Design and Simulation of Stellar Occultation Infrared Band Constellation

Abstract

This study provides an in-depth analysis of the characteristics of stellar occultation events. Using 10 target star sources, the influence of orbital elements on the number, duration, and distribution of stellar occultation events was simulated and analyzed, and the constellation configuration was designed. The results showed the following points: (1) the orbital inclination had the greatest influence on the number of occultation events, with obvious upward and downward trends in the range of 10–40° and 150–180°, and the amount of occultation data remained at about 303 times under the other angle conditions. The orbital height had an effect on the number of occultations, but the amplitude was small. (2) The use of four orbits had an impact on the occultation duration. The duration decreased with an increase in the orbit height and inclination, the distribution was symmetrical with the perigee angular distance, and it increased with an increase in the ascending intersection right ascension. (3) The higher the orbital height, the less comprehensive the longitudinal and latitudinal distribution of occultation events. With an orbital inclination of less than 150°, the greatest occultation event was covered to encompass the entire world. The other two orbital elements had negligible effects on the longitudinal and latitudinal distribution of occultation events. (4) The elevation of the occultation event increased with an increase in the orbital altitude, but the azimuth showed no obvious change trends. A considerable number of normal occultations can be obtained with an orbital inclination of less than 120°. The other two orbital elements had a negligible effect on the distribution of altitude and azimuth of occultation events. A stellar occultation constellation configuration was designed based on the simulation results, and the results showed that the following parameters of satellites can be used to realize the global distribution of occultation events: orbital height of 500 km, orbital inclination of 97.3771°, perigee angular distance of 40°, and ascending node right ascension steps of 40°. This configuration will ensure that an adequate number of normal occultations are obtained, which will ensure the quality of data inversion under the condition of 152 infrared target star sources.

1. Introduction

Atmospheric stellar occultation technology was first proposed by Hays and Roblein in the 1960s [1,2], and it was then successfully used to detect the vertical distribution of ozone in the Earth’s atmosphere [3]. During the 50 years of its development, stellar occultation technology was used to detect the atmospheres of Venus [4], Mars [5,6,7,8], Jupiter [9], Earth [10,11,12] and other planets. Through the detection of particle composition, temperature, and aerosols in the atmosphere, this technology has been used to conduct space environment and weather research, such as that focusing on planetary atmospheric composition characteristics [13,14], climatology [15], and the Earth’s thermosphere ionosphere system [16,17]. The independent development of stellar occultation technology has made its use very significant for promoting research of the middle and upper atmosphere, but its use in constellation design, observation, and prediction is also of utmost value.

It is known that the orbital elements of satellites have a great impact on the number and distribution of stellar occultation events and the duration of occultation events [18,19], and the number and duration of occultation events determine the size of the storage device required for the occultation receiver. However, if the duration of occultation is excessive, the area required to detect the occultation event will also be too large to meet the requirements of data inversion. The degree to which a star deviates from the satellite orbital plane affects the projection of its velocity in the orbital plane; when the projection is small, the vertical velocity of the corresponding occultation tangent point is reduced, which results in a longer occultation duration. The distribution of occultation events involves the occultation observation area, which directly affects the occultation observation performance. Therefore, the influence of satellite orbital parameters on the number and distribution of stellar occultation events requires in-depth study.

In this study, we simulated and calculated the influence and characteristics of satellite orbital elements, including the orbital height, orbital inclination, perigee angular distance, and ascending intersection right ascension on the number, duration, longitude, and latitude distribution, elevation, and azimuth of occultation. There were 10 target star sources. A constellation of star occultation was then designed by considering that large numbers of occultation, short duration, and global coverage were ensured.

2. Methods Used to Simulate Occultation Events

2.1. Principles of Simulating Occultation Events

Considering that the Earth’s atmosphere is a vacuum and ignoring the influence of the satellite’s perturbation force, the process used to simulate events was as follows: the target star was located at an infinite distance, ignoring the motion of stars. Ten target stars were identified and the simulation start and end times were set (total length of 24 h and event interval of 10 s). Starting from the simulation start time, the positions of stars and satellites were calculated to determine whether they were in a state of occultation. If they were in an occultation state, the number, duration, longitude and latitude, distribution, elevation, and azimuth occultation events were further calculated. When one occultation event was completed, the next occultation event was simulated until the end of the occultation event simulation and all target stars had been included. For the calculation process employed, see [20].

