A subunit light pressure perturbation calculation method for antenna satellites

Abstract

The application relates to a sub-unit light pressure perturbation calculation method for an antenna satellite, and aims to solve the problem of inaccurate solar light pressure calculation of a large satellite antenna, which leads to poor satellite orbit prediction and attitude control precision, and provides a sub-unit light pressure perturbation calculation method for an antenna satellite. The method specifically comprises the following steps: step one, determining a sun exposure factor according to the position relationship among the sun, the earth and the antenna satellite in an ECI coordinate system; step two, calculating the light pressure projection area of the satellite; step three, calculating the light pressure perturbation force borne by each part according to the sun exposure factor in step one and the light pressure projection area in step two; and step four, judging whether the set time length is reached, if not, repeating steps one to three, otherwise, ending. The application is used in the field of antenna satellite light pressure perturbation acquisition.

Description

TECHNICAL FIELD

[0001] The present application relates to a light pressure perturbation calculation method of an antenna satellite. BACKGROUND

[0002] With the rapid development of space technology and the increasing demand for global communication, building high-performance communication infrastructure has become a top priority. In this context, large satellite antennas, as a core component of space infrastructure, have become increasingly important. These antennas not only support data and communication services around the world, but also are the key technology for global wide-area coverage, deep space exploration missions, and disaster emergency response. In addition, with the expansion of earth observation, space science research, and commercial satellite services, the capabilities of large satellite antennas in data collection and other aspects have become the key to driving progress in these fields. By improving the capacity and stability of space communication networks, large antennas enable satellites to handle and transmit massive amounts of data, supporting complex scientific research and commercial operations. From climate monitoring to astrophysics research, from global positioning systems to broadband internet services, large satellite antennas play a vital role everywhere, and their technological innovation and application are directly related to the operational efficiency of various industries and the well-being of all mankind. Developing large satellite antenna technology is not only a manifestation of enhancing national technological power, but also an integral part of the global communication development trend. The dynamic model, as the core of satellite antenna design and control, plays a crucial role in improving mission success rate, reducing risk, and optimizing orbit operation.

[0003] For space large structure satellites equipped with large structures such as antennas, the accuracy of the dynamic model is an important factor to ensure the structural stability and functionality of the satellite. Due to the unique and complex structure of such satellites, their large surface area makes solar pressure the main factor of perturbation. Traditional solar pressure calculation usually sets the satellite surface-to-mass ratio as a constant value, although it simplifies the design and calculation in some aspects, but the fixed surface-to-mass ratio also means that the sensitivity of the satellite to solar pressure is fixed, which sacrifices the accuracy of the dynamic model. An overly simplified model may not accurately predict and respond to actual dynamic conditions, which may pose additional challenges to orbit maintenance and attitude control. SUMMARY

[0004] The purpose of the present application is to solve the problem of inaccurate solar pressure calculation of large satellite antennas, which leads to poor accuracy of satellite orbit prediction and attitude control, and to propose a sub-unit light pressure perturbation calculation method for antenna satellites.

[0005] A sub-unit light pressure perturbation calculation method for antenna satellites specifically includes the following steps:

[0006] Step one, in the ECI coordinate system, according to the position relationship of the sun, the earth and the antenna satellite, determine the sun exposure factor;

[0007] Step two, calculate the light pressure projection area of the satellite;

[0008] Step three, calculate the light pressure perturbation force on each part according to the solarization factor of step one and the light pressure projection area of step two;

[0009] Step four, determine whether the set time length is reached, if not, repeat steps one to three, otherwise, end.

[0010] The beneficial effects of the present application are:

[0011] 1. The present application is aimed at the problem of complex satellite antenna structure and difficulty in accurately calculating its light pressure perturbation. By decomposing the satellite into several key units and calculating the solar light pressure received by each unit, the overall light pressure perturbation can be more accurately predicted. This method allows detailed consideration of the specific properties of each unit (such as area, material, shape and orientation), thereby improving the accuracy and reliability of the overall model.

[0012] 2. The present application is beneficial to improve the orbit prediction and attitude control accuracy of satellites and spacecraft. By calculating the influence of solar light pressure with high precision, the accuracy of orbit prediction can be significantly improved, the attitude control ability can be enhanced, and the use of fuel can be optimized. This is particularly critical for tasks that require high precision pointing, such as earth observation, astronomical observation and interstellar communication, etc. In addition, using solar light pressure for orbit and attitude control can also reduce the consumption of propellant, prolong the life of the satellite, and thus improve the economic efficiency and sustainability of the mission.

