A method for relative phase adjustment of low-Earth orbit satellite constellations using only atmospheric drag

Abstract

This invention relates to a method for relative phase adjustment of a low-Earth orbit satellite constellation using only atmospheric drag, belonging to the field of satellite orbit control technology. The method includes: determining the maximum and minimum windward areas of the satellite based on a satellite structural model; calculating the actual average windward area over the entire orbital period when the satellite maintains its maximum and minimum windward areas in the Earth's shadow region; calculating the average atmospheric drag over the entire orbital period when the satellite maintains its maximum and minimum windward areas in the Earth's shadow region, calculating the average atmospheric drag difference, and then calculating the relative orbital control quantity based on the average atmospheric drag difference; using the satellite with the lowest orbital altitude after separation from the launch vehicle as the reference satellite, formulating a constellation phase deployment strategy based on the relative orbital control quantity, and executing the constellation phase deployment strategy to complete the relative phase adjustment of the constellation. This invention is simple to operate, requires few commands, can be started or stopped at any time, does not affect the overall satellite safety, energy balance, or payload services, does not occupy telemetry and control resources, and achieves high constellation phase control accuracy.

Description

Technical Field

[0001] This invention relates to the field of satellite orbit control technology, and specifically to a method for adjusting the relative phase of a low-Earth orbit satellite constellation using only atmospheric drag. Background Technology

[0002] With the increasing number of low-Earth orbit (LEO) satellites and the more frequent construction of satellite constellations, the demand for constellation phase adjustment control has also increased significantly. Traditional constellation phase adjustment requires thruster-based orbit control. The orbit control tasks for satellites within the constellation all require calculation of relevant parameters on the ground based on measured orbit information. Subsequently, multiple telemetry and control (TT&C) arcs are used to inject orbit control parameters, inject pre-control state preparation commands, monitor orbit control status, and inject post-control state recovery commands. When the number of satellites in a constellation is large, numerous uplink command injection operations are required, consuming significant TT&C resources for monitoring and handling satellite safety issues. The number of ground stations required also increases substantially, and satellite payload services may be reduced or temporarily suspended due to mission conflicts. Furthermore, if there is a large propellant leak or propulsion failure, phase adjustment cannot continue, failing to achieve the expected phase control objectives and resulting in phase adjustment failure. Summary of the Invention

[0003] To address the problems of traditional constellation phase adjustment methods, such as the large number of uplink command operations and the consumption of significant telemetry and control resources, as well as the failure of constellation phase adjustment due to excessive propellant leakage or propulsion damage, this invention proposes an orbit control method for relative phase adjustment of low-Earth orbit satellite constellations with SADA using only atmospheric drag.

[0004] To solve the above problems, the present invention adopts the following technical solution:

[0005] A method for relative phase adjustment of a low-Earth orbit satellite constellation utilizing only atmospheric drag, the method comprising the following steps:

[0006] Step 100: Based on the structural model of the satellite with SADA, determine the maximum and minimum windward areas of the satellite;

[0007] Step 200: Calculate the actual average windward area of ​​the satellite during the entire orbital period when it maintains the maximum and minimum windward areas in the Earth's shadow region, respectively;

[0008] Step 300: Based on the actual average windward area calculated in Step 200, calculate the average atmospheric drag of the satellite during the entire orbital period when it maintains the maximum and minimum windward areas in the shadow area. Subtract the two calculated average atmospheric drags to obtain the average atmospheric drag difference, and then calculate the relative orbital control quantity based on the average atmospheric drag difference.

[0009] Step 400: Using the satellite with the lowest orbital altitude after separation from the launch vehicle as the reference satellite, formulate a constellation phase deployment strategy based on the relative orbital control values ​​calculated in Step 300, and execute the constellation phase deployment strategy to complete the relative phase adjustment of the constellation.

