Polar sustainable observation point determination method based on refraction type solar sail spacecraft

Abstract

The invention relates to a polar region sustainable observation point determination method based on a refraction type solar sail spacecraft, which comprises the following steps of: establishing a light pressure dynamic model of the refraction type solar sail spacecraft and based on a circular restrictive three-body problem (CR3BP) framework; generating an improved kinetic equation containing a refraction light pressure item, solving to obtain a space coordinate set of artificial translation points in the sun-earth system, and calculating an observation half-cone angle between each translation point in the space coordinate set and a target observation point in the polar observation geometric constraint model through coordinate transformation; the method comprises the following steps of: discretizing an earth revolution period, solving a continuity condition of observation coverage to obtain a feasible region meeting full-period polar region continuous observation, performing space matching on a space coordinate set of an artificial translation point and the feasible region, and screening out an optimal observation point position meeting requirements. According to the method, the sustainable observation area of the polar region can be enlarged by about two times, meanwhile, the sustainable observation position is determined based on a space geometry method without problem simplification, and compared with a traditional analytical solution method adopting a simplified problem, the calculation efficiency is high, and the precision is high.

Description

Technical Field

[0001] The present invention relates to a technology in the field of satellite control, specifically a method for determining polar sustainable observation points based on a refractive solar sail spacecraft. Background Art

[0002] Current polar monitoring relies on polar-orbiting satellites and highly eccentric Molniya satellites, but a single satellite cannot provide continuous coverage and requires the coordination of multiple satellites. While observation technology based on reflective solar sails leverages the characteristics of the Earth-Sun triple orbit and requires only a single satellite for continuous coverage, its observation performance is limited by the dynamic characteristics of the sail. Summary of the Invention

[0003] In response to the above-mentioned deficiencies in the prior art, the present invention proposes a method for determining polar sustainable observation points based on a refractive solar sail spacecraft. The method adopts the dynamic model of a circular restricted three-body problem to determine the Sun-Earth artificial libration point corresponding to the refractive solar sail spacecraft, significantly reducing the demand for ground station observation elevation angles. While achieving an approximately two-fold expansion of the polar sustainable observation area, the method determines the sustainable observation position based on a spatial geometry method that does not require problem simplification. Compared with the traditional analytical solution method after simplifying the problem, the method has high computational efficiency and accuracy.

[0004] The present invention is achieved through the following technical solutions:

[0005] The present invention relates to a method for determining sustainable observation points at the Earth's polar regions based on a refractive solar sail spacecraft. The method comprises the following steps: establishing a light pressure dynamics model of the refractive solar sail spacecraft and generating an improved dynamics equation containing a refractive light pressure term based on a circular restricted three-body problem (CR3BP) framework, solving the equation to obtain a set of spatial coordinates of artificial libration points in a Sun-Earth system, and calculating an observation semi-cone angle between each libration point in the spatial coordinate set and a target observation point in a polar observation geometric constraint model through coordinate transformation. The method further comprises solving a continuity condition of observation coverage after discretizing the Earth's orbital period to obtain a feasible domain that satisfies full-cycle continuous polar observation. The method then spatially matches the set of spatial coordinates of the artificial libration points with the feasible domain to screen out optimal observation points that meet the requirements.

[0006] The light pressure dynamics model refers to the characteristic tangential acceleration a of the refractive solar sail spacecraft. tang =γP tang (a norm =γP norm ), where: P tang is the characteristic tangential radiation pressure of the refractive solar sail spacecraft, P normis the characteristic normal radiation pressure, tangential refers to the direction parallel to the sail surface, and normal refers to the direction perpendicular to the sail surface. The characteristic tangential (normal) radiation pressure of a refractive solar sail spacecraft is characterized by the tangential (normal) radiation pressure generated by the refractive solar sail spacecraft when it is irradiated by the sun at a distance of 1 astronomical unit from the sun. γ is the area-to-mass ratio of the refractive sail, and a tang is the characteristic tangential acceleration, a norm is the characteristic normal acceleration.

