Phase modulation method and system for reducing shadow time on a lunar orbit using orbital transfer

Abstract

The application discloses a phase modulation method and system for reducing shadow time on a lunar orbit by orbit transfer, which judges whether a satellite is in the shadow of the moon or the shadow of the earth according to parameters such as a lunar center inertia coordinate system and a satellite position; the period of an intermediate orbit and the semi-major axis of the intermediate orbit are calculated according to the time of the orbit transfer, the intermediate orbit is used as a transition orbit, the total shadow time of the satellite in a day is judged and calculated; the phases of the satellite reaching a lunar orbit are selected as 1-360 degrees in turn, the shadow time of each phase in a day is calculated, the phase with the shortest shadow time is selected, if the phase is not less than a set intersection degree when the shadow time is the shortest, the period of the transition orbit is adjusted according to the phase, and the new transition orbit period and the orbit semi-major axis are calculated; the above steps are repeated with the new transition orbit as a standard until the phase is less than a set angle when the shadow time is the shortest, and then the transition orbit transferred to the target orbit after the period can avoid the influence of the earth shadow and the moon shadow.

Description

Technical Field

[0001] This invention relates to the field of lunar exploration orbit design technology, specifically a phasing method that reduces the shadow time in the lunar orbit by utilizing orbit transfer. More specifically, it relates to designing a transfer transition orbit to adjust the phase of the satellite as it reaches the target orbit while transferring the orbit to the lunar mission orbit, in order to avoid the influence of long Earth shadows. Background Technology

[0002] Communication conditions between Earth and the far side of the Moon and the polar regions are poor, and relying solely on tracking and control stations on Earth is insufficient to meet the complex needs of future lunar exploration. Therefore, a lunar communication, navigation, and remote sensing system is needed to provide relay communication, navigation, and remote sensing services for users on the lunar surface and in lunar orbit. A highly elliptical frozen lunar orbit has become the core of current lunar polar exploration and the establishment of lunar research stations. However, satellites in lunar orbit cannot avoid entering the Earth's shadow and the Moon's shadow. When satellites are in shadow for extended periods, they may lose energy, and currently, there are no methods to avoid long periods of shadow in lunar orbit. By rationally designing transition orbits for orbit transfer, the timing of the satellite's arrival at the lunar mission orbit can be adjusted simultaneously, thereby avoiding prolonged periods of shadow. Summary of the Invention

[0003] The technical problem to be solved by this invention is how to rationally design the transition orbit for orbit transfer, which can simultaneously adjust the time when the satellite arrives at the lunar orbit, thereby avoiding the satellite entering a long Earth shadow period.

[0004] The present invention solves the above-mentioned technical problems through the following technical means:

[0005] A phasing method for reducing the shadowing time in a lunar orbit by utilizing orbital transfer includes the following steps:

[0006] Step 1: Define the lunar-centered inertial coordinate system, obtain the satellite position, satellite velocity, solar position, Earth position, orbit transfer time, and target orbit parameters;

[0007] Step 2: Based on the data obtained in Step 1, determine whether the satellite is in the shadow of the moon or the earth;

[0008] Step 3: Calculate the period and semi-major axis of the intermediate orbit based on the orbit transfer time, and use the intermediate orbit as the transition orbit; determine and calculate the total time the satellite is in shadow during the day based on Step 2.

[0009] Step 4: Select the phases of the lunar orbit to be 1-360 degrees. Calculate the shadow time for each phase in a day according to Step 3. Select the phase with the shortest shadow time. If the phase with the shortest shadow time is not less than the set angle, adjust the period of the transition orbit according to the phase and calculate the new transition orbit period and the semi-major axis of the orbit.

[0010] Step 5: Using the new transition orbit as a standard, repeat Step 4 until the shadow time is the shortest and the phase is less than the set angle. After the transition orbit of this cycle is transferred to the target orbit, the effects of the ground shadow and the moon shadow can be avoided.

[0011] Furthermore, orbit phasing is performed simultaneously with the orbit transfer, as executed in step one, and includes the following steps:

[0012] Step 1.1: Define the lunar inertial frame of reference and obtain the orbit transfer time and target orbit parameters;

[0013] Step 1.2: On a day when a long shadow may occur, obtain the satellite position, satellite velocity, sun position, moon position, and earth position in the lunar inertial frame at each time interval Δt.

