## 6 Thermal System Design
### Defining the Thermal Load
The background temperature of space at this altitude is 2.7 K. As stated earlier in the report, the pressure is of an extremely small magnitude at this orbit and is assumed to be negligible, assuming a vacuum. Temperatures of the outer surfaces of CubeSats are typically 100 degrees when facing the Sun's radiation and \(-100\) degrees when in Earth's or CubeSat's shadow. This represents an extreme temperature range, at which the CubeSat's subsystems would begin to fail towards the extremes, it is, therefore, necessary to regulate temperature to ensure components do not fail in such a harsh environment. The following table, Table 27 details typically operational temperatures for key CubeSat subsystems. \begin{table}
\begin{tabular}{c c} \hline \hline
**Component** & **Typical Operating Temperature Range (Degrees Celsius)** \\ \hline RAVAN Payload & 0 to 60 \\ Electronics (Clyde-Space, 2017) & \(-40\) to 85 \\ Battery (Clyde-Space, 2017) & 5 to 20 \\ Structure (Pumpkin Incorporated, 2015) & \(-40\) to 65 \\ Solar Cells (GaAs Material) (Spectrolab, 2010) & \(-100\) to 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 27: Typical Operating temperatures for CubeSat Sub Systems (Clyde-Space, 2017) (Pumpkin Incorporated, 2015) [21, 48]. Figure 47: Fluctuations in Earths IR Output throughout an Orbit Cycle [64]. The advantage of selecting a Sun-synchronous orbit is that the CubeSat's orbit plane remains at a fixed angle relative to the Sun's position [10]. This is advantageous as every orbit the CubeSat completes is over locations on Earth which have the same local time, and as Earth is rotating too the craft can cover approximately the whole course of Earth in a day. This is very useful for the RAVAN payload as it can measure imbalance over all locations, highlighting hotspots and regions which produce more emissions which is extremely useful when developing climate control programs for greenhouse gas reduction [9]. As the Beta angle for this mission is 0 degrees, the CubeSat will pass over the Sub-Solar Point of Earth. This location is where the Sun is directly overhead, has the most intense Albedo radiation value and has the longest eclipse time as the entirety of Earth's diameter shadows it. As this angle increases, the Albedo load decreases as it is further from the SSP point, but as a trade off the CubeSat will be exposed to the Sun for a longer period of each orbit as the eclipse time reduces. When the beta angle reaches the maximum value of 90 degrees, there is no eclipse and the albedo load is negligible. For an orbit between 0 and (\(-\)) 90 degrees, the eclipse fraction for the assumed circular orbit can be found using (Figure 48 for illustration). \[t_{E}=\frac{1}{180^{\circ}}*\cos^{-1}(\frac{\left(H^{2}+2*R*H\right)^{0.5}}{ \left(R+H\right)*\cos(\beta)}) \tag{35}\]  
where:  
\[|\beta|<\beta^{*}\]  
\[\beta^{*}=\sin^{-1}\left(\frac{R_{earth}}{R_{earth}+H}\right)=73.4^{\circ} \tag{36}\]  
Therefore, use is valid as 0 < 73.4. For a circular orbit:  
\[R=R_{earth}+H_{orbit} \tag{37}\]  
\[R=6,370,000\;\mathrm{m}+600,000\;\mathrm{m}=6,970,000\;\mathrm{m}\]  
However, once the period for orbit has been calculated, a much more concise method can be implied to determine the time spent in eclipse and the time spent in direct solar radiation. The period is found using the following equation:  
\[T_{satellite}=\sqrt{\frac{4*\pi^{2}}{7*M_{earth}}*a^{3}} \tag{38}\]  
\[T_{satellite}=\sqrt{\frac{4*\pi^{2}}{6.67*10^{-11}*5.972*10^{24}}*6,970,000^{3}} =5793\;\mathrm{s}=96\;\mathrm{min}\;30\;\mathrm{s}\]  
Assuming the satellite orbits in a circular motion, and Earth's shadow causing eclipse is cylindrically shaped, the following formula can be employed to find the time spent in eclipse.