[0007] The improved dynamic equation containing the refractive light pressure term is: the non-inertial system rotating around the heliocentric The tangential and normal dynamic equations that the artificial translation point in must satisfy are: Where: μ = μ2 / (μ1+μ2) is the dimensionless gravitational constant, μ1 is the gravitational constant of the sun, μ2 is the gravitational constant of the earth, the dimensionless length unit [L] is the distance between the two celestial bodies, the dimensionless mass unit [M] is the sum of the masses of the two celestial bodies, and the time unit [T] is [[L] 3 / G[M]] 0.5 ; Normalized effective potential is the direction of the Earth's revolution around the sun, and the normalized gravitational potential energy at the location of the refractive solar sail spacecraft r1(r2) is the normalized distance from the refractive solar sail spacecraft to the sun (earth), and the normal acceleration of the refractive solar sail spacecraft is and tangential acceleration r is the normalized distance from the refractive solar sail spacecraft to the center of the Sun and Earth.

[0008] The set of spatial coordinates is obtained by numerically solving the tangential and normal dynamic equations that the artificial libration point in the non-inertial system rotating around the heliocentric geocenter must satisfy.

[0009] The observation semi-cone angle satisfies the position constraint, that is, Where: The observation semi-cone angle φ is the sum of the line connecting the refractive solar sail spacecraft and the cone vertex. The angle between the axes, {X, Y, Z} is the coordinate of the refractive solar sail spacecraft in the geocentric inertial system, and the height of the cone vertex is ∈ is the minimum observation elevation angle, θ lat is the observable Earth latitude, R e is the radius of the Earth.

[0010] The feasible domain that satisfies the full-cycle polar continuous observation is: the refractive solar sail spacecraft in the non-inertial system Constraints on sustainable observation space position under Where: Angle φ non is the line connecting the refractive solar sail spacecraft and the vertex of the sustainable observation cone and The angle between the axes {x, y, z} is the angle between the refractive solar sail spacecraft and the non-inertial system. Coordinates, cone apex angle φ conti =θ lat -∈-θ ec , vertex height θ ec is the obliquity of the ecliptic, and μ is the dimensionless gravitational constant.

[0011] The matching refers to: according to the obtained coordinates of the artificial libration point of the refractive solar sail spacecraft, substituting the constraints of the sustainable observation space position to determine whether the corresponding artificial libration point has the conditions for continuous observation, and screening out the optimal observation point that meets the requirements.

[0012] The present invention relates to a system for implementing the above-mentioned method, comprising: a refractive solar sail dynamics simulation unit, an artificial libration point calculation unit, a continuous observation performance evaluation unit, and a result output unit, wherein: the refractive solar sail dynamics simulation unit calculates the attitude and corresponding light pressure through optical simulation based on the structural parameter design information of the sail, and obtains the dynamics of the refractive solar sail in various directions by combining properties such as surface-to-mass ratio; the artificial libration point calculation unit obtains the position of the artificial libration point and the corresponding sail surface attitude control parameters through orbital dynamics numerical simulation and isotropic force balance analysis based on the dynamic model of the refractive solar sail; the continuous observation performance evaluation unit selects the position of the artificial libration point for sustainable observation based on the artificial libration point position information and the constraint conditions of the sustainable observation space position, and evaluates the sustainable observation performance of each sustainable observation point; the result output unit selects the optimal observation point that meets the requirements based on the spatial coordinate set of the sustainably observed artificial libration points and the corresponding sustainable observation performance, and outputs the spatial coordinates of the optimal artificial libration point, the corresponding attitude of the refractive solar sail, and various structural parameters of the sail. Technical Effects