[0010] Compared with the prior art, the present invention has the following beneficial effects:

[0011] This invention proposes a method for relative phase adjustment of constellations composed of low-Earth orbit satellites with SADA (Satellite Adaptive Assistance) without propulsion, utilizing only atmospheric drag. In this method, the satellite adjusts the windward area of ​​its solar panels by rotating the SADA angle, locking the windward area in the Earth's shadow region at its maximum or minimum. The difference in atmospheric drag experienced by different windward areas is used as a control variable to formulate and execute a constellation phase deployment strategy, ultimately completing the relative phase adjustment of the constellation. This invention is simple to operate, requires few commands, can be started or stopped at any time, does not affect the overall satellite safety, satellite energy balance, or payload services, and does not occupy telemetry and control resources. Furthermore, due to the small relative wind drag attenuation, the constellation phase control accuracy is high. Attached Figure Description

[0012] Figure 1 This is a flowchart of the method for adjusting the relative phase of a low-Earth orbit satellite constellation using only atmospheric drag, as described in an embodiment of the present invention.

[0013] Figure 2 This is a graph showing the change of atmospheric density over time within one orbital period. Detailed Implementation

[0014] The technical solution of the present invention will now be described in detail with reference to the accompanying drawings and preferred embodiments.

[0015] like Figure 1 As shown, this embodiment provides a method for relative phase adjustment of a low-Earth orbit satellite constellation with SADA that utilizes only atmospheric drag. The method includes the following steps:

[0016] Step 1 (S100): Based on the structural model of the satellite with SADA, determine the maximum and minimum windward areas of the satellite;

[0017] Step 2 (S200): Based on the maximum and minimum windward areas determined in Step 1, and considering the difference in atmospheric density between the sunlit and shadowed areas, calculate the actual average windward area of ​​the satellite during the entire orbital period when it maintains the maximum and minimum windward areas in the shadowed area.

[0018] Step 3 (S300): Based on the actual average windward area calculated in Step 2, calculate the average atmospheric drag of the satellite during the entire orbital period when it maintains the maximum and minimum windward areas in the Earth's shadow area. Subtract the two calculated average atmospheric drags to obtain the average atmospheric drag difference, and then calculate the relative orbital control quantity based on the average atmospheric drag difference.

[0019] Step 4 (S400): Considering the different separation velocities of each satellite during satellite-rocket separation, this step takes the satellite with the lowest orbital altitude after satellite-rocket separation as the reference satellite. Taking into account the phase control, the amount of phase change during uncontrolled drift, and the time limit for phase adjustment, a constellation phase deployment strategy is formulated based on the relative orbital control amount calculated in Step 3. The constellation phase deployment strategy is executed to complete the relative phase adjustment of the constellation.

[0020] The steps in this embodiment will be described in detail below.

[0021] S100: Determination of the satellite's maximum and minimum windward areas.

[0022] Since the Solar Array Drive Assembly (SADA) can rotate, the satellite's solar panels can rotate to any angle. Therefore, the satellite's maximum windward area is the sum of the solar panel area and the satellite's windward area, and the satellite's minimum windward area is the satellite's windward area. The actual maximum and minimum windward areas are determined based on the structural model of a satellite with SADA.

[0023] S200: Calculation of actual average windward area.

[0024] When satellites with SADA (Satellite Adaptor and Radiation Assist) adjust their constellation phase using atmospheric drag, the satellite needs to recharge in the sunlit area, and the SADA and solar panels rotate towards the sun, making adjustment impossible. However, in the shadow area, the satellite does not need to recharge by the sun, and the windward area of ​​the solar panels can be controlled by locking the SADA, so that the satellite maintains its maximum or minimum windward area in the shadow area.

