# Aerostat-Based Observation of Space Objects in the Stratosphere
## 2 Astronomical Observation Conditions in Stratosphere  
### Atmospheric Transmittance and Sky Back-Ground  
The aerostat for performing high-altitude detection tasks generally works in the altitude range of 18 km to 35 km in the stratosphere. The work height selection is directly related to the weight of the pod composed of the detection payload and flight control equipment [6]. The air is very thin in this altitude range. For example, at a 20 km altitude, the air density is 0.0888 kg/m\({}^{3}\) and the pressure is 55.18 hPa, which are 7.24% and 5.44% [7] of the values at sea level, respectively. A rare air environment leads to good atmospheric transmittance for astronomical observation. According to the data published on the official website [8] of the European Southern Observatory (La Paranal) at 2635 m, the atmospheric transmittance at 0\({}^{\circ}\), 30\({}^{\circ}\) and 60\({}^{\circ}\) zenith distances are drawn in the wavebands of 500 nm to 1700 nm. As shown in Figure 1, good atmospheric transmittance is available at this observation altitude, but several absorption bands exist in the near-infrared wave range that causes the atmosphere to be completely opaque. The LOWTRAN software (LOWTRAN7) was used to calculate the atmospheric transmittance in the visible band (500 nm-800 nm) and near-infrared band (900 nm-1700 nm) at a 20 km altitude in the stratosphere. LOWTRAN is a low-resolution propagation model and computer code for predicting atmospheric transmittance and background radiance by inputting atmospheric profiles and other parameters [9]. It can also be used to calculate solar/lunar scattered radiance. As shown in Figure 2, the results are much better than the station La Paranal, where the values of transmittance in the visible band and near-infrared band are more than 0.91 and 0.988, respectively, even though they are at different zenith distances. Therefore, the atmosphere in the stratosphere is very close to transparency for visible and near-infrared bands.  
Figure 1: Atmospheric transmittance in visible and near-infrared bands with zenith distances of 0\({}^{\circ}\), 30\({}^{\circ}\), and 60\({}^{\circ}\) at the station La Paranal of the European Southern Observatory.  
Figure 2: The calculated value of atmospheric transmittance of visible and near-infrared bands at 20 km of altitude in Beijing. (**a**) 500 nm–800 nm; (**b**) 900 nm–1700 nm.  
On the other hand, the sky background for stratosphere-based observations is also better than the ground-based observation because the atmosphere scattering in the stratosphere is much weaker than in the troposphere. This advantage is significant for astronomical observation during the daytime, especially in the morning and evening. Taking 02:00:00 (UTC) in a day around the summer solstice in Beijing as an example, the sky background magnitudes in the visible band (500 nm-800 nm) and near-infrared bands (900 nm-1700 nm) were calculated using LOWTRAN. As shown in Figure 3, the sky background in both the visible band and the near-infrared bands is lighter than 4 mag/arcsec\({}^{2}\) (hereafter, we use mag for short) on the ground, which greatly limits the observation ability during the daytime. As for the stratosphere observation, the sky background is darker than 6.5 mag for the visible band and 7.5 mag for the near-infrared band, which are 2.0-2.5 times darker than ground-based observations and practical for daytime observation.  
The magnitude can be calculated by a simple relation from flux as follows:  
\[E_{2}/E_{1}=10^{-0.4(m_{2}-m_{1})} \tag{1}\]  
Here, \(E\) is the flux of the object, \(m\) is the magnitude, while the subscripts stand for different objects. In the visible and infrared bands, the sky background at a 20 km altitude is about 4 mag darker than the ground, which means that the sky background radiance at 20 km is 2.5% of the ground.