[0013] 3. The present application is beneficial to improve mission planning and execution. High-precision solar light pressure calculation helps to develop more reasonable mission plans, especially in satellite formation flight and cooperative observation missions. For long-term tasks, an accurate solar light pressure model helps to predict and respond to long-term orbital drift and attitude changes, improving mission success rate. At the same time, accurate assessment and prediction of the orbit changes caused by solar light pressure can help to enhance risk management and collision avoidance, improve the accuracy of collision risk assessment, and plan effective collision avoidance maneuvers to reduce the risk of collision in the space environment.

[0014] 4. The present application is beneficial to improve scientific experiments and data quality, especially for scientific satellites carrying precision instruments, which can correct the small disturbances caused by solar light pressure and ensure the accuracy and reliability of the data. BRIEF DESCRIPTION OF DRAWINGS

[0015] Figure 1 is a flowchart of the method of the present application;

[0016] Figure 2The parabolic surface of the antenna is fitted with the center point M of the antenna umbrella surface as the origin, the velocity direction of the antenna satellite as the x" axis, the direction pointing to the center of the earth as the z" axis, and the y" axis determined by the right-hand rule; points L, F, R and B are four points on the boundary of the antenna umbrella surface which are symmetric to the center; and θ represents the direction of the sunlight; The curve on the antenna umbrella surface which is tangent to the sunlight is shown;

[0017] Figure 3 The projection diagram of the antenna parabolic surface under different solar incidence angles is shown;

[0018] Figure 4 The diagram of the variation of the projection area of the antenna under different incidence angles calculated by the Macro Model (MM) and the High Precision Analytical Model (HPAM) of the present application is shown;

[0019] Figure 5 The diagram of the variation of the projection area of the satellite antenna under different dates is shown;

[0020] Figure 6 The diagram of the light pressure perturbation force on the antenna with a roll angle of 6° at the equinox point is shown, wherein Fx, Fy and Fz are three components of the light pressure perturbation force on the antenna satellite in the orbital coordinate system, and Tx, Ty and Tz are three components of the light pressure perturbation torque on the antenna satellite in the orbital coordinate system. DETAILED DESCRIPTION

[0021] Embodiment One: Combination Figure 1 The present embodiment is a sub-unit light pressure perturbation calculation method for an antenna satellite, which specifically comprises the following steps:

[0022] The technical solution adopted by the present application to solve the above technical problem is a sub-unit light pressure perturbation calculation method which comprehensively considers the shape, structure and attitude of a satellite antenna, and the method specifically comprises the following steps:

[0023] Step One: In the ECI coordinate system, the exposure factor is determined according to the positional relationship among the sun, the earth and the antenna satellite.

[0024] Step Two: The light pressure projection area of the satellite is calculated.

[0025] Step Three: The light pressure perturbation force on each part is calculated according to the exposure factor in Step One and the light pressure projection area in Step Two.

[0026] Step Four: It is determined whether the set time length is reached, if not, Steps One to Three are repeated, otherwise, the process is ended.

[0027] Specific implementation two: the embodiment is different from the specific implementation one: in the step one in the ECI coordinate system, the sun, the earth, the antenna satellite three position relations are determined according to the sun, the earth, the antenna satellite three position relations; The specific process is:

[0028] The ECI coordinate system is the geocentric inertial coordinate system, and the origin of the ECI coordinate system is located at the earth center; The z axis is along the direction of the earth rotation axis, and points to the north pole from the earth center; The x axis is in the equatorial plane, and points to the vernal equinox from the earth center; The y axis satisfies the right hand rule with the x and z axes;

[0029] Let the ECI coordinates of the antenna satellite be r sat =[r satx r saty r satz ] T , the ECI coordinates of the sun are r sun =[r sunx r suny r sunz ] T , the included angle α of the antenna satellite and the sun relative to the earth center is obtained based on the ECI coordinates of the antenna satellite and the ECI coordinates of the sun;

[0030] Based on the included angle α of the antenna satellite and the sun relative to the earth center, the determination condition of the satellite in the earth shadow area is obtained, and the expression is:

[0031]

[0032] Wherein, r e is the earth radius; The upper index T represents the transpose;

[0033] If the above determination condition (2) is not satisfied, the sun exposure factor k=1.