[0014] Furthermore, a method for determining whether a satellite is within the moon's shadow or the earth's shadow is executed in step two, including the following steps:

[0015] Step 2.1: Given the radius and position of the Sun, the radius and position of the central celestial body, and a point in space, the following method can be used to determine whether the point is located in the penumbra or umbra of the central celestial body;

[0016] The radius of the central celestial body is denoted as R. C The location is denoted as the origin; the radius of the sun is denoted as R. S Its position vector is denoted as r. S Let U and P be the points where the tangents of the Sun and the central celestial body intersect; then the position vectors of U and P can be calculated by the following formula:

[0017]

[0018]

[0019] Step 2.2: Determine whether the detector is located within the cone of the penumbra and umbra. Point A represents point P in the penumbra or point U in the umbra, and point SC represents the detector. The semi-cone angle of the cone is denoted as α.

[0020]

[0021] Let β be the angle between the detector and the axis of the cone.

[0022]

[0023] If β is less than α, it means that the detector is located inside the cone;

[0024] Step 2.3: Determine whether the detector and the cone apex are on the same side of the obscuring celestial body. As shown in the diagram, if the angle formed by the cone apex, the detector, and the center of the obscuring celestial body is obtuse, they are on the same side; if the angle is acute, they are on opposite sides.

[0025] The specific method for determining this can be calculated using the following formula:

[0026] (r SC -r A )·r SC (5)

[0027] If the above expression is less than zero, it means that they are on the same side; if the above expression is greater than zero, it means that they are on opposite sides.

[0028] Or calculate:

[0029] (r A -r SC )·r SC (6)

[0030] If the above expression is greater than zero, it means that they are on the same side; if the above expression is less than zero, it means that they are on opposite sides.

[0031] Step 2.4: If the detector and the vertex of the umbra cone are on the same side of the occluding celestial body, then the detector is in the umbra; if the detector and the vertex of the penumbra cone are on opposite sides of the occluding celestial body, then the detector is in the penumbra.

[0032] Furthermore, a transition orbit is selected and the total time the satellite is in shadow is calculated. This is performed in step three and includes the following steps:

[0033] Step 3.1: The period of the transition orbit is selected as half of the sum of the period of the target orbit and the transfer time. The semi-major axis of the transition orbit is calculated based on the period.

[0034] Let the period of the transition orbit be T0, and the period of the target orbit be T. H The transfer time is T. r The period of the transition orbit can be calculated by the following formula:

[0035]

[0036] The semi-major axis of the transition orbit can be calculated based on the orbital period, in the following formula, where 'a' represents the semi-major axis of the orbit, and 'μ' represents the gravitational constant of the central celestial body, here representing the lunar gravitational constant:

[0037]

[0038] Step 3.2: Calculate the total time the satellite is in shadow, starting from the initial time, during a day when a long shadow may occur;

[0039] Divide the day into equal intervals Δt and obtain the satellite position, satellite velocity, sun position, moon position, and earth position of each node in the lunar center inertial frame. Assume there are L sets of data, and calculate the total shadow time.

[0040] Furthermore, the shadowing time under different phase differences is calculated, and the period of the transition orbit is adjusted according to the phase with the smallest shadowing time. This is performed in step four and includes the following steps:

[0041] Step 4.1: Select the phases of the lunar orbit to be 1-360 degrees, and calculate the shadow time of each phase in a day according to Step 3;

[0042] Step 4.2: Select the phase with the shortest shadow time. If the phase difference is not less than 0.5 degrees when the shadow time is shortest, adjust the period of the transition orbit according to the phase difference and calculate the adjusted period of the transition orbit.

[0043] Let the minimum phase be α, the transition orbit period be T0, and the adjusted transition orbit period be T1. Adjust the transition orbit period according to the phase difference.

[0044] Step 4.3: Calculate the semi-major axis of the orbit based on the adjusted transition orbit period. In the following formula, 'a' represents the semi-major axis of the orbit, and 'μ' represents the gravitational constant of the central celestial body, which here represents the gravitational constant of the Moon:

[0045]

[0046] The present invention also provides a phasing system for reducing the shadowing time in lunar orbit by utilizing orbital transfer, comprising:

[0047] Orbit parameter definition module: used to define the lunar inertial coordinate system, obtain satellite position, satellite velocity, solar position and Earth position, as well as the parameters of orbit transfer time and target orbit;

[0048] Judgment module: used to determine whether the satellite is in the shadow of the moon or the shadow of the earth based on the data obtained in step one;

[0049] Calculation module: used to calculate the period and semi-major axis of the intermediate orbit based on the orbit transfer time, using the intermediate orbit as a transition orbit; and to determine and calculate the total time the satellite is in shadow during the day based on step two.

