## 4 Mechanical Design and Thermal Modelling of 6U CubeSat
### Environmental Load Studies and Orbit Parameters  
Optimization is carried out on the satellite such that the design is able to handle the environmental heat loads for any orbital inclination and earth seasons. Orbital inclination varying from \(0<i<97.3\) degrees is studied to confirm the design is optimum for all the external heat load conditions. The variation of beta angles for every inclination is extracted from Systems Tool Kit (STK) software and verified with a commercial thermal analysis software, Thermal Desktop(r). Thermal simulations are carried out for four Earth seasons and seasonal environmental heat loads and the Earth's seasonal variations are shown in Figure 11. All the Earth-bound Low Earth Orbits (LEO) will experience the same environmental thermal loads during its mission period, and they affect the thermal behaviour of the satellite components. Hence, the thermal design should consider all these fluctuations of the thermal loads. For the given orbital parameters, worst case mission conditions will be identified for the given satellite configurations and analyzed numerically. In general, for satellite thermal design, two extreme cases are the worst conditions. 1. Worst cold condition: Satellite at LEO will experience coldest temperature in orbit once a year, and it will happen during the Northern hemisphere summer where the satellite will receive lesser flux from the sun. Earth is located at aphelion, and most of the electronics and payloads are turned off. Beginning of the life (BOL) thermo-optical parameters are used. 2. Worst hot condition: Satellite at LEO receives 10% higher than the satellite would receive during summer. This happens during winter conditions. Earth is located at perihelion, and all the electronics and payloads are operating at their peak power. End of the life (EOL) thermo-optical parameters are used. Figure 11: Variation in environmental heat loads due to Earth’s season. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Components** & **Materials** & **Coating** & **Absorptivity** & **Emissivity** \\ \hline Solar Panels & FR4 & FR4 default & 0.6 & 0.7 \\ Payload external & Al & Yellow Chrome & 0.2 & 0.37 \\ Radiator & Al 6061-T6 & Silver Teflon & 0.09 & 0.95 \\ Battery & Al 6061-T6 & Polylimide + Al + PEEK & 0.43 & 0.52 \\ Cryocooler Cold finger & Copper & Default copper & 0.4 & 0.05 \\ Heat Exchanger & Al 6061-T6 & Black anodize & 0.73 & 0.86 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Surface properties—Used. The orbital properties are illustrated pictorially in Figure 11. In addition to these properties, other important properties that should be considered for thermal calculations are beta angle, orbital inclination, and orbit type. Beta angle (\(\beta\)) is defined as the angle between the solar vector and satellite orbital plane. This angle varies as the orbit precesses around the Earth and as the Earth moves around the sun. This angle correlates to how much sun light falls onto the satellite surfaces. For a higher beta angle, the satellite spends more of the orbit in the sun. This angle varies with the inclination of the orbit. If the orbit is not sun synchronous, \(\beta\) will move through the range as given in Equation (23) [41], but it has some limitations for higher inclination orbits. \[\beta=\pm(23.5+|i|) \tag{23}\]  
where, \(i\)--orbital inclination, varies from \(-90^{\circ}\leq\beta\leq+90^{\circ}\). Beta angles where the sun is north of the orbit plane are considered positive. However, due to orbit precession, the right ascension of ascending node varies with time and hence the \(\beta\) equation is modified as in Equation (24) [11]. \[\beta=\sin^{-1}\cos\Gamma\sin\Omega\sin i-\sin\Gamma\cos\epsilon^{\prime}\cos \Omega\sin i+\sin\Gamma\sin\Gamma\cos i \tag{24}\]  
where, \(\Gamma\)--Ecliptic true solar longitude, \(\Omega\)--Right ascension of ascending node (RAAN), \(\epsilon^{\prime}\) is Obliquity of the ecliptic (currently the tilt is at 23.5), and \(i\) is the orbit's inclination.