[0034] The other steps and parameters are the same as those in the specific implementation one.

[0035] Specific implementation three: the embodiment is different from the specific implementation one or two: the included angle α of the antenna satellite and the sun relative to the earth center is obtained based on the ECI coordinates of the antenna satellite and the ECI coordinates of the sun; The specific process is:

[0036] Then the included angle α of the antenna satellite and the sun relative to the earth center is:

[0037]

[0038] In the formula, |r sat | represents the modulus of the satellite position vector in the ECI coordinate system; · represents multiplication, r satx represents the x axis coordinate of the antenna satellite in the ECI coordinate system, and r satyr represents the y-axis coordinate of the antenna satellite in the ECI coordinate system, r satz r represents the z-axis coordinate of the antenna satellite in the ECI coordinate system, r sunx r represents the x-axis coordinate of the sun in the ECI coordinate system, r suny r represents the y-axis coordinate of the sun in the ECI coordinate system, r sunz r represents the z-axis coordinate of the sun in the ECI coordinate system.

[0039] The other steps and parameters are the same as those in embodiment one or two.

[0040] Embodiment four: different from one of embodiments one to three, the step two is to calculate the light pressure projection area of the satellite, and the specific process is as follows:

[0041] Step two one, according to the structure of the antenna satellite, the antenna satellite is divided into solar wing unit, star body unit and antenna unit;

[0042] Step two two, the solar wing unit is regarded as a flat structure with length m and width n, and the light pressure projection area of the solar wing is calculated;

[0043] Step two three, the star body unit is regarded as a cuboid structure with length l, width w and height h, and the light pressure projection area of the star body unit in the illumination direction is calculated;

[0044] Step two four, the antenna unit is regarded as a parabolic structure, and due to the complexity of the parabolic structure, the light pressure projection area of the antenna unit in the illumination direction is obtained.

[0045] The other steps and parameters are the same as those in one of embodiments one to three.

[0046] Embodiment five: different from one of embodiments one to four, the step two two is to regard the solar wing unit as a flat structure with length m and width n, and calculate the light pressure projection area of the solar wing;

[0047] The specific process is as follows:

[0048] Since the main structure of the large satellite antenna is composed of a star body, two symmetrical solar wings and an antenna, it is divided into solar wing unit, star body unit and antenna unit for light pressure modeling, and the light pressure projection area in the illumination direction is calculated.

[0049] Let the antenna satellite running speed vector be v, then the unit vector of the antenna satellite orbit coordinate system is as follows:

[0050]

[0051] In the formula, (x o ,y o ,z o) represents a three-axis unit vector of the antenna satellite orbit coordinate system in the ECI coordinate system; |v| represents the modulus of the antenna satellite running velocity vector;

[0052] The origin of the antenna satellite orbit coordinate system x'y'z' is the center of mass of the antenna satellite, the x' axis is the velocity direction of the antenna satellite, the z' axis points to the direction of the earth center, and the y' axis is determined by the right-hand rule;

[0053] Based on the unit vector of the antenna satellite orbit coordinate system, the incident angle β of sunlight is obtained;

[0054] Based on the incident angle β of sunlight, the light pressure projection area of the solar wing is obtained, and the expression is

[0055] S sol = m x n x |sin β| (4).

[0056] The other steps and parameters are the same as one of the first to fourth embodiments.

[0057] Embodiment six: The embodiment is different from one of the first to fifth embodiments in that: based on the unit vector of the antenna satellite orbit coordinate system, the incident angle β of sunlight is obtained, and the expression is:

[0058]

[0059] In the formula, · represents dot product.

[0060] The other steps and parameters are the same as one of the first to fifth embodiments.

[0061] Embodiment seven: The embodiment is different from one of the first to sixth embodiments in that: in steps two and three, the star body unit is regarded as a cuboid structure with length, width and height of l, w and h respectively, and the light pressure projection area of the star body unit in the illumination direction is calculated; the specific process is:

[0062] When the sun is at the equinox point, for any incident angle β of sunlight, the light pressure projection area of each sunlit surface of the cuboid structure is calculated; the expression is:

[0063] S WX = l x w x |sin β| + w x h x |cos β| (6)

[0064] In the formula, S WX represents the light pressure projection area of the star body unit in the illumination direction.