[0050] Transition orbit parameter adjustment module: Select the phases of the lunar orbit to be 1-360 degrees in sequence. Calculate the shadow time of each phase in a day according to step three. Select the phase with the shortest shadow time. If the phase with the shortest shadow time is not less than the set angle, adjust the period of the transition orbit according to the phase and calculate the new transition orbit period and the semi-major axis of the orbit.

[0051] Iteration module: Used to repeat step four with the new transition track as the standard until the phase is less than the set angle when the shadow time is the shortest.

[0052] Furthermore, orbit phasing is performed simultaneously with orbit transfer, executed within the orbit parameter definition module, and includes the following steps:

[0053] Step 1.1: Define the lunar inertial frame of reference and obtain the orbit transfer time and target orbit parameters;

[0054] Step 1.2: On a day when a long shadow may occur, obtain the satellite position, satellite velocity, sun position, moon position, and earth position in the lunar inertial frame at each time interval Δt.

[0055] Furthermore, a method for determining whether a satellite is within the moon's shadow or the earth's shadow is executed in the determination module, including the following steps:

[0056] Step 2.1: Given the radius and position of the Sun, the radius and position of the central celestial body, and a point in space, the following method can be used to determine whether the point is located in the penumbra or umbra of the central celestial body;

[0057] The radius of the central celestial body is denoted as R. C The location is denoted as the origin; the radius of the sun is denoted as R. S Its position vector is denoted as r. S Let U and P be the points where the tangents of the Sun and the central celestial body intersect; then the position vectors of U and P can be calculated by the following formula:

[0058]

[0059]

[0060] Step 2.2: Determine whether the detector is located within the cone of the penumbra and umbra. Point A represents point P in the penumbra or point U in the umbra, and point SC represents the detector. The semi-cone angle of the cone is denoted as α.

[0061]

[0062] Let β be the angle between the detector and the axis of the cone.

[0063]

[0064] If β is less than α, it means that the detector is located inside the cone;

[0065] Step 2.3: Determine whether the detector and the cone apex are on the same side of the obscuring celestial body. As shown in the diagram, if the angle formed by the cone apex, the detector, and the center of the obscuring celestial body is obtuse, they are on the same side; if the angle is acute, they are on opposite sides.

[0066] The specific method for determining this can be calculated using the following formula:

[0067] (r SC -r A )·r SC (14)

[0068] If the above expression is less than zero, it means that they are on the same side; if the above expression is greater than zero, it means that they are on opposite sides.

[0069] Or calculate:

[0070] (r A -r SC )·r SC (15)

[0071] If the above expression is greater than zero, it means that they are on the same side; if the above expression is less than zero, it means that they are on opposite sides.

[0072] Step 2.4: If the detector and the vertex of the umbra cone are on the same side of the occluding celestial body, then the detector is in the umbra; if the detector and the vertex of the penumbra cone are on opposite sides of the occluding celestial body, then the detector is in the penumbra.

[0073] Furthermore, selecting a transition orbit and calculating the total time the satellite is in shadow are performed in the calculation module, including the following steps:

[0074] Step 3.1: The period of the transition orbit is selected as half of the sum of the period of the target orbit and the transfer time. The semi-major axis of the transition orbit is calculated based on the period.

[0075] Let the period of the transition orbit be T0, and the period of the target orbit be T. H The transfer time is T. r The period of the transition orbit can be calculated by the following formula:

[0076]

[0077] The semi-major axis of the transition orbit can be calculated based on the orbital period, in the following formula, where 'a' represents the semi-major axis of the orbit, and 'μ' represents the gravitational constant of the central celestial body, here representing the lunar gravitational constant:

[0078]

[0079] Step 3.2: Calculate the total time the satellite is in shadow, starting from the initial time, during a day when a long shadow may occur;

[0080] Divide the day into equal intervals Δt and obtain the satellite position, satellite velocity, sun position, moon position, and earth position of each node in the lunar center inertial frame. Assume there are L sets of data, and calculate the total shadow time.

[0081] Furthermore, the shadowing time under different phase differences is calculated, and the period of the transition orbit is adjusted according to the phase with the smallest shadowing time. This is performed in the transition orbit parameter adjustment module, including the following steps:

[0082] Step 4.1: Select the phases of the lunar orbit to be 1-360 degrees, and calculate the shadow time of each phase in a day according to Step 3;

[0083] Step 4.2: Select the phase with the shortest shadow time. If the phase difference is not less than 0.5 degrees when the shadow time is shortest, adjust the period of the transition orbit according to the phase difference and calculate the adjusted period of the transition orbit.