[0013] The present invention uses a refractive solar sail spacecraft to conduct sustainable observations of the Earth's poles and thereby determine polar sustainable observation points based on the refractive solar sail. Compared with the use of traditional reflective solar sail spacecraft, the observation elevation angle requirement for ground stations is reduced and the observation performance is greatly improved, which can achieve an expansion of the polar sustainable observation area by about 2 times; this sustainable observation point determination method determines the sustainable observation position based on a spatial geometry method that does not require problem simplification. Compared with the traditional analytical solution method after simplifying the problem, this method has higher computational efficiency and higher computational accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 Schematic diagram of the system of the present invention;

[0015] Figure 2 Non-inertial system Schematic diagram and relationship diagram between non-inertial system and geocentric inertial system;

[0016] Figure 3 Geocentric inertial system Schematic diagram;

[0017] Figure 4 This is a schematic diagram of the change of the observable range cone due to the Earth's revolution in a non-inertial system;

[0018] Figure 5 The dynamic properties of the refractive solar sail spacecraft used in the experiment of the present invention;

[0019] Figure 6 Schematic diagram of the space coordinate set of artificial libration points for sustainable observation by a refractive solar sail spacecraft;

[0020] Figure 7 The relationship curve between the refractive solar sail under different surface-to-mass ratios and the cross-section vertex angle under optimal observation performance;

[0021] Figure 8 This is a comparison chart of the coverage of different sails when the minimum ground station observation elevation angle is 20°;

[0022] Figure 9 This is a comparison chart of the minimum ground station observation elevation angles for different sails when the observation latitude range is within the Arctic Circle. DETAILED DESCRIPTION

[0023] like Figure 1 As shown, this embodiment relates to a method for determining sustainable Earth polar observation points based on a refractive solar sail spacecraft, taking Earth polar observation under the Sun-Earth triple system as an example, specifically including:

[0024] Step 1: Establish the light pressure dynamics model of the refractive solar sail spacecraft: The characteristic tangential radiation pressure P of the refractive solar sail spacecraft tang and characteristic tangential radiation pressure P norm The characteristic tangential (normal) radiation pressure of a refractive solar sail spacecraft is characterized by the tangential (normal) radiation pressure generated by the refractive solar sail spacecraft when it is irradiated by the sun at a distance of 1 astronomical unit from the sun; the area-to-mass ratio γ of the refractive sail; the characteristic tangential acceleration a of the refractive solar sail spacecraft tang and characteristic normal acceleration a norm , the characteristic tangential (normal) acceleration can be calculated by the characteristic tangential (normal) radiation pressure, which are a tang =γP tang(a norm =γP norm ).

[0025] Step 2. Based on the framework of the circular restricted three-body problem (CR3BP), an improved dynamic equation with a refractive light pressure term is constructed, and the spatial coordinate set of the artificial libration point in the Sun-Earth system is numerically solved: in the plane circular restricted three-body problem, all variables are dimensionless; the parameter μ = μ2 / (μ1+μ2) is defined as the dimensionless gravitational constant, where μ1 is the gravitational constant of the Sun and μ2 is the gravitational constant of the Earth. The dimensionless gravitational constant in the Sun-Earth system is 3.0404E-6, the dimensionless length unit [L] is the distance between the Sun and the Earth, and its value is 1AU, i.e., 1 astronomical unit. The dimensionless mass unit [M] is the sum of the masses of the two celestial bodies, which is 1.989E30. The time unit [T] is [[L] 3 / G[M]] 0.5 .

[0026] Introducing a non-inertial system rotating around the heliocentric like Figure 2 As shown, the origin O is located at the center of mass of the sun and the earth. The axis always points from the center of mass of the sun and the earth to the direction of the earth. The axis direction is the normal direction of the Earth's orbital plane. The direction of the axis is determined by Axis and The axis is determined by the right-hand rule; the non-inertial system is always orbiting The shaft rotates and the rotation speed is constant.

[0027] Step 3: Determine the tangential and normal dynamic equations that the artificial libration point needs to satisfy and solve them using a numerical method to obtain the position of the artificial libration point of the refractive solar sail spacecraft in the Sun-Earth three-body system.

