Introduction

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into account the different scenarios (grass, clouds, ice, dessert, etc) [107] to be found when overpassing an Earth region, global data collected by several space missions using radiometers [18] is statistically treated to identify the potential extreme cases to be analysed.

Outgoing Longwave Radiation corresponds to the infrared radiation emitted by the Earth, which is also dependent on the surface scenario. Ice surfaces emit less IR radiation than a dessert surface, but the albedo is higher. These two parameters are partially correlated and cannot be analysed separately.

When analysing a defined orbit, several variables take part in determining the extreme environmental conditions that can be encountered. Due to their different characteristics, Sun-Synchronous orbits must be analysed separately. They have a precession period of a year so satellites always pass over any subsatellite point at the same local mean solar time. As they always maintain the same relationship with the Sun, the β angle or SBA (angle between the Sun direction and the orbit plane) is almost constant during the year and it provides a more stable thermal environment. However, satellite thermal environment in Sun-Synchronous orbits strongly depends on the beta angle. When β = 0^◦ (dawn/dusk orbit), the orbit plane is placed perpendicular to the Sun’s rays, and there are no eclipses, regardless of the altitude. The albedo heat load is near zero. In the opposite case, when β

= 90^◦ (local noon or local midnight), the orbit plane is parallel to the direction of solar rays and the orbit appears edgewise to the Sun. The subsatellite point passes over the sub-solar point on the Earth, which has several implications.

When trying to define the extreme thermal environmental conditions of this kind of orbit, the problem is greatly simplified if the beta angle is a constant. This is because the study of multiple orbits with respect to the Sun is reduced to a unique relationship of the Sun-orbit system related through the SBA. However, when having an inclined LEO,β is not constant and the precession motion should be taken into account. Obtaining the worst-case orbit (based on beta angle) should be the first step. Then, albedo, and OLR worst-case values can be obtained accounting for the constraints of the orbit (latitude range, SZA and epoch).

While the thermal environment is independent of the satellite system, values that lead it to the extreme temperatures are not the same for every satellite.

Thermo-optical properties are the main driving parameter. The influence of the α/ε ratio of the exposed surfaces on the extreme environment should be considered.

If α/ε >>1 the hottest environment will correspond to the highest values of albedo.

Since albedo and OLR are partially correlated, OLR values will not be maximum.

Choosing a hot case of extreme values of both, albedo and OLR, would lead to an

overestimated worst-case since they will not occur at the same time. Otherwise, if α/ε << 1, the system is more sensitive to changes in infrared radiation. For that reason, the hottest environment will be the one with higher OLR and the coldest, the one with the lowest.

The thermal analysis of orbiting systems has usually been carried out by means of the analysis of a single orbit with the extreme environmental conditions based on statistics [17]. Single values of albedo and OLR for a complete orbit do not seem very realistic since its variation along the orbit could be significant. Moreover, the dependence on the SZA and latitude is being neglected or averaged. This approximation would be suitable for very massive systems with long response times.

The time constant (or characteristic time) of the system will characterize the thermal response to the environmental changes. Systems with a long-time constant will not be sensitive to short period variations. For that reason, using averaged values will be a good approximation. Systems with a short-time constant will have a short response to small changes in the thermal environment. If a too long average time is used for averaging the albedo and OLR values, shorter peaks, which could lead the system to the extreme minimum and maximum temperatures, are not being considered.

The aim of the work explained in this paper is to update the existing methodolo- gies adapting them to the current status of the technology, where the capabilities of the software analysis allows the thermal engineers to develop even more complex and accurate analyses.

The study performed in this chapter has used global data of 2018 from CERES data [46]. Albedo, OLR and SZA values for each pixel are the base for the environment characterization through the satellite propagation. The combination of these three parameters define the LEO thermal environment. Values that led the system to their minimum or maximum temperatures define the worst cases. They have been determined for different orbits and different satellite’s characteristics.

One example of CERES retrieved data is shown in Figure 5.1, where there are only albedo values at the TOA where SZA is lower than 90^◦, which means that the Sun direction is parallel to the subsolar surface plane.

The content of this chapter is organized as follows.

• Firstly, a review of the chronology of the thermal environment selection criteria used by the NASA since the beginning of their space activities is summarized in Section 5.2. This historical analysis provides a good perspective of the need for updating the existing methodology to this new era of space exploration and exploitation.

5. Low Earth Orbit thermal environment for space thermal design 133

Figure 5.1: CERES global map of albedo (upper blue), OLR (upper red) and SZA (lower) corresponding to the 12:00 h UTC of 1^st Jan 2018.

• In order to evaluate the influence of the thermal environmental parameters on a specific system, a system thermal model is presented in Section 5.3, and the influence of the system characteristics are broken down in Section 5.4.

• The influence of the orbital parameters on the worst-case thermal environment is analysed in Section 5.5.

• A case of study based on a Sun-Synchronous orbit is developed in Section 5.6 with the aim of showing the process followed to select the worst-case thermal environmental parameters based on the methodology here proposed. The resulting albedo and OLR profiles are shown and compared to the NASA criteria in order to analyse the advantages and disadvantages of the presented methodology.

• The influence on small satellites is analytically analysed in Section 5.7.