[0084] Let the minimum phase be α, the transition orbit period be T0, and the adjusted transition orbit period be T1. Adjust the transition orbit period according to the phase difference.

[0085] Step 4.3: Calculate the semi-major axis of the orbit based on the adjusted transition orbit period. In the following formula, 'a' represents the semi-major axis of the orbit, and 'μ' represents the gravitational constant of the central celestial body, which here represents the gravitational constant of the Moon:

[0086]

[0087] The advantages of this invention are:

[0088] This invention avoids the long Earth shadow problem by designing a transitional orbit for orbit transfer before the satellite enters its lunar mission orbit, without consuming additional fuel. At the same time, the satellite does not need to perform additional maneuvers to avoid the long Earth shadow during the lunar mission, saving valuable fuel during the mission and reducing maneuver control errors. This invention is applicable to the highly elliptical frozen orbit type around the moon and is of great significance for the orbit design of spacecraft related to lunar polar exploration and the establishment of lunar research stations in my country.

[0089] This invention discloses a method for determining whether a satellite is in the shadow of the moon or the earth based on the acquired data; calculating the period and semi-major axis of the intermediate orbit based on the orbit transfer time; using the intermediate orbit as a transition orbit; determining and calculating the total time the satellite is in shadow throughout the day; selecting phases from 1 to 360 degrees for reaching the lunar orbit; calculating the shadow time for each phase throughout the day; selecting the phase with the shortest shadow time; if the phase with the shortest shadow time is not less than a set angle, adjusting the period of the transition orbit based on the phase; calculating the new transition orbit period and semi-major axis; using the new transition orbit as a standard, repeating the above steps until the phase with the shortest shadow time is less than the set angle; after this period, the transition orbit transfers to the target orbit, avoiding the influence of the earth's shadow and the moon's shadow. Attached Figure Description

[0090] Figure 1This is a schematic diagram of shadow formation in the method of Embodiment 1 of the present invention;

[0091] Figure 2 This is a schematic diagram illustrating the method for determining whether a satellite is in shadow in Embodiment 1 of the present invention.

[0092] Figure 3 This is a flowchart illustrating the calculation of the total shadow time in the method of Embodiment 1 of the present invention;

[0093] Figure 4 This refers to the total shadowing time under different phases in the method of Embodiment 1 of the present invention;

[0094] Figure 5 This is a flowchart of adjusting the transition orbit period in the method of Embodiment 1 of the present invention;

[0095] Figure 6 This refers to the total shadowing time of different phases under the final transition orbit in the method of Embodiment 1 of the present invention;

[0096] Figure 7 This is a flowchart of the method in Embodiment 1 of the present invention. Detailed Implementation

[0097] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0098] Example 1

[0099] This embodiment discloses a phasing method for reducing the shadowing time on the lunar orbit by utilizing orbital transfer, such as... Figure 7 As shown, the specific implementation steps are as follows:

[0100] Step 1: Define the lunar-centered inertial coordinate system, obtain the start time and orbital parameters of phasing, satellite position, satellite velocity, solar position and Earth position, as well as the end time of orbit phasing and the parameters of the target orbit.

[0101] Step 1.1: Define the lunar inertial frame and obtain the orbit transfer time and target orbit parameters.

[0102] In this example, the orbit transfer takes 3 days, the target orbit period is 12 hours, and the orbital altitude is 200 kilometers.

[0103] Step 1.2: On a day when a long shadow may occur, obtain the satellite position, satellite velocity, sun position, moon position, and earth position in the lunar inertial frame at each time interval Δt.

[0104] The possible duration of a long Earth shadow is from 00:00:00.000 on March 25, 2024 to 00:00:00.000 on March 26, 2024, with a time interval of 120 seconds. At the start of the first time interval, the satellite's three-axis coordinates are [4589.8554, 3865.0253, -2172.2422] km, and its three-axis velocities are [0.3918, 0.01416, -0.7650] km / s. The solar three-axis coordinates are [1.4912764188×10]. 8 1.0751191304×10 7 4.65014724×10 6 ]km, the Earth's three axes coordinates are [4.05471×10 5 1.220403×10 4 -0.453686×10 4 ]km.

[0105] Step 2: Based on the data obtained in Step 1, determine whether the satellite is in the shadow of the moon or the shadow of the earth.