[0065] The other steps and parameters are the same as one of the first to sixth embodiments.

[0066] Eighth embodiment: Different from the first to seventh embodiments, the antenna unit is regarded as a parabolic structure in step two four, and the light pressure projection area of the antenna unit in the light direction is obtained due to the complexity of the parabolic structure;

[0067] The specific process is:

[0068] 1) The antenna surface can be modeled as a paraboloid, which is a special form of a quadratic surface. The general equation of a quadratic surface is:

[0069] a0+a1x”+a2y”+a3z”+a4x”y”+a5y”z”+a6z”x”+a7x” 2 +a8y” 2 +a9z” 2 =0 (7)

[0070] In the formula, a0, a1, a2, a3, a4, a5, a6, a7, a8, a9 represent parameters; x”, y”, z” represent the coordinate values of the three axes in the Cartesian coordinate system;

[0071] The Cartesian coordinate system x”y”z” is:

[0072] The center of the antenna umbrella surface is taken as the origin, the velocity direction of the antenna satellite is the x” axis, the direction pointing to the center of the earth is the z” axis, and the y” axis is determined by the right-hand rule;

[0073] The surface equation contains 10 unknown parameters;

[0074] The parameter a0 determines the position offset of the surface;

[0075] The parameters a1 to a3 are linear terms that affect the translation of the surface;

[0076] The parameters a4 to a6 represent the correlation between two directions, which affect the shear effect between the two directions;

[0077] The parameters a7 to a9 represent the curvature in three directions.

[0078] The solution of the antenna surface equation requires more than ten parameters, which can be analyzed by finite element software for each part of the antenna. Then the parabolic surface of the antenna is fitted as shown in Figure 2 The parabolic surface equation of the antenna can be obtained;

[0079] The general equation of the quadratic surface (formula 7) is fitted by using the finite element software, and the parabolic surface equation of the antenna is as follows:

[0080] 0=ax” 2 +ay” 2 -z” (8)

[0081] Where a represents a parameter; N is the total height of the antenna structure; z”≤N;

[0082] For the form 0=ax" 2 +ay” 2 -z" antenna unit, assuming the direction of the sun's rays is Find the light pressure projection area of ​​the antenna unit in the direction of illumination, that is, find the area of ​​the parabola with the normal vector The projected area of ​​the plane y'cosθ+z'sinθ=0;

[0083] Where θ represents the direction of sunlight;

[0084] The solar perturbation force is primarily determined by the projected area of ​​the satellite exposed to incident sunlight. The effective exposure area is related to the solar incident angle θ. When θ = 0°, sunlight directly illuminates the side of the antenna, resulting in the smallest projected area. When θ = 90°, sunlight directly illuminates the antenna surface, resulting in the largest projected area. The incident angle changes continuously with the movement of the geosynchronous satellite and the sun, such as Figure 3 shown.

[0085] Parabola equation 0 = ax" 2 +ay” 2 The surface gradient of "-z" is

[0086] 2) When When , the light pressure projection area of ​​the antenna unit in the illumination direction is calculated based on the light pressure projection area formula (19);

[0087] 3) In When θ is equivalent to π-θ, ​​substitute it into the light pressure projection area formula (19) to calculate the light pressure projection area of ​​the antenna unit in the illumination direction;

[0088] where θ is given by get;

[0089] 4) When θ is equivalent to θ-π, substitute it into the light pressure projection area formula (19) to calculate the light pressure projection area of ​​the antenna unit in the illumination direction;

[0090] where θ is given by get;

[0091] 5) In When θ is equivalent to 2π-θ, substitute it into the light pressure projection area formula (19) to calculate the light pressure projection area of ​​the antenna unit in the illumination direction;

[0092] where θ is given by get.

[0093] Other steps and parameters are the same as those in Specific Embodiments 1 to 7-1.

[0094] Specific embodiment 9: This embodiment differs from any one of the specific embodiments 1 to 8 in that: When , the light pressure projection area of ​​the antenna unit in the illumination direction is calculated based on the light pressure projection area formula (19); the specific process is:

[0095] 21) When When the parabola is continuous, the contour curve of the projected area is obtained by projecting the gradient and the normal vector perpendicularly.