[0025] Because atmospheric density is affected by temperature, it is higher in sunny areas and lower in shadow areas. The average atmospheric density of a satellite varies significantly across sunny and shadow areas and throughout its orbital period. Therefore, taking atmospheric density into account, the formula for calculating the actual average windward area of ​​the satellite throughout its orbital period is as follows:

[0026]

[0027] in:

[0028] This represents the satellite's actual average windward area over the entire orbital period while maintaining minimum windward area in the Earth's shadow region. This is the actual average windward area of ​​the satellite during the entire orbital period when the satellite maintains its maximum windward area in the Earth's shadow region.

[0029] ΔS is the projected area of ​​the solar panel in the direction of the satellite's flight velocity;

[0030] S min S is the minimum windward area of ​​the satellite. max This represents the satellite's maximum windward area.

[0031] T is the orbital period;

[0032] t hold The duration during which the satellite maintains its minimum or maximum windward area throughout its entire orbital period;

[0033] This represents the time-averaged atmospheric density over the entire orbital period.

[0034] The time-averaged atmospheric density is the atmospheric density when the satellite maintains its minimum or maximum windward area throughout its entire orbital period.

[0035] S300: Calculation of mean atmospheric drag difference and corresponding orbit control quantities.

[0036] The average atmospheric drag of the satellite is calculated based on the time-averaged atmospheric density used by S200 throughout its entire orbital period and the actual average windward area of ​​the satellite throughout its entire orbital period. The specific calculation formula is as follows:

[0037]

[0038] Among them, C d ρ is the atmospheric drag coefficient, and v is the satellite's flight speed.

[0039] The relative orbital control required for constellation phase adjustments comes from the difference in mean atmospheric drag, and its calculation formula is as follows:

[0040]

[0041] Based on the average atmospheric drag difference, the formula for calculating relative orbital control quantities is as follows:

[0042]

[0043] Where m is the satellite mass, t is the orbit control duration, and a is the semi-major axis of the satellite orbit.

[0044] S400: Develop and implement astrological phase deployment strategies.

[0045] To avoid satellite collisions, the separation velocities of each satellite are different when they separate from the rocket, and the orbital altitudes of the satellites after entering orbit are also different. Here, the satellite with the lowest orbital altitude after separation is used as the reference satellite to formulate the constellation phase deployment strategy, and the average atmospheric drag difference calculated by S300 is used for fine-grained phase drift control.

[0046] The phase drift of satellites mainly targets satellites with the second lowest and highest orbital altitudes. These satellites are more likely to fail to achieve phase alignment within the specified timeframe due to their close orbital altitude to the reference satellite. Therefore, the reference satellite needs to actively lower its orbit using the mean atmospheric drag difference to accelerate the phase drift angular velocity of other satellites. The formula for calculating the difference in orbital angular velocity dω between the controlled satellite and the comparison satellite is as follows:

[0047]

[0048] Where μ is the Earth's gravitational constant, t is the orbital control duration, and a sat For the semi-major axis of the controlled satellite's orbit, a target To compare the semi-major axis of a satellite's orbit, this formula can be used to compare a reference satellite that has started to drift with other satellites when phase drift begins, and it can also be used to compare other satellites with an uncontrolled reference satellite when phase braking occurs.

[0049] Step 410: Before performing reference star phase drift control, calculate the reference star phase drift control duration that meets the constraints.

[0050] Due to the limited control capability of the mean atmospheric drag difference, satellites will experience a certain amount of inter-satellite phase drift during phase drift initiation and phase braking control, which needs to be considered and calculated. Therefore, before performing phase drift initiation control, it is necessary to calculate the total time spent on constellation deployment, which should meet the following constraints:

[0051]

[0052] in:

[0053] t total t start t process and t end These represent the total time spent on final constellation deployment, the time spent on the initial drift of the reference star phase, the time spent on the uncontrolled natural drift of the highest star, and the time spent on braking the highest star phase. limit Total constellation deployment time limited by mission metrics;