An occultation event was identified when the following occurred:

• The tangent of the occultation event was between the two points connecting the star and the satellite, as this ensured that the stellar light passed through the Earth’s atmosphere;
• The variation range of the tangent height of the occultation event was between −150 km and 150 km.

2.2. Satellite Orbit Number Setting

The satellite operation can be described using a set of orbital parameters, including orbital height H, orbital inclination I, perigee angular distance AP, ascending node right ascension RAAN, orbital semi major axis A, and orbital eccentricity E. We used the control variable method to study the influence of the satellite orbit parameters on the characteristics of the stellar occultation events; in this respect, when considering the influence of one satellite orbit parameter on the characteristics of the occultation events, other orbital parameters were set as the default values [21].

Table 1. Satellite orbit parameter settings.

	H (km)	I (°)	AP (°)	RAAN (°)	a (km)	E (10−4)
1	300:50:1000	87.2385	56.7242	277.2985	8212.98015	3.419
2	807.137	10:10:180	56.7242	277.2985	8212.98015	3.419
3	807.137	87.2385	10:10:360	277.2985	8212.98015	3.419
4	807.137	87.2385	56.7242	10:10:360	8212.98015	3.419

provides the associated details, and the numbers 1, 2, 3, and 4 therein represent the experimental groups.

If we take the first group as an example, when I = 87.2385°, AP = 56.7242°, RAAN = 277.2985°, a = 8212.98015 km, E = 3.419 × 10⁻⁴ remains unchanged, we changed the orbital height, starting at 300 km and ending at 1000 km, with a change interval of 50 km, and conducted 15 groups of simulation experiments. The effects of orbital height changes on the number, duration, and distribution of occultation events were then studied, and the same principle was used to study the other experimental groups. The bold parameters in each case represent variations, the other five parameters are invariants, and the selection ranges of the four parameters considering H, I, AP, and RAAN are given in Table 1. We employed one satellite, ten target stars, and a time interval of 10 s. The Earth’s radius of 6371 km was used to analyze how the characteristics of the number of orbits influenced the characteristics of the occultation events.

3. Analysis of Simulation Results

3.1. Influence of Orbital Elements on the Number of Occultation Events

The number of occultation events changed with H, as shown in Figure 1a, and a slight decrease and downward trend occurred with an increase in H. The maximum value occurred at an orbital height of 400 km. The variation in the number of occultation events with I is shown in Figure 1b; the number was relatively stable in the range of 40–150°, but it increased in the range of 10–40°, with an increase in I. The number decreased in the range of 150–180° with an increase in I and was symmetrically distributed. As shown in Figure 1c, there was no change in the number of occultation events with changes in AP, and the average number of occultations was 303. Furthermore, as shown in Figure 1d, there was no change in the number of occultation events in association with the changes in RAAN.

Based on an analysis of the impact of the above orbit parameters on the number of occultation events, when designing the orbit of the LEO satellite, it should be considered that more occultation events can be obtained when I is in the range of 40–150°.

3.2. Influence of Orbital Elements on the Duration of Occultation Events

According to the azimuth distribution of occultations, the stellar occultation events were divided into normal occultations and lateral occultations. Lateral occultations occurred in an azimuth range of 20–45°, 135–180°, and 200–320°. The detection area of lateral occultation events is usually very large, and it cannot meet the needs of the Earth symmetry approximation of the atmospheric local in data inversion. Therefore, only normal occultation durations were studied here. The occultation duration was considered to be the mean of all the normal occultation events under a certain variable.

Figure 2 shows the variations in the occultation duration with the altitude of the orbital satellite, and the average occultation duration was 87–140 s within an orbital altitude range of 300–1000 km. There was a negative correlation between orbital altitude and the occultation duration. Figure 3 shows the variations in the occultation duration with orbital inclination; the duration ranged from 86 s to 102 s and was observed to decrease with an increase in inclination. Figure 4 shows the variation characteristics of the occultation duration with AP, and it was observed to be symmetrically distributed with AP; in the range of 0–180°, the occultation duration increases with an increase in AP, but the opposite change trend is observed in the range of 180–360°. However, the occultation duration varies from 91.86 to 91.84, with only a minimal change. Figure 5 shows the variations in the occultation duration with RAAN; the occultation duration increases with an increase in RAAN and variation ranges from 91.892 s to 91.908 s.

According to the above characteristics associated with the variations in the occultation duration with orbital parameters, the data obtained following data inversion were more accurate when the occultation duration was shorter. Therefore, a high orbit and large inclination were designed. Although the AP and RAAN were found to have influence on the variations in the occultation duration, they were not considered here because their effective ranges were very small.

