Contents
5.5 Influence of orbit characteristics
5. Low Earth Orbit thermal environment for space thermal design 147
5.5.1 Latitude and longitude
Analysing the distribution of albedo and OLR in the Earth coordinates, a strong dependence can be found in the latitude variable as shown in Figure 5.7. Albedo tends to increase its mean value with the latitude. This phenomenon is due to two main reasons:
• The characteristics of the surface in the pole regions: These areas are mainly covered by ice which has a high reflectivity (albedo) and a lower temperature (OLR).
• The Solar Zenith Angle range: Polar regions have a narrower range of SZA during the year with higher values closer to 90◦. As said, the albedo coefficient increases with the SZA.
To take into account this dependence, different inclination orbits have been analysed. In addition, its relationship with the SZA should be considered. Higher albedo coefficient values are paired with higher SZA. Selecting a unique albedo value based on its maximum values along its orbit would lead to an oversized system. This maximum albedo coefficient would probably not be reached in areas with lower SZA associated where the albedo heat flux is higher. A time-dependant profile would solve this problem.
(a) Surface. (b) 1.5 km.
Figure 5.7: Heatmap of the average values of (a) albedo and (b) OLR for a whole year.
5.5.2 Inclination
As has been previously explained, the dependence of the albedo and the OLR with the latitude can be partially reduced analysing separately orbits with different inclinations. By doing so, the widest range of albedo and OLR correspond to the
polar orbits with an inclination around 90◦because they pass over the whole range of latitudes. While decreasing the inclination, the range become narrower and the mean albedo is displaced towards lower values while the mean OLR is displaced to higher values as shown in Figure 5.8. There, albedo and OLR distributions are represented for different orbit inclinations where boxes show the quartiles of each data set.
(a) (b)
Figure 5.8: Boxplot of the distribution of (a) albedo and (b) OLR as a function of the orbit inclination.
5.5.3 Right Ascension of the Ascending Node
As previously studied, albedo and OLR do not have a considerable dependence with the longitude. Considering this relationship when analysing the influence of the orbital parameters, there would not be significant difference between orbits with different RAAN angles. This fact represents an advantage because it allows us to discard one parameter from the analysis. It means that when analysing a long period of time, where different RAAN values would appear for different orbits, its influence is negligible.
5.5.4 Epoch
Analysing the albedo and OLR distributions throughout the year is important to decouple the worst-case selection from the epoch variations. The mainly varying parameter during the year is the solar irradiance which goes from 1412 W/m2 when Earth is in its perihelium to around 1316 W/m2 in the aphelion. In order to check the influence of the epoch, other annual variations must be minimized such as the SBA dependence. To do so, a Sun-Synchronous orbit has been used and the distributions of albedo and OLR obtained are shown in Figure 5.9. A slight difference can be observed in both, the albedo and OLR values throughout the year. Albedo mean values keep almost constant, but the percentiles change
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significantly. In contrast, OLR mean values tend to higher values during the North- Hemisphere summer while percentiles are almost stable. This difference could be due to changes in the solar declination which varies from 23◦ to -23◦ during the year, being 0◦ in June and January or due to the indirect influence of the higher value of the solar irradiance during the summer.
(a) (b)
Figure 5.9: Boxplot of (a) albedo and (b) OLR along the year.
If we analyse a whole year of temperature response of a satellite with the characteristics shown in Table 5.2, with a constant Solar Irradiance, the temperature range throughout the year for a constant SBA is only due to the albedo and OLR changes. As shown in Figure 5.10, temperature fluctuations are wider for smaller characteristic times. These systems are more coupled to the environmental changes, and extreme maximum and minimum temperatures will be due to the peaks widths and amplitude that cannot be identified by the analysis made in Figure 5.9. In contrast, systems with higher characteristic times will be more coupled to the mean value of the heat load and its behaviour could be completely different to the less massive systems. This variation can also be appreciated in the trend of albedo and OLR mean values shown in Figure 5.9.
5.5.5 Albedo, OLR and SZA
This relationship has been widely studied since the first methodologies for the worst- case selection [14]. Albedo and OLR values are partially correlated in a way that selecting the maximum or minimum values of these two parameters together would lead to an unlikely situation. Highest albedo values are paired with minimum OLR values and vice-versa. In addition, as shown in Figure 5.11, a strong dependence with the SZA can be appreciated even more in the albedo distribution. This dependence corresponds to the ADMs used for obtaining the upward albedo and OLR flux for different SZA based on multiple scenarios [42].
Figure 5.10: Temperature response of different systems for a Sun-Synchronous orbit with constant SBA.
The selection of these two parameters shall be performed attending to their dependence with the SZA. To do so, the long period variations and the maximum and minimum direct solar radiation in the selected orbit needs to be obtained.
Figure 5.11: Distribution of viewed albedo and OLR values considering their dependence to SZA (color coded as shown on the left).
5.5.6 SZA, SBA and direct solar radiation (eclipses)
The relationship between these two angles can be analytically obtained based on Ref [117]. For a given orbit, the SZA, which is show in Figure 5.12, varies between 90◦ and the absolute value of the Solar Beta Angle. Ignoring values of SZA >90◦ where no albedo heat flux exists, using this relationship, the range of SZA can be bounded for selecting the worst-case environments.
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Figure 5.12: SZA evolution for a LEO satellite during a whole year.
As the solar heat load is usually the maximum contributor, maximum tem- peratures are usually obtained when the eclipse duration in an orbit is minimum.
Attending to the SBA, this fact occurs when the SBA has a value around 90◦ which means that the Sun direction is perpendicular to the orbit plane. However, there are many orbits that never reach this value and in other cases, as shown in Figure 5.5, maximum temperatures may not correspond to the maximum orbital heat load but to the maximum heat flux. This is the case of low time constant systems which are more coupled to the thermal environmental changes.
In contrast, the eclipse duration is maximum when the SBA is near 0◦. However, if the interest is not focused over the whole system but over a part of it, maximum temperatures may not occur when the SBA is maximum but when there is a direct solar incidence over it. So, in this case, the influence of the orientation should also be considered. An interesting analysis about the SBA ranges for different orbits has been performed in Ref. [118] in order to get robust designs for a wide range of orbits.
The methodology here proposed is based on the selection of SBA for a considered orbit and a system in order to determine the maximum or minimum albedo and OLR profiles from a wide period of time. As known, there is only one type of LEO where the SBA keeps constant throughout the year. This is the Sun-synchronous orbit which has a precession motion which is equivalent to an Earth orbital period around the Sun. A problem arises when a non Sun-synchronous orbit is analysed, because the SBA variation results in a wide range of orbital albedo and OLR profiles.
In this case, the worst-case SBA should be firstly selected as explained in [29].