Planetary and space thermal environment

1. Introduction 13

flies towards the west at an average speed of about 30 km/h. Considering a typical float altitude of 40 km, this results in the system having an effective view of a local point during about 12 hours.

Here, main parameters that take part in the planetary and space thermal environment are explained as well as some geometric factor that are essential for understanding the following sections. The particularities in each case will be then presented in Chapter 4 and Chapter 5 for the planetary and space characterization, respectively.

1.3.1.1 Solar irradiance

For most spacecraft, direct solar radiation is the greatest heat source. The solar constant or solar irradiance is defined as the solar radiation flux that falls on a unit are of a surface normal to the line of the Sun direction at 1 Astronomical Unit (AU) outside the atmosphere and it has an average value of G_S,1AU= 1361.5 W/m².

However, this solar constant is not really constant since a 11-year cycle make energy emitted by the Sun varies reaching monthly-averaged values from 1360.8 W/m² to 1363.0 W/m². However, larger variations up to ± 5 W/m² are common on time scales of days to weeks.

Close to the Earth, from a Low Earth Orbit, solar irradiance is also affected by the distance to the Sun which is not constant throughout the year due to the eccentricity associated to the elliptical orbit of the Earth. This variation (around 1.7 % along the year) makes solar irradiance to vary from a minimum value of 1315 W/m² when the Earth is at is aphelion to a maximum value of 1410 W/m² at its perihelion. This variation can be estimated using the inverse square law as,

GS,r =GS,1AU

1

r², (1.1)

Due to the large distance to the Sun, it can be considered as a source point and its rays as parallel for thermal calculations.

Another important aspect of the solar radiation is the spectral distribution. It can be approximated by a blackbody spectrum at 5780 K reaching a maximum at a wavelength of 0.5 µm (0.45 µm in the real one). The solar spectral distribution, which is mostly contained in a wavelength range from 0.15 to 10 µm (around 99 %) is shown in Figure 1.4.

For some applications where solar irradiance is required below the top of atmosphere (TOA), the absorption of the atmosphere should be considered. As shown in Figure 1.5, gases in the atmosphere have a considerable level of absorption

Figure 1.4: Spectral distribution of solar irradiance at 1 AU and its approximation by a blackbody at 5780 K (dashed line) [36].

in some ranges of the spectrum. This makes that the solar irradiance decreases when approaching to the Earth surface. This effect will be later analysed when character- izing the thermal environment during the ascent phase of stratospheric balloons.

Figure 1.5: Wavelength absorption by atmospheric gases compared to normalized spectral distribution of blackbodies at 6000 K and 250 K [37].

The direct absorbed solar flux, ˙Q_solari for an element i whose surface normal

1. Introduction 15

vector forms an angle γ_i with the Sun direction can be easily calculated by,

Q˙_S,i =α_iA⊥G_Scosγ_i (1.2) Nevertheless, reflected solar fluxes by nearby elements should be also considered.

1.3.1.2 Solar Zenith Angle

At any location on Earth, the angle of incidence of the solar rays varies. From a thermal point of view, it has several implications. The Solar Zenith Angle (SZA) is defined as the angle between two vectors: (1) the vector from the Earth’s centre to a given location and (2) the vector from the Earth’s centre to the Sun. As the solar rays at a distance of 1 AU can be considered parallel, this angle is the same as the angle between the first vector and the vector between a surface or orbital point and the Sun. This angle varies between 0° (for the Sun at zenith) and 180° (for the Sun at nadir). When the Sun is at the horizon for a surface location, SZA is 90°. As will be studied, it not only does have a direct influence on the angle of incidence over the satellite surfaces but also it indirectly affects the albedo heat load reaching the system.

1.3.1.3 Solar Beta Angle

Solar Beta Angle (SBA) is defined as the minimum angle between the Earth-Sun vector and the orbital plane. This angle can take values between ± 90° and it directly depends on the orbit inclination by β =±(ϵ+|i|) where ϵ is the Earth’s obliquity of the ecliptic which is about 23.4°. Its influence on the thermal behavior of a satellite in space may be divided in,

• It determines the time spent in eclipses as shown in Figure 1.6 [38].

• The intensity and direction of heating incident on spacecraft surfaces changes with β.

• The SZA range for a satellite in space is limited by |β| and 180°.

Figure 1.6: Fraction of orbit in eclipse as a function of the SBA and the altitude [38]

1.3.1.4 Albedo

Albedo is the fraction of the incident solar radiation that is reflected or scattered by a planet surface or atmosphere. It is usually expressed as a fraction or percentage which is called albedo coefficient, a. As part of the solar radiation it can be assumed that the spectral distribution is the same as the direct solar radiation which approximates a blackbody with a temperature of 5780 K. Due to the roughness of a planet’s surface, the albedo is assumed to be diffuse as a first approximation.

