (Pa-s or N-s/m\({}^{2}\)), which measures the fluid's resistance to shear. The low atmospheric pressure and resulting slow wind speeds contribute to a small value for Reynolds number. This means that viscous forces dominate over inertial forces in Martian atmospheric flows, significantly influencing the aerodynamics of any objects interacting with the Martian air. Based on this hypothesis, the speeds of the carriage and ink injection must be adjusted to achieve Reynolds numbers around \(10^{3}\). Moreover, the ink injection must be matched to the carriage speed. However, this alignment was not feasible for very high flow rates (Table 1), as will be discussed in the results. The forward velocity of the trolley can be calculated using the following mathematical relation:  
\[u_{t}=(0.022\cdot F+0.0565)\cdot\frac{1}{60} \tag{2}\]  
where  
* \(u_{t}\) is the trolley's velocity [m/s];
* \(F\) is the frequency of the engine [Hz]. It is essential to calculate the influence of the engine on the Martian atmosphere to determine the importance of conducting laboratory studies with thermal variation and to verify their proper execution. To this end, the Grashof number was calculated to study the impact of the engine on the atmosphere and, subsequently, on the MEDA station. This dimensionless number, which represents the ratio of buoyancy forces to viscous forces, is critical for understanding flow behavior in low Reynolds number environments, such as Mars. Previous studies have indicated that the Grashof number significantly affects thermal convection processes under Martian conditions ([PERSON] et al., 2024) [10], influencing how heat from the MMRG propagates through the atmosphere. Temperature data from the MMRTG obtained from previous studies by [PERSON] et al. (2020) [2] were used, corresponding to 414 K (141 \({}^{\circ}\)C).