[0028] Step 4: Establish a polar observation geometric constraint model and calculate the observation semi-cone angle φ between the position of each libration point and the target observation position through coordinate transformation. Specifically, it includes: introducing the geocentric inertial system like Figure 3 As shown, the origin of the coordinate system is at the center of mass of the earth. The axis always points towards the vernal equinox of the ecliptic plane. The axis coincides with the Earth's rotation axis, and its positive direction follows the direction of the Earth's rotational angular momentum. The direction of the axis is determined by Axis and Axis is determined by the right-hand rule; Earth-centered inertial system Non-inertial frame The relationship between Figure 2 As shown, Axis and The angle between the axes is the obliquity of the ecliptic θ ec , its value is 23.5°; introduce the minimum observation elevation angle ∈ and the observable earth latitude θ lat and the Earth's radius R e In the geocentric inertial system, the observable range is a cone of infinite height, and the apex of the cone is at the geocentric inertial system. On axis, height of cone apex Given that the refractive solar sail spacecraft is within the observable range, it can be obtained that the position constraint of the refractive solar sail spacecraft in the geocentric inertial system at the current moment is Where: Angle φ is the sum of the line connecting the refractive solar sail spacecraft and the cone vertex. The angle between the axes, {X, Y, Z} are the coordinates of the refractive solar sail spacecraft in the geocentric inertial system.

[0029] Step 5: Discretize the Earth's revolution period in time, solve the continuity condition of observation coverage, and determine the feasible domain that satisfies the full-cycle continuous polar observation. Specifically, consider the geocentric inertial system. The central axis of the observable range cone coincides with the polar axis, and the earth always revolves around the sun's geocentric center at a certain angular velocity, so in the non-inertial system In the observable range, the cone is always precessing in the opposite direction at this angular velocity, and the rotation axis of the precession is the same as that in the non-inertial system. The angle between the Earth's polar axis and the precessing axis is always the obliquity of the ecliptic θ. ec .

[0030] like Figure 4 As shown in the figure, the yellow area is the observable range cone at the summer solstice in the northern hemisphere, and the green area is the observable range cone at the winter solstice in the northern hemisphere. Starting from the winter solstice, the central axis of the observable range cone revolves around the axis (The axis It only refers to the direction, not the axis in the non-inertial system. ) continuously precesses and returns to its original position after one revolution cycle. During the entire cycle, the overlapping coverage is the sustainable observation range of the refraction sail, as shown in the overlapping part in the figure. This range is also the feasible domain of the continuous polar observation mission carried out by the refraction sail deployed at the artificial Lagrange point; according to the spatial geometric relationship, the sustainable observation range is also a cone, and the cone vertex angle φ conti =θ lat -∈-θ ec , vertex height The refractive solar sail spacecraft is obtained in the non-inertial system Constraints on sustainable observation space position under Where: Angle φ nonis the line connecting the refractive solar sail spacecraft and the vertex of the sustainable observation cone and The angle between the axes {x, y, z} is the angle between the refractive solar sail spacecraft and the non-inertial system. 's coordinates.

[0031] Step 6: Based on the position of the artificial libration point in the Sun-Earth three-body system and the restricted range of the sustainable polar observation space position obtained in the above steps, the two areas are intersected to determine the sustainable observation position of the artificial libration point at the Earth's poles.

[0032] After specific actual experiments, the cross-section angle is 1 to 40 degrees and the surface quality ratio is 30m 2 / kg~130m 2 The above system can be started by inputting parameters of / kg, and the solar radiation pressure curve of the refractive solar sail can be obtained through the refractive solar sail dynamics simulation unit. Figure 5 As shown, the artificial translation point calculation unit can obtain the artificial translation point space coordinate set corresponding to the parameter range as shown in Figure 6 The blue dots in the middle are the locations of the artificial libration points that can be observed continuously and selected by the continuous observation performance evaluation unit. Figure 6 As shown by the red dot in the middle, in addition, the continuous observation performance evaluation unit can output the relationship curve between the refractive solar sail under different surface quality ratios and the cross-section vertex angle under the optimal observation performance, as shown in the figure below. Figure 7 shown.