[0054] θ start θ target2 and θ BeforeStart2 These represent the phase increase of the second lowest star during the phase drift of the reference star, the target phase of the second lowest star, and the phase of the second lowest star before the phase drift, respectively, θ.end The phase that drifts during the highest star phase braking, θ process θ TargetHighest and θ BeforeStartEnd These are the phases added during the uncontrolled natural drift of the highest star, the target phase of the highest star, and the phase of the reference star before the drift of the highest star;

[0055] dω start and dω BeforeStart2 dω represents the difference in orbital angular velocity between the second lowest star and the reference star at the end of phase drift and the difference in orbital angular velocity between the second lowest star and the reference star before phase drift, respectively. end dω represents the difference in orbital angular velocity between the highest star and the reference star before the highest star's phase braking. BeforeStartEnd The difference in orbital angular velocity between the highest star and the reference star before phase drift begins can be calculated using formula (5), i.e., when calculating dω. start and dω BeforeStart2 At that time, the second lowest satellite corresponds to the comparison satellite in formula (5), and the reference satellite corresponds to the controlled satellite in formula (5). dω is calculated. end and dω BeforeStartEnd At that time, the highest-ranking satellite corresponds to the controlled satellite in formula (5), and the reference satellite corresponds to the comparison satellite in formula (5).

[0056] Based on the above constraints, the phase drift control duration that meets the conditions can be calculated for phase drift control of the reference star.

[0057] Step 420: Perform phase drift control on the reference star according to the phase drift control duration. After the phase drift ends, the reference star returns to the mode of maintaining the minimum windward area in the shadow area.

[0058] Step 430: The constellation undergoes uncontrolled natural drift and phase braking. The phase braking control of each satellite is independent of each other and satisfies the following formula:

[0059]

[0060] Where, θ target For the target phase of the controlled satellite, θ now The phase before the controlled satellite phase braking, dω stop t represents the difference in orbital angular velocity relative to the reference satellite before the controlled satellite's phase braking. stop The time spent applying phase braking to a controlled satellite.

[0061] Once all satellites have been adjusted to the target phase through phase control, the relative phase adjustment is complete, and the constellation has completed phase deployment.

[0062] The relative phase adjustment method for low-Earth orbit satellite constellations with SADA proposed in this invention utilizes only atmospheric drag. It is simple to operate, requires few commands, and can be started or stopped at any time without affecting the overall satellite safety, the satellite's energy balance, or payload services. It does not occupy telemetry and control resources. At the same time, due to the relatively small attenuation of wind resistance, the constellation phase control accuracy is high.

[0063] The relative phase adjustment method for a low-Earth orbit satellite constellation with SADA, proposed in this invention and utilizing only atmospheric drag, has been implemented and verified on a certain constellation. This constellation consists of 20 satellites with an orbital altitude of 500 km and an orbital period of 5676.98 s. Simulation calculations based on the satellite structural model show that the minimum windward area of ​​the satellite is 0.092 m². 2 The maximum windward area is 0.382m². 2 The area of ​​the windsurfing board is 0.29m². 2 When solar activity is calculated using an F10.7 index of 150 and a Kp index of 3, the change in atmospheric density over one orbital period is as follows: Figure 2 As shown in the figure, the yellow and red rectangular areas represent the satellite's SADA locked angle, meaning the satellite maintains its maximum or minimum frontal area. Calculations are performed based on atmospheric density data to obtain... According to formula (2), when the windward area of ​​the shadow area is kept to the minimum, the average atmospheric drag is about 10.43 μN and the orbital attenuation in 1 day is about 81 m. When the windward area of ​​the shadow area is kept to the maximum, the average atmospheric drag is about 13.23 μN and the orbital attenuation in 1 day is about 103 m. The difference in attenuation between the minimum and maximum windward areas of the shadow area is about 22 m.

[0064] The constellation requires all aspects to be adjusted within 6 months. Taking star 1 as the reference star, the orbital altitude and aspect distribution of the 20 stars before the phase deployment begins are shown in Table 1.