3.3. Influence of Orbital Elements on the Longitudinal and Latitudinal Distribution of Occultation Events

According to the parameter settings in Table 1, the effects of satellite orbit altitude, inclination, AP, and RAAN on the longitudinal and latitudinal distribution of stellar occultation events were studied. As shown in Figure 6, H was used to analyze the number and distribution of occultation events that occurred at 300 km and 900 km, and the orbital altitude was found to have no effect on the latitudinal range covered by the occultation event. However, the number of occultations tended to be concentrated at lower latitudes with an increase in orbital height. A low orbit is more capable of providing full longitudinal coverage.

Figure 7 shows the changes in the number and distribution of stellar occultation events associated with longitudinal and latitudinal coverage associated with changes in the orbital inclination, where I was set as 60°, 120°, and 180°, respectively. An analysis of the latitudinal distribution of occultation events showed that they mainly occurred in low latitude areas under the three conditions (few occurred under different coverages). The full latitude coverage was realized at an inclination angle of 120°, and the number of events was more symmetrically distributed than under the condition of 60°. A comparison between the longitudinal distributions of the occultation numbers under these conditions showed that it was uniform when I = 60° or 120°, but when I = 180°, the events were mainly distributed in the range of −30–30° and 150–180°. These results show that the inclination angle should be less than 150° to realize the global coverage of occultation events.

Figure 8 shows the changes in the number of occultation events with changes in longitude and latitude and AP. The AP of the satellite was set as 30°, 90°, and 150°, respectively. By analyzing the latitudinal distribution of the occultation numbers, the events were found to be mainly distributed in the low latitude areas, and there was no change in their distribution with a different angular distance. The longitudinal distribution of the occultation events was then analyzed. Under the condition of a low angular distance, the occultation events covered all latitudes, and there was little difference in their quantitative distribution. With an increase in AP, the occultation events were distributed in the range of −60° to 60°, but they were more concentrated in the range of −30° to 30°; this indicates that the perigee angular distance has a greater impact on the longitudinal distribution of occultation events compared to the latitudinal distribution, but it does not affect the global distribution.

Figure 9 shows the changes in the longitudinal and latitudinal distribution of occultation events with changes in the elevation angle right ascension (30°, 90°, and 150°, respectively). The conclusion was the same as that for AP. Changing RAAN will affect the number of occultations in different longitudes and latitudes but will not affect the global coverage.

3.4. Influence of Orbital Elements on Elevation and Azimuth Distribution of Occultation Events

According to the setting of the track parameters shown in Table 1, the changes in elevation and azimuth with track height are given in Figure 10, where elevation is the angle between the tangent direction of the satellite motion and the connecting direction of the satellite and the star. When H = 300 km, elevation was approximately 12° and 22°, and when H = 900 km, elevation was approximately 26° and 32°, which indicated that the elevation of the occultation events increased with the orbital altitude. The azimuth of the occultation event showed no obvious change trend in association with the changes in the orbital altitude.

Figure 11 shows the changes in the elevation and azimuth with track inclination. As shown in the figure, when I was 60°, 120°, and 180°, respectively, there were no significant variations in the size and quantity of the elevation. When I = 180°, the azimuth was mainly in the range of 0–20°, 210–240°, and 300–330°. Approximately 50% of the quantity occurs as lateral occultation, and the quality of the subsequent data inversion cannot be guaranteed. When I = 120°, a considerable event is lateral occultation. Therefore, the inclination angle of the track tends to be less than 120°.

Figure 12 shows the variations in the elevation, azimuth with orbital AP. When AP was 30°, 60°, and 150°, respectively, there were no considerable changes in the size and quantity of the elevation and azimuth; this result indicates that the satellite orbital AP has a minimal effect on the distribution of elevation and azimuth occultation events.

Figure 13 shows the variations in the elevation and azimuth with orbit RAAN. When RAAN was 30°, 60°, and 150°, respectively, the height angle was approximately 24° and 30°, and there was little change in the value. There were no significant changes in the coverage and distribution quantity of the azimuth.