[0033] Further combined with specific application analysis and comparison with the observation performance of traditional reflective solar sails, given the minimum observation elevation angle ∈ = 20° and the need to observe all areas within the Arctic Circle, that is, θ lat =66.5°, as shown in the following example: Figure 8 and Figure 9 As shown in Figure 2, the observation performance comparison of traditional reflective sail and refractive solar sail spacecraft with the same surface-to-mass ratio at their respective optimal libration points is shown. Figure 8 As shown in the figure, under the same surface-to-mass ratio, when the minimum ground station observation elevation angle is 20°, the observation coverage of the refractive sail is wider. The refractive solar sail spacecraft with the maximum acceleration capability can cover a latitude of about 55°, while the traditional reflective sail can only conduct sustainable observations at a position around 70° north latitude. If the earth is approximated as a sphere, according to the spherical surface area formula, the area of the sustainable observation area is increased by 1.9988 times; Figure 9 As shown, when the observation latitude is within the Arctic Circle, the surface-to-mass ratio of the reflective sail needs to reach 80m 2 / kg is required for continuous observation, and the corresponding minimum observation elevation angle is 5°, which places high demands on ground station hardware. In contrast, a refractive solar sail spacecraft can achieve a minimum observation elevation angle of approximately 27°, significantly improving observation performance. Clearly, refractive solar sail spacecraft have greater advantages in artificial libration point observation missions in the Sun-Earth triad system.

[0034] The above-mentioned specific implementation can be partially adjusted in different ways by those skilled in the art without departing from the principles and purpose of the present invention. The scope of protection of the present invention shall be based on the claims and shall not be limited by the above-mentioned specific implementation. All implementation schemes within its scope shall be subject to the constraints of the present invention.

Claims

1. A method for determining sustainable observation points at the Earth's polar regions based on a refractive solar sail spacecraft, characterized in that: By establishing a light pressure dynamics model for a refractive solar sail spacecraft and based on the circular restricted three-body problem (CR3BP) framework, an improved dynamics equation containing a refractive light pressure term is generated and solved to obtain the spatial coordinate set of artificial libration points in the Sun-Earth system. The observation semi-cone angle between each libration point in the spatial coordinate set and the target observation point in the polar observation geometric constraint model is calculated through coordinate transformation. After solving the continuity condition of observation coverage by discretizing the Earth's orbital period to obtain a feasible domain that satisfies full-cycle continuous polar observation, the spatial coordinate set of the artificial libration point is spatially matched with the feasible domain to screen out the optimal observation point that meets the requirements. The light pressure dynamics model refers to the characteristic tangential acceleration a of the refractive solar sail spacecraft. tang =γP tang (a norm =γP norm ), where: P tang is the characteristic tangential radiation pressure of the refractive solar sail spacecraft, P norm is the characteristic normal radiation pressure, tangential refers to the direction parallel to the sail surface, and normal refers to the direction perpendicular to the sail surface; the characteristic tangential (normal) radiation pressure of a refractive solar sail spacecraft is characterized by the tangential (normal) radiation pressure generated by the refractive solar sail spacecraft when it is irradiated by the sun at a distance of 1 astronomical unit from the sun, γ is the area-to-mass ratio of the refractive sail, and a tang is the characteristic tangential acceleration, a norm is the characteristic normal acceleration.

