# UVSQ-SAT, a Pathfinder CubeSat Mission for Observing Essential Climate Variables
## 3 Materials and Methods
### The Space Segment: The UVSQ-SAT CubeSat Payload
#### 3.2.1 The ERS Sensors

Table 2: _Cont._and a goniophotometer (REFLET 180S) to obtain the BRDFs (five angles of incidence (0\({}^{\circ}\), 30\({}^{\circ}\), 36\({}^{\circ}\), 60\({}^{\circ}\), 72\({}^{\circ}\)) in the 400-800 nm wavelength range in steps of 10 nm). The large field of view of both sensors on each side of UVSQ-SAT allows measuring all fluxes (TSI, OLR, OSR, black-body flux of the sensor (\(\sigma T^{4}\)), residual fluxes (Moon, planets, etc.)). Considering that we know the value of the solar flux (TSI measurement obtained from space based solar radiometers), the sensors' temperatures (UVSQ-SAT housekeeping data), the residual fluxes (ephemerides of various bodies of the solar system obtained from Institut de mecanique celeste et de calcul des ephemerides (IMCCE)), then we can determine OLR and OSR from a two equation System (S) based on the following thermo-dynamical equations using 12 nodes (N = 12 thermopiles). \[C_{i}\frac{\partial T_{i}}{\partial t} =A_{i}\cos(\theta_{i})\frac{d^{2}}{d_{Sat-S}^{2}}\int_{\lambda} SI(\lambda)\alpha_{i}(\lambda)d\lambda\ +A_{i}F_{i-Earth}\int_{\lambda}\epsilon_{i}(\lambda)EI(\lambda)d\lambda\] \[+A_{i}\frac{d^{2}}{d_{Sat-S}^{2}}F_{i-a}\int_{\lambda}aSI(\lambda )\alpha_{i}(\lambda)d\lambda+\sum_{j=1}^{N}GL_{i-j}(T_{j}-T_{i})+\sigma\sum_{j =1}^{N}GR_{i-j}(T_{j}^{4}-T_{i}^{4})+Qr_{i} \tag{1}\]  
where \(i\) is an ERS thermopile element, \(C_{i}\) is the capacitance of thermopile \(i\) (J/K), \(T_{i}\) is the temperature of thermopile \(i\) (K), \(t\) is the time (s), \(A_{i}\) is the surface area of thermopile \(i\) (m\({}^{2}\)), \(\theta_{i}\) is the angle between the solar direction and the normal of the thermopile, \(d\) is the Earth-Sun distance (km), \(d_{Sat-S}\) is the spacecraft-Sun distance (km), \(SI(\lambda)\) is the spectral solar irradiance in Wm\({}^{-2}\)um\({}^{-1}\), \(\lambda\) is the wavelength in um, \(\alpha_{i}(\lambda)\) is the solar absorption of thermopile \(i\), \(F_{i-Earth}\) is the Earth view factor, \(\epsilon_{i}(\lambda)\) is the normal emittance of thermopile \(i\), \(EI(\lambda)\) is the spectral Earth irradiance in Wm\({}^{-2}\)um\({}^{-1}\), \(F_{i-a}\) is the albedo view factor, \(a\) is the Earth's albedo, \(GL\) is the conductive couplings of thermopile \(i\) (W/K), \(GR\) is the radiative couplings of thermopile \(i\) (W/K) \(\sigma\) is the Stefan-Boltzmann constant (5.6704 \(\times 10^{-8}\) Wm\({}^{-2}\)K\({}^{-4}\)), and \(Qr_{i}\) is the absorbed residual power (Moon, planets, etc.). This yields solving a set of N differential non-linear equations to obtain OLR \(\left(\int_{\lambda}EI(\lambda)d\lambda\right)\) and OSR \(\left(\int_{\lambda}a\ SI(\lambda)d\lambda\right)\) data without having knowledge of the satellite's attitude. Then, for ERS data processing, the first step will consist of developing deep learning methods to estimate the attitude of the UVSQ-SAT CubeSat using all housekeeping data (platform and payload inertial measurement units, three axis payload compass, coarse platform photodiodes for solar orientation, power on each solar panel, etc.). Indeed, UVSQ-SAT does not have an active Attitude Determination and Control System (ADCS), which allows precise pointing of the CubeSat. This is one of the reasons why the UVSQ-SAT CubeSat is equipped with broadband ERS sensors (with a large field of view) on each side. For a second time, we will determine top of atmosphere OLR and OSR as a time  
Figure 3: Earth Radiative Sensors (ERS) measurement principle. On each side of UVSQ-SAT, there are these two sensors. TSI, Total Solar Irradiance; OLR, Outgoing Longwave Radiation; OSR, Outgoing Shortwave Radiation. function from the rough preliminary equations System (S) given below, originating from Equation (1). The total solar irradiance will be considered as known and obtained from space based radiometers.