[0096]

[0097] Where, Represents the parabola equation 0 = ax" 2 +ay” 2 - surface gradient of z”, z”≤N; represents the normal vector; represents the dot product;

[0098] The tangent plane is

[0099]

[0100] Substitute (10) into the parabola equation 0 = ax" 2 +ay” 2 -z", get the curve

[0101]

[0102] To find the curve The projection of (x', y', z') is replaced by Substituting into equation (11), eliminating k and obtaining the curve The equation of the projection profile curve is

[0103]

[0104] Since the parabola is not a complete closed surface, consider the non-tangent case;

[0105] 22) The parabola boundary Γ is

[0106]

[0107] 23) When When , the contour curve of the projection of the antenna unit is the projection of the boundary Γ on the projection plane y”cosθ+z”sinθ=0;

[0108] When θ=0, the curve Go to Curve

[0109] Find the critical angle θ0; the specific process is:

[0110] When and parabolic equation 0=ax" 2 +ay" 2 -z"no intersection, then the projection of the profile curve is the projection of boundary Γ on y"cosθ+z"sinθ=0, the critical value Critical angle

[0111] When , the light and parabolic tangent point, then the projection of the profile curve is the projection of boundary Γ on y"cosθ+z"sinθ=0;

[0112] When 0≤θ≤θ0, the projection is complex, the projection is curve and curve on y"cosθ+z"sinθ=0;

[0113] 24), find the point O coordinates and point P coordinates; the specific process is:

[0114] Equations

[0115]

[0116] The point O coordinates and point P coordinates

[0117] 25), based on 24) point O coordinates and point P coordinates, calculate The projection area S1 of the curve surrounded by straight line OP; expressed as:

[0118]

[0119] In the formula, t1 represents an intermediate variable; · represents point multiplication;

[0120] 26), based on 24) point O coordinates and point P coordinates, for The projection area S2 of the curve surrounded by straight line OP is expressed as:

[0121]

[0122] Curve and curve The projection area of the curve surrounded by curve on ycθ+zsinθ=0 is

[0123] S=S1+S2 (18)

[0124] 27) Based on 23), 25) and 26) and the light pressure projection area formula (19), the light pressure projection area of the antenna unit in the light direction is calculated; the expression is

[0125]

[0126] Other steps and parameters are the same as one of the first to eighth embodiments.

[0127] The tenth embodiment is different from one of the first to ninth embodiments in that: in the step three, the light pressure perturbation force of each part is calculated according to the insolation factor of the step one and the light pressure projection area of the step two; the specific process is:

[0128] If k = 0, the solar light pressure perturbation force is 0;

[0129] If k = 1, the solar light pressure perturbation force is not 0, and the solar light pressure perturbation force F SPP is calculated, and the calculation formula is:

[0130]

[0131] Wherein, C R is the satellite surface reflection coefficient, which represents the absorption and reflection ability of the satellite surface material to the sunlight; p SR is the solar light pressure constant, generally 4.56 × 10 -6 N / m 2 ; k is the insolation factor; in the satellite operation process, the satellite is in the shadow area of the earth back, and will not be illuminated by the sunlight, at this time, k = 0 is taken; when the satellite is not in the shadow area, k = 1 is taken; AU is 1 astronomical unit, 1 AU = 1.495978707 × 10 11 ; |r sun | is the modulus of the position vector of the sun in the ECI coordinate system; S Ref is the light pressure projection area of the satellite; e D is the unit vector of the satellite pointing to the sun.

[0132] Other steps and parameters are the same as one of the first to ninth embodiments.

[0133] Embodiment:

[0134] According to the first embodiment, the algorithm of the application is tested in the simulation environment. By using the macro model and the projection area calculation method of the high-precision analytical light pressure perturbation force model, the relationship between the projection area and the incident angle is obtained by simulation analysis, as shown in Figure 4 The two methods show similar trends, and the maximum error is 1000 m 2The present application is more scientific and rigorous, and more consistent with the actual situation of photovoltaic perturbation force. On March 21 and April 21, the photovoltaic projection area of the antenna satellite was simulated for 24 hours using a macroscopic model and a high-precision analytical photovoltaic perturbation force model, as shown in Figure 5 FIG. 2. On March 21, 2020, the maximum and minimum projection areas of the antenna surface calculated by the two models were equal, with a maximum difference of 1314.7 m 2 between the two. The difference between the entire antenna satellite and the antenna surface was very small, mainly due to the influence of the satellite body and solar wing, indicating that their shadowed areas can be ignored. After one month of on-orbit operation, the maximum difference between the two models was 1314.8 m 2 , which was not much different from March 21. Although the maximum projection area of the antenna surface was equal on the two dates, a difference of about 694.2 m 2 was measured at the minimum value. This shows that as the position of the sun changes along the ecliptic plane, the photovoltaic perturbation force of the antenna satellite becomes more complex, increasing the error in the macroscopic model. In contrast, the high-precision analytical photovoltaic perturbation force model improves the calculation accuracy.

[0135] Figure 6 FIG. 3 is a diagram of the photovoltaic perturbation force and torque obtained by on-orbit simulation of the vernal equinox, with a satellite roll angle of 6°. At the beginning of the simulation, the Earth, satellite, and sun are collinear, and the Z-axis of the satellite always points to the center of the Earth. From 6 to 18 h, the angle between the Z-axis and the solar radiation pressure is less than 90°, and the perturbation force is positive, reaching a peak at 12 h. From 18 to 0 h and then to 6 h, the angle is greater than 90°, so the perturbation force is negative, reaching a peak at 0 / 24 h. From 0 to 12 hours, the satellite moves from the aphelion to the perihelion, and the solar radiation pressure along the velocity direction (X-axis) behaves as a resistance, which is negative. At 6 h, the solar radiation pressure is minimal due to the antenna surface incident angle of about 90°. From 18 to 0 h and then to 6 h, the satellite moves from the perihelion to the aphelion, and the solar radiation pressure along the velocity direction (X-axis) is a positive thrust. Since the satellite has a roll angle of 6° along the Z-axis, the solar radiation pressure does not pass through the center of mass, thereby generating a Z-axis torque. The solar radiation pressure curve exhibits an equal-length shadow effect around 0 hours.

[0136] The present application can also have other various embodiments, and those skilled in the art can make various corresponding changes and modifications to the present application without departing from the spirit and essence of the present application. However, these corresponding changes and modifications should all belong to the protection scope of the claims attached to the present application.