2. The method for determining sustainable observation points at the Earth's polar regions based on a refractive solar sail spacecraft according to claim 1, wherein: The improved dynamic equation containing the refractive light pressure term is: the non-inertial system rotating around the heliocentric The tangential and normal dynamic equations that the artificial translation point in must satisfy are: Where: μ = μ2 / (μ1+μ2) is the dimensionless gravitational constant, μ1 is the gravitational constant of the sun, μ2 is the gravitational constant of the earth, the dimensionless length unit [L] is the distance between the two celestial bodies, the dimensionless mass unit [M] is the sum of the masses of the two celestial bodies, and the time unit [T] is [[L] 3 / G[M]] 0.5 ; Normalized effective potential is the direction of the Earth's revolution around the sun, and the normalized gravitational potential energy at the location of the refractive solar sail spacecraft r1(r2) is the normalized distance from the refractive solar sail spacecraft to the sun (earth), and the normal acceleration of the refractive solar sail spacecraft is and tangential acceleration r is the normalized distance from the refractive solar sail spacecraft to the center of the Sun and Earth.

3. The method for determining sustainable observation points at the Earth's polar regions based on a refractive solar sail spacecraft according to claim 1, wherein: The set of spatial coordinates is obtained by numerically solving the tangential and normal dynamic equations that the artificial libration point in the non-inertial system rotating around the heliocentric geocenter must satisfy.

4. The method for determining sustainable observation points at the Earth's polar regions based on a refractive solar sail spacecraft according to claim 1, wherein: The observation semi-cone angle satisfies the position constraint, that is, Where: The observation semi-cone angle φ is the sum of the line connecting the refractive solar sail spacecraft and the cone vertex. The angle between the axes, {X, Y, Z} is the coordinate of the refractive solar sail spacecraft in the geocentric inertial system, and the height of the cone vertex is ∈ is the minimum observation elevation angle, θ lat is the observable Earth latitude, R e is the radius of the Earth.

5. The method for determining sustainable observation points at the Earth's polar regions based on a refractive solar sail spacecraft according to claim 1, wherein: The feasible domain that satisfies the full-cycle polar continuous observation is: the refractive solar sail spacecraft in the non-inertial system Constraints on sustainable observation space position under Where: Angle φ non is the line connecting the refractive solar sail spacecraft and the vertex of the sustainable observation cone and The angle between the axes {x, y, z} is the angle between the refractive solar sail spacecraft and the non-inertial system. Coordinates, cone apex angle φ conti =θ lat -∈-θ ec , vertex height θ ec is the obliquity of the ecliptic, and μ is the dimensionless gravitational constant.

6. The method for determining sustainable observation points at the Earth's polar regions based on a refractive solar sail spacecraft according to claim 1, wherein: The matching refers to: according to the obtained coordinates of the artificial libration point of the refractive solar sail spacecraft, substituting the constraints of the sustainable observation space position to determine whether the corresponding artificial libration point has the conditions for continuous observation, and screening out the optimal observation point that meets the requirements.

7. A system for determining sustainable observation points of the Earth's polar regions for implementing the method according to any one of claims 1 to 6, characterized in that: include: A refractive solar sail dynamics simulation unit, an artificial libration point calculation unit, a continuous observation performance evaluation unit, and a result output unit, wherein: the refractive solar sail dynamics simulation unit calculates the attitude and corresponding light pressure through optical simulation based on the structural parameter design information of the sail, and combines properties such as the surface-to-mass ratio to obtain the dynamics of the refractive solar sail in all directions; the artificial libration point calculation unit obtains the position of the artificial libration point and the corresponding sail surface attitude control parameters through orbital dynamics numerical simulation and isotropic force balance analysis based on the dynamic model of the refractive solar sail; the continuous observation performance evaluation unit selects the position of the artificial libration point for sustainable observation based on the position information of the artificial libration point and the constraints of the sustainable observation space position, and evaluates the sustainable observation performance of each sustainable observation point; the result output unit selects the optimal observation point that meets the requirements based on the spatial coordinate set of the sustainably observed artificial libration points and the corresponding sustainable observation performance, and outputs the spatial coordinates of the optimal artificial libration point, the corresponding attitude of the refractive solar sail, and various structural parameters of the sail.

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