[0065] Table 1. Satellite orbital altitude and phase distribution before constellation phase adjustment.

[0066]

[0067]

[0068] Based on the attenuation difference, i.e., the relative orbital control amount, the phase adjustment strategy of the constellation is calculated as shown in Table 2.

[0069] Table 2 Zodiac Aspect Adjustment Strategies

[0070] 1 15 —— —— 15 2 —— 3 24 42 3 —— 11 31 57 4 —— 12 39 66 5 —— 7 49 71 6 —— 17 51 83 7 —— 27 53 95 8 —— 29 58 102 9 —— 41 58 114 10 —— 39 64 118 11 —— 36 71 122 12 —— 45 71 131 13 —— 55 71 141 14 —— 47 79 141 15 —— 51 81 147 16 —— 57 83 155 17 —— 55 88 158 18 —— 58 90 163 19 —— 61 93 169 20 —— 58 98 171

[0071] As shown in Table 2, the constellations complete their phase deployment within 171 days at the latest, meeting the 6-month time requirement.

[0072] In the actual execution of atmospheric drag phasing, satellites were deployed slowly in the early stages of constellation deployment because some satellites were still undergoing early testing. However, due to stronger solar activity and higher atmospheric density in the later stages, the wind drag attenuation exceeded the budgeted value, leading to faster constellation deployment. The actual phase adjustment results of the constellation are shown in Table 3.

[0073] Table 3 shows the actual aspect adjustments of the zodiac signs.

[0074] 1 0 17 0 2 -18 48 -17.992 3 -36 74 -36.000 4 -54 83 -53.991 5 -72 80 -72.009 6 -90 88 -90.006 7 -108 103 -108.010 8 -126 120 -126.005 9 -144 120 -143.993 10 -162 121 -162.007 11 -180 121 -180.003 12 -198 120 -197.991 13 -216 127 -216.000 14 -234 129 -233.990 15 -252 130 -252.010 16 -270 134 -270.006 17 -288 135 -287.993 18 -306 135 -305.990 19 -324 147 -323.997 20 -342 152 -342.010

[0075] Actual on-orbit constellation phase deployment results show that the constellation completed phase deployment in 152 days, faster than predicted by the strategy, meeting the 6-month time requirement, and the actual satellite phase control accuracy was 0.01°. Practical application results demonstrate that the relative phase adjustment method presented in this invention can achieve constellation phase deployment with high control accuracy, meeting the requirements of on-orbit applications.

[0076] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0077] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention patent should be determined by the appended claims.

Claims

1. A method for relative phase adjustment of a low-Earth orbit satellite constellation utilizing only atmospheric drag, characterized in that, Includes the following steps: Step 100: Based on the structural model of the satellite with SADA, determine the maximum and minimum windward areas of the satellite; Step 200: Calculate the actual average windward area of ​​the satellite during the entire orbital period when it maintains the maximum and minimum windward areas in the shadow region; Step 300: Based on the actual average windward area calculated in Step 200, calculate the average atmospheric drag of the satellite during the entire orbital period when it maintains the maximum and minimum windward areas in the shadow area. Subtract the two calculated average atmospheric drags to obtain the average atmospheric drag difference, and then calculate the relative orbital control quantity based on the average atmospheric drag difference. Step 400: Using the satellite with the lowest orbital altitude after separation from the launch vehicle as the reference satellite, formulate a constellation phase deployment strategy based on the relative orbital control values ​​calculated in Step 300, and execute the constellation phase deployment strategy to complete the relative phase adjustment of the constellation.