4. Discussion and Constellation Design

4.1. Analysis of Track Element Results

The stellar occultation events that occurred within 24 h were simulated. By changing the orbital parameters of the LEO satellite, including H, I, AP, RAAN, the effects of the satellite orbit parameters on the number, duration, longitude and latitude distribution, elevation, and azimuth distribution of stellar occultation events were analyzed, and the following conclusions were obtained:

• The orbital inclination had the greatest influence on the number of occultation events, and it showed obvious upward and downward trends. The orbital height had a slight influence on the number of occultations. To obtain more occultation events, the orbit inclination should range between 40° and 150°.
• There was a negative correlation between orbital altitude and the occultation duration. According to the analysis results, four orbit elements had an impact on the duration of occultation. To decrease the duration, it is necessary to select a higher orbit height and a larger orbit inclination.
• By analyzing the distribution of stellar occultation events, it was established that the influence of the perigee angular distance and ascending node right ascension can be ignored because the two have no impact on global coverage, as the distribution of events mainly relates to the orbital height and inclination. Under the condition of achieving a global distribution and a high occultation quality, it is necessary to select a lower orbit and orbital conditions with an inclination lower than 120°.

There are no international studies on occultation using infrared sources for constellation design, and the influence of orbital elements on the number and distribution characteristics of occultation events has not been analyzed. However, the leo-leo occultation distribution has been studied in China. Duxiaoyong et al. quantitatively discussed the impact of orbital parameters on the number and distribution of the leo-leo occultation events, and found that the orbital parameters with the greatest impact on the number and latitude distribution of occultation events were (in order) orbital inclination, orbital altitude, right ascension of the ascending node, and perigee angular distance. Of these, the RAAN was found to have little effect on the distribution with respect to longitude and latitude, but it had a considerable effect on the quantity. AP was found to have little effect on the occultation number and distribution. In addition, these parameters were found to have no effect on the longitudinal distribution of the occultation events. These results are, therefore, consistent with the stellar occultation simulation results presented here.

4.2. Constellation Configuration Design

The constellation design is based on the following conditions:

• Global coverage of occultation events at a large orbital inclination;
• Use of the simplest satellite system with a low orbit to record the highest number of occultation events within the shortest operation time. In this paper, the optimum orbit altitude was 500 km;
• Sunlight interference should be avoided, the sun maintained in synchronous orbit, and the solar zenith angle should be greater than 110°;
• The orbit should be designed as a repetitive orbit;
• With respect to the time domain coverage, the ascending intersection step and the initial approach point angle step should be set according to the tangent point position.

According to the solar synchronous orbit and the constraint conditions for selecting I < 120°, the orbit inclination was calculated quantitatively. The relationship between a semi major axis, a, of a solar synchronous orbit, $a_0$, and track inclination, $i_0$ was determined as follows:

$$cos i_0=-0.09856{\left(1-e^2\right)}^2{\left(\frac{a_0}{R_e}\right)}^{3.5},$$

(1)

where $R_e$ is the radius of the earth (6371 km), e is orbital eccentricity (0), and $a_0$ is 6871 km. After calculation, the track inclination was found to be 97.3771°.

The Earth’s radius, r, is 6371 km and the orbit height is 500 km. Through a simulation calculation, the coverage range of the satellite sight distance was found to be ± 20 degrees. See Figure 14 for the principle.

$$\cos \left(\theta \right)=\frac{r}{r+h}$$

(2)

Therefore, the ascending intersection right ascension step is 40°. After conducting the above calculation, the number of orbits can be obtained, as shown in

Table 2. Number of constellation design orbits.

I (°)	RAAN (°)	H (km)	AP (°)	E
97.3771	40 (step)	500	40	0

.

As shown in Figure 15, the constellation design of star occultation was obtained using STK, and nine stars were used to meet the goal of global monitoring using star occultation.

The received signal of star sources was simulated according to the designed occultation signal receiving system, and the infrared star sources were selected within the corresponding apparent magnitude range under the condition that the signal-to-noise ratio was greater than 100. Figure 16 shows the coordinate distribution of all the target stars in the infrared band. As shown in the figure, the target stars are not concentrated in a certain area but are distributed throughout the entire sky area. Therefore, with an increase in the number of target star sources, not only can the global coverage of occultation events be achieved, but more data can be obtained.

5. Conclusions

In this study, the influence of orbital elements on the number, duration, and distribution characteristics of occultation were quantitively analyzed, a constellation design method based on infrared star sources was established and the results provided. Under the condition of 152 target star sources, not only can global coverage be achieved, but more observation events can be obtained. Under this condition, occultation events can be predicted to provide data for forward modeling and laying the foundation for further realization of an end-to-end simulation platform integrating event simulation, observation simulation, and data inversion. Most importantly, this provides a powerful means of achieving global environmental monitoring.