[0106] Step 2.1: Given the radius and position of the Sun, the radius and position of the central celestial body, and a point in space, the following method can be used to determine whether the point is located in the penumbra or umbra of the central celestial body.

[0107] The radius of the central celestial body is denoted as R. C The location is denoted as the origin; the radius of the sun is denoted as R. S Its position vector is denoted as r. S The points where the tangents of the Sun and the central celestial body intersect are denoted as U and P, respectively, as follows: Figure 1 As shown.

[0108] The position vectors of U and P can then be calculated using the following formula:

[0109]

[0110]

[0111] If we calculate the lunar shadow, with the Moon as the central celestial body, the Sun's radius is 695,508 km, and the Earth's radius is 6,378.14 km. U The vector is [-1.38022828×10 6 -0.09950602×10 6-0.04303873×10 6 ], r P The vector is [1.355143×10 6 0.097697×10 6 0.042256×10 6 ].

[0112] Step 2.2: Determine whether the detector is located within the cone of the penumbra and umbra, such as... Figure 2 As shown in the figure, point A represents the penumbra point P or the umbra point U, and point SC represents the detector.

[0113] Let α be the semi-cone angle of the cone, then...

[0114]

[0115] Let β be the angle between the detector and the axis of the cone.

[0116]

[0117] If β is less than α, it means that the detector is located inside the cone.

[0118] If point A represents the umbra point U, r A Indicates r U Calculations show that α = 0.5263 and β = 0.0030. Since β is less than α, it indicates that the detector is located inside the cone.

[0119] If point A represents point P of the penumbra, r A Indicates r P Calculations show that α = 0.5371 and β = 0.0031. Since β is less than α, it indicates that the detector is located inside the cone.

[0120] Step 2.3: Determine whether the detector and the cone apex are on the same side of the obscuring celestial body. As shown in the figure, if the angle formed by the cone apex, the detector, and the center of the obscuring celestial body is obtuse, then they are on the same side; if the angle is acute, then they are on opposite sides.

[0121] The specific method for determining this can be calculated using the following formula:

[0122] (r SC -r A )·r SC (twenty three)

[0123] If the above expression is less than zero, it means that the expression is on the same side; if the above expression is greater than zero, it means that the expression is on the opposite side.

[0124] Or calculate:

[0125] (r A -r SC )·rSC (twenty four)

[0126] If the above expression is greater than zero, it means that the expression is on the same side; if the above expression is less than zero, it means that the expression is on the opposite side.

[0127] If point A represents the umbra point U, r A Indicates r U After calculation, (r) A -r SC )·r SC = -6.667 × 10 9 Therefore, the starting point of the first time interval is located on the opposite side of the umbra.

[0128] If point A represents point P of the penumbra, r A Indicates r P After calculation, (r) A -r SC )·r SC =6.464×10 9 Therefore, the starting point of the first time interval is located on the same side as the penumbra.

[0129] Step 2.4: If the detector and the vertex of the umbra cone are on the same side of the occluding celestial body, then the detector is in the umbra; if the detector and the vertex of the penumbra cone are on opposite sides of the occluding celestial body, then the detector is in the penumbra.

[0130] The judgment result of step 2.3 indicates that the starting point of the first time interval is located on the opposite side of the umbra point, therefore the satellite is not in shadow during the first time interval.

[0131] Step 3: Calculate the period and semi-major axis of the intermediate orbit based on the orbit transfer time. Using the intermediate orbit as a transition orbit, calculate the total time the satellite is in shadow.

[0132] Step 3.1: The period of the transition orbit is selected as half of the sum of the period of the target orbit and the transfer time. The semi-major axis of the transition orbit is calculated based on the period.

[0133] Let the period of the transition orbit be T0, and the period of the target orbit be T. H The transfer time is T. r The period of the transition orbit can be calculated by the following formula:

[0134]

[0135] In this example, the transfer to the lunar orbit takes 3 days, the period of the target lunar orbit is 12 hours, so the period of the transition orbit is 42 hours.

[0136] The semi-major axis of the transition orbit can be calculated based on the orbital period, in the following formula, where 'a' represents the semi-major axis of the orbit, and 'μ' represents the gravitational constant of the central celestial body, here representing the lunar gravitational constant:

[0137]

[0138] Given the lunar gravitational constant μ = 4902.800066, the semi-major axis of the transition orbit is a = 14160 km.

[0139] Step 3.2: Calculate the total time the satellite is in shadow, starting from the initial time, during a day when a long shadow will appear.