Claims

1. A method for calculating the optical pressure perturbation of a satellite antenna, characterized by: The method specifically comprises the following steps: Step 1: In the ECI coordinate system, determine the insolation factor based on the positional relationship between the sun, the earth, and the antenna satellite; Step 2: Calculate the light pressure projection area of ​​the satellite; Step 3: Calculate the light pressure perturbation force on each part based on the insolation factor obtained in step 1 and the light pressure projection area obtained in step 2; Step 4: Determine whether the set time length has been reached. If not, repeat steps 1 to 3. Otherwise, end. The light pressure projection area of ​​the satellite is calculated in step 2; the specific process is: Step 21: According to the antenna satellite structure, the antenna satellite is divided into a solar wing unit, a star unit and an antenna unit; Step 22: Consider the solar wing unit as a flat plate structure with a length of m and a width of n, and calculate the light pressure projected area of ​​the solar wing; Step 2: Consider the star unit as a rectangular parallelepiped structure with a length of l, a width of w, and a height of h, respectively, and calculate the light pressure projection area of ​​the star unit in the direction of illumination; Step 24: Consider the antenna unit as a parabolic structure and obtain the light pressure projection area of ​​the antenna unit in the direction of illumination; In step 24, the antenna unit is regarded as a parabolic structure to obtain the light pressure projection area of ​​the antenna unit in the direction of illumination; The specific process is: 1) The antenna surface is modeled as a parabola, which is a special form of a quadratic surface. The general equation of a quadratic surface is: a0+a1x”+a2y”+a3z”+a4x”y”+a5y”z”+a6z”x”+a7x” 2 +a8y” 2 +a9z” 2 =0(7) Where a0, a1, a2, a3, a4, a5, a6, a7, a8, and a9 represent parameters; x', y', and z' represent the coordinate values ​​of the three axes in the Cartesian coordinate system; The Cartesian coordinate system x"y"z" is: With the center of the antenna canopy as the origin, the speed direction of the antenna satellite is the x-axis, the direction pointing to the center of the earth is the z-axis, and the y-axis is determined by the right-hand rule; Finite element software is used to fit the general equation of the quadratic surface, and the parabolic equation of the antenna is obtained as follows: 0=ax” 2 +month” 2 -z”(8) Where a represents a parameter; N is the total height of the antenna structure; z”≤N; For the form 0=ax" 2 +ay” 2 -z" antenna unit, assuming the direction of the sun's rays is Find the light pressure projection area of ​​the antenna unit in the direction of illumination, that is, find the area of ​​the parabola with the normal vector The projected area of ​​the plane y'cosθ+z'sinθ=0; Where θ represents the direction of sunlight; Parabola equation 0 = ax" 2 +ay” 2 The surface gradient of "-z" is 2) When When , the light pressure projection area of ​​the antenna unit in the light direction is calculated based on the light pressure projection area formula; 3) In When θ is equivalent to π-θ, ​​substitute it into the light pressure projection area formula to calculate the light pressure projection area of ​​the antenna unit in the direction of illumination; where θ is given by get; Where (x o ,y o ,z o ) represents the three-axis unit vector of the antenna satellite orbit coordinate system in the ECI coordinate system; r sun Indicates the ECI coordinate of the sun; 4) When θ is equal to θ-π, substitute it into the light pressure projection area formula to calculate the light pressure projection area of ​​the antenna unit in the direction of illumination; where θ is given by get; 5) In When θ is equal to 2π-θ, substitute it into the light pressure projection area formula to calculate the light pressure projection area of ​​the antenna unit in the direction of illumination; where θ is given by get; In the above 2) When , the light pressure projection area of ​​the antenna unit in the light direction is calculated based on the light pressure projection area formula; the specific process is: 21) When When the parabola is continuous, the contour curve of the projected area is obtained by projecting the gradient and the normal vector perpendicularly. Where, Represents the parabola equation 0 = ax" 2 +ay” 2 - surface gradient of z”, z”≤N; represents the normal vector; represents the dot product; The tangent plane is Substitute (10) into the parabola equation 0 = ax" 2 +ay” 2 -z", get the curve Replace (x", y", z") with Substituting into equation (11), eliminating k and obtaining the curve The equation of the projection profile curve is 22) The parabola boundary Γ is 23) When When , the contour curve of the projection of the antenna unit is the projection of the boundary Γ on the projection plane y”cosθ+z”sinθ=0; When θ=0, the curve Go to Curve Find the critical angle θ0; the specific process is: when and the parabola equation 0 = ax" 2 +ay” 2 -z” has no intersection point, the projected contour curve is the projection of the boundary Γ on y”cosθ+z”sinθ=0, and the critical value is critical angle when When , the light has no tangent point with the parabola, then the projected contour curve is the projection of the boundary Γ on y'cosθ+z'sinθ=0; When 0≤θ≤θ0, the projection is a curve With curve Projection on y'cosθ+z'sinθ=0; 24) Find the coordinates of point O and point P; the specific process is: simultaneous equations Get the coordinates of point O and point P coordinates 25) Based on the coordinates of point O and point P in 24), calculate The projected area S1 of the curve formed with the straight line OP is expressed as: In the formula, t1 represents the intermediate variable; · represents the dot product; 26) Based on the coordinates of point O and point P in 24), for The projected area S2 of the curve formed with the straight line OP is expressed as: curve With curve The projected area of ​​the enclosed curve at ycosθ+zsinθ=0 is S=S1+S2 (18) 27) Based on 23), 25) and 26) and the light pressure projection area formula (19), calculate the light pressure projection area of ​​the antenna unit in the illumination direction; the expression is 2. The method for calculating the optical pressure perturbation of an antenna satellite according to claim 1, characterized in that: In step 1, in the ECI coordinate system, the insolation factor is determined based on the positional relationship between the sun, the earth, and the antenna satellite. The specific process is as follows: The ECI coordinate system is a geocentric inertial coordinate system with its origin at the Earth's center of mass. The z-axis is along the Earth's rotation axis, pointing from the Earth's center to the North Pole. The x-axis is in the equatorial plane, pointing from the Earth's center to the vernal equinox. The y-axis, x-axis, and z-axis satisfy the right-hand rule. Let the ECI coordinate of the antenna satellite be r sat =[r satx r saty r satz ] T , the ECI coordinate of the sun is r sun =[r sunx r suny r sunz ] T , based on the ECI coordinates of the antenna satellite and the ECI coordinates of the sun, the included angle α between the antenna satellite and the sun relative to the center of the earth is obtained; Based on the angle α between the antenna satellite and the sun relative to the center of the earth, the determination condition for the satellite's insolation factor k=0 in the earth's shadow area is obtained, and the expression is: Among them, r e is the radius of the Earth; the superscript T indicates the transpose; If the above judgment condition (2) is not satisfied, the exposure factor k=1.