2. The method for adjusting the relative phase of a low-Earth orbit satellite constellation using only atmospheric drag as described in claim 1, characterized in that, The constellation phase deployment strategy includes the following steps: Step 410: Before performing reference star phase drift control, calculate the reference star phase drift control duration that satisfies the following constraints: in: t total t start t process and t end These represent the total time spent on final constellation deployment, the time spent on the initial drift of the reference star phase, the time spent on the uncontrolled natural drift of the highest star, and the time spent on braking the highest star phase. limit Total constellation deployment time limited by mission metrics; θ start θ target2 and θ BeforeStart2 These represent the phase increase of the second lowest star during the phase drift of the reference star, the target phase of the second lowest star, and the phase of the second lowest star before the phase drift, respectively, θ. end The phase that drifts during the highest star phase braking, θ process θ TargetHighest and θ BeforeStartEnd These are the phases added during the uncontrolled natural drift of the highest star, the target phase of the highest star, and the phase of the reference star before the drift of the highest star; dω start and dω BeforeStart2 dω represents the difference in orbital angular velocity between the second lowest star and the reference star at the end of phase drift and the difference in orbital angular velocity between the second lowest star and the reference star before phase drift, respectively. end dω represents the difference in orbital angular velocity between the highest star and the reference star before the highest star's phase braking. BeforeStartEnd This represents the difference in orbital angular velocity between the highest star and the reference star before phase drift begins. Step 420: Perform phase drift control on the reference star according to the phase drift control duration, and after the phase drift ends, the reference star maintains the minimum windward area in the shadow area. Step 430: The constellation undergoes uncontrolled natural drift and phase braking. Once all satellites have been adjusted to the target phase, the relative phase adjustment is complete.

3. The method for adjusting the relative phase of a low-Earth orbit satellite constellation using only atmospheric drag as described in claim 2, characterized in that, The formula for calculating the difference in angular velocity of each orbit in step 410 is as follows: Where μ is the Earth's gravitational constant, t is the orbital control duration, and a sat For the semi-major axis of the controlled satellite's orbit, a target To compare the semi-major axis of the satellite's orbit.

4. The method for adjusting the relative phase of a low-Earth orbit satellite constellation using only atmospheric drag as described in claim 2, characterized in that, In step 430, the phase braking control of each satellite is independent of each other and all satisfy the following formula: Where, θ target For the target phase of the controlled satellite, θ now The phase before the controlled satellite phase braking, dω stop t represents the difference in orbital angular velocity relative to the reference satellite before the controlled satellite's phase braking. stop The time spent applying phase braking to a controlled satellite.

5. The method for relative phase adjustment of low-Earth orbit satellite constellations utilizing only atmospheric drag according to any one of claims 1 to 4, characterized in that, The formula for calculating the actual average windward area in step 200 is as follows: in, and These represent the actual average windward area of ​​the satellite during the entire orbital period, corresponding to the minimum and maximum windward areas of the satellite in the Earth's shadow region, respectively; ΔS is the projected area of ​​the solar panel in the direction of the satellite's flight velocity; S min and S max These represent the satellite's minimum and maximum windward areas, respectively; T is the orbital period; t hold The duration during which the satellite maintains its minimum or maximum windward area throughout its entire orbital period; This represents the time-averaged atmospheric density over the entire orbital period. The time-averaged atmospheric density is the atmospheric density when the satellite maintains its minimum or maximum windward area throughout its entire orbital period.

6. The method for relative phase adjustment of low-Earth orbit satellite constellations utilizing only atmospheric drag according to any one of claims 1 to 4, characterized in that, The formula for calculating average atmospheric drag in step 300 is as follows: in, and C represents the average atmospheric drag over the entire orbital period when the satellite maintains its maximum and minimum windward area in the Earth's shadow region. d ρ is the atmospheric drag coefficient, and v is the satellite's flight speed.

7. The method for relative phase adjustment of low-Earth orbit satellite constellations utilizing only atmospheric drag according to any one of claims 1 to 4, characterized in that, The formula for calculating the relative orbital control quantity Δa in step 300 is as follows: Where m is the satellite mass, t is the orbit control duration, and a is the semi-major axis of the satellite orbit. This represents the average atmospheric drag difference.

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