[0140] Divide a day into equal intervals Δt and obtain the satellite position, satellite velocity, sun position, moon position, and earth position of each node in the lunar inertial frame. Assume there are L sets of data. The process for calculating the total shadow time is shown in the figure below.

[0141] The system determines whether the satellite is in shadow for each time interval. If it is in shadow, the total shadow time is increased by 120 seconds. After determining each time interval, the total time the satellite is in shadow throughout the day can be obtained.

[0142] Step 4: Make the phases differ sequentially by 1 to 360 degrees, calculate the shadow time for each phase difference, select the phase with the shortest shadow time, if the phase difference is not 0 when the shadow time is shortest, adjust the period of the transition orbit according to the phase difference, and calculate the new transition orbit period and the semi-major axis of the orbit.

[0143] Step 4.1: Select the phases of the lunar orbit to be 1-360 degrees, and calculate the shadow time of each phase in a day according to Step 3.

[0144] Figure 5 Based on the transition orbit selected in step three, after transferring to the lunar mission orbit, with an initial phase of 1-360 degrees, it can be seen that the satellite experiences the shortest Earth shadow time when the phase is 56 degrees.

[0145] Step 4.2: Select the phase with the shortest shadow time. If the phase difference is not less than 0.5 degrees when the shadow time is shortest, adjust the period of the transition orbit according to the phase difference and calculate the adjusted period of the transition orbit.

[0146] Let the minimum phase be α, the transition orbit period be T0, and the adjusted transition orbit period be T1. The process for adjusting the transition orbit period based on the phase difference is as follows. Figure 4 In this example, the minimum phase is 56 degrees, dt = 6.53 hours, and the adjusted orbital period is 35.47 hours.

[0147] Step 4.3: Calculate the semi-major axis of the orbit based on the adjusted transition orbit period. In the following formula, 'a' represents the semi-major axis of the orbit, and 'μ' represents the gravitational constant of the central celestial body, which here represents the gravitational constant of the Moon:

[0148]

[0149] Using the above formula, the semi-major axis of the adjusted transition track is 12651 km.

[0150] Step 5: Using the new transition orbit as a standard, repeat Step 4 until the shadow time is the shortest and the phase difference is less than 0.5 degrees. After this cycle, the transition orbit will transfer to the target orbit, avoiding the influence of the Earth's shadow and the Moon's shadow.

[0151] Step 5.1: Using the orbital period and semi-major axis adjusted in Step 4 as the new transitional orbit, repeat Step 4.1 and Step 4.2 until the phase difference is less than 0.5 when the shadow time is the smallest. The transitional orbit at this time is the final transitional orbit. After the transitional orbit of this period is transferred to the target orbit, the influence of the Earth shadow and the Moon shadow can be avoided.

[0152] First time: Shortest shadow time phase difference: 56, recommended phase adjustment orbit semi-major axis: 13737.2553km.

[0153] Second time: Shortest shadow time phase difference: 30, recommended phase adjustment orbit semi-major axis: 13508.1034km.

[0154] Third time: Shortest shadow time phase difference: 21, recommended phase adjustment orbit semi-major axis: 13346.5346km.

[0155] Fourth time: Shortest shadow time phase difference: 15, recommended phase adjustment orbit semi-major axis: 13230.5273km.

[0156] 5th time: Shortest shadow time phase difference: 11, recommended phase adjustment orbit semi-major axis: 13145.1312km.

[0157] 6th time: Shortest shadow time phase difference: 8, recommended phase adjustment orbit semi-major axis: 13082.8503km.

[0158] 7th time: Shortest shadow time phase difference: 6, recommended phase adjustment orbit semi-major axis: 13036.0421km.

[0159] 8th time: Shortest shadow time phase difference: 4, recommended phase adjustment orbit semi-major axis: 13004.79km.

[0160] 9th time: Shortest shadow time phase difference: 3, recommended phase adjustment orbit semi-major axis: 12981.3262km.

[0161] 10th time: Shortest shadow time, phase difference: 2, recommended phase adjustment orbit semi-major axis: 12965.6719km.

[0162] 11th time: Shortest shadow time phase difference: 2, recommended phase adjustment orbit semi-major axis: 12950.0082km.

[0163] 12th time: Shortest shadow time phase difference: 1, recommended phase adjustment orbit semi-major axis: 12942.1727km.

[0164] 13th time: Shortest shadow time, phase difference: 0, recommended phase adjustment orbit semi-major axis