3. The method for calculating the optical pressure perturbation of a satellite antenna according to claim 2, wherein: The angle α between the antenna satellite and the sun relative to the center of the earth is obtained based on the ECI coordinates of the antenna satellite and the ECI coordinates of the sun. The specific process is: Then the angle α between the antenna satellite and the sun relative to the center of the earth is: Where, |r sat ∣ represents the modulus of the satellite's position vector in the ECI coordinate system; ·Represents the multiplication sign, r satx Indicates the x-axis coordinate of the antenna satellite in the ECI coordinate system, r saty Indicates the y-axis coordinate of the antenna satellite in the ECI coordinate system, r satz Indicates the z-axis coordinate of the antenna satellite in the ECI coordinate system, r sunx represents the x-axis coordinate of the sun in the ECI coordinate system, r suny represents the y-axis coordinate of the sun in the ECI coordinate system, r sunz Indicates the z-axis coordinate of the sun in the ECI coordinate system.

4. The method for calculating the optical pressure perturbation of a satellite antenna according to claim 3, wherein: In step 22, the solar wing unit is regarded as a flat plate structure with a length of m and a width of n, and the light pressure projection area of ​​the solar wing is calculated; the specific process is: Let the antenna satellite velocity vector be v, then the unit vector of the antenna satellite orbital coordinate system is as follows: In the formula, (x o ,y o ,z o ) represents the three-axis unit vector of the antenna-satellite orbit coordinate system in the ECI coordinate system; |v| represents the modulus of the antenna-satellite velocity vector; The origin of the antenna satellite orbital coordinate system x'y'z' is the center of mass of the antenna satellite, the x' axis is the velocity direction of the antenna satellite, the z' axis points to the center of the earth, and the y' axis is determined by the right-hand rule; Based on the unit vector of the antenna satellite orbit coordinate system, the incident angle β of the sunlight is obtained; Based on the incident angle β of sunlight, the light pressure projection area of ​​the solar wing is obtained, which is expressed as S sol =m×n×|sinβ| (4)。 5. The method for calculating the optical pressure perturbation of a satellite antenna according to claim 4, characterized in that: The unit vector based on the antenna satellite orbit coordinate system is used to obtain the incident angle β of sunlight, which is expressed as: Where · represents the dot product.

6. The method for calculating the optical pressure perturbation of a satellite antenna according to claim 5, characterized in that: In steps 2 and 3, the star unit is regarded as a rectangular parallelepiped structure with a length, width, and height of l, w, and h respectively, and the light pressure projection area of ​​the star unit in the illumination direction is calculated; the specific process is: When the sun is at the vernal equinox, for any incident angle β of sunlight, calculate the light pressure projection area of ​​each sun-receiving surface of the rectangular structure; the expression is: S WX =l×w×|sinβ|+w×h×|cosβ| (6) Where S WX It represents the light pressure projection area of ​​the star unit in the direction of illumination.

7. The method for calculating the optical pressure perturbation of a satellite antenna according to claim 6, characterized in that: In step 3, the light pressure perturbation force on each part is calculated based on the exposure factor of step 1 and the light pressure projection area of ​​step 2. The specific process is: If k = 0, the pressure force of sunlight is 0; If k = 1, the solar pressure force is not 0, and the solar pressure force F is calculated. SPP , the calculation formula is: Among them, C R is the satellite surface reflection coefficient; ρ SR is the solar pressure constant; k is the insolation factor; AU is 1 astronomical unit, 1AU=1.495978707×10 11 ;|r sun | is the modulus of the sun's position vector in the ECI coordinate system; S Ref is the satellite's light pressure projection area; e D is the unit vector pointing from the satellite to the sun.

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