However, the albedo coefficient has a considerable dependence on the SZA increasing its value with it as will be explained. The altitude dependence is important across the atmosphere. This is because part of the solar radiation can be reflected by the clouds instead of the surface. In addition, atmospheric absorption makes the incoming solar radiation to increase for higher altitudes. Albedo, as well as OLR are usually referred to the top of the atmosphere which is a virtual surface located at about 30 km. For quantifying the albedo radiation for any satellite, TOA should be considered as the source of radiation.

Albedo coefficient is highly variable across the globe. It mainly depends on the type of surface below and the presence or not of clouds, their type, etc. Reflectivity increases with the cloud cover where typical values of 0.8 can be reached. Continental areas generally have higher albedo values than ocean areas where the most of incident radiation is absorbed. Here albedo coefficient values range between 0.05 and 0.1. In contrast, ice covered surfaces reflects most of the incoming solar radiation reaching values up to 0.95. This local variability makes albedo has a high dependence of the latitude. Polar regions, where surfaces are mostly covered by snow or ice, the

1. Introduction 17

cloud presence is higher and the SZA increases, have a higher averaged albedo.

From a spacecraft point of view, albedo coefficient depends on the orbit inclination since the averaged values for polar orbits are around 0.4 versus equatorial orbits, where albedo coefficient is typically around 0.25. The mean value for albedo in the Earth is taken as 0.3 which can be compared with the higher albedo coefficient of Venus (≈ 0.65) and the lower of Mars (≈ 0.15).

When quantifying the heat loads on a spacecraft, it is important to bear in mind that there is only an albedo flux when a portion of the Earth viewed by the satellite is in sunlit. However, its calculation is complex and requires computational implementation. Nevertheless, simplified albedo models which are accurate enough usually assumes that it directly depends on the SZA cosine of the sub-satellite Earth point being the albedo heat load maximum at the sub-solar point. It becomes zero when the SZA is 90° what means Sun is in the horizon. From an element i on board a satellite, albedo heat flux can be calculated assuming the Earth is an sphere with an homogeneous albedo coefficient,

Q_a,i =aG_SA_iFi−Ecosθ, (1.3) where a is the albedo coefficient, G_S the solar irradiance, A_i the surface area of the element i, Fi−E the View Factor from the element i to the Earth, and θ the SZA which is between ±π/2.

1.3.1.5 Outgoing Longwave Radiation

OLR is the emitted radiation by the planet. It is a combination of the radiation emitted in the wavelength band by the atmospheric gases, the Earth surface and the top of the clouds. Although the spectral distribution is complex, from a thermal point of view it can be assumed a greybody spectrum at a temperature between 250 K and 300 K. As is the case with the albedo, OLR is assumed to be diffuse and it is also referred to the TOA in order to eliminate the altitude dependence throughout the atmosphere.

Assuming the Earth is in thermal balance, a relationship between the emitted radiation and the absorbed solar radiation can be assessed. From a thermal point of view, OLR can be quantified in terms of the blackbody equivalent temperature of the planet, T_E. Considering the Earth to be an sphere of radius R_E, it can be estimated by,

T_E = ⁴

sG_S(1−a)

4σ , (1.4)

It can be deduced that OLR increases as the reflected energy decreases, what means that the emitted radiation depends on the albedo coefficient. Even though Equation (1.4) is not directly applicable to the local characteristics across the globe, it is true that albedo coefficient is partially correlated with OLR as was presented by Anderson et al. and will be explained later. Solving Equation (1.4) for a mean albedo value of 0.3, an equivalent temperature of 255 K is obtained. OLR at the TOA, which is expressed as q_E, can be calculated as q_E = σT_E⁴ obtaining a value of 240 W/m². However, variability of the OLR across the globe is high obtaining values from 70 W/m² to 350 W/m².

Surface temperature and its emissivity would determine the OLR values. How- ever, cloud cover also influences OLR because they block the upcoming radiation from the surface. On average, dessert regions have a higher associated OLR and it decreases while approaching to polar regions. Thus, high inclination orbits would have a wider range of values with an associated lower OLR flux. As pointed out by Anderson et al., nighttime variations do not affects the OLR distribution for orbits with an inclination lower than 60°. However, for higher inclination orbits, OLR measured values during the night periods tend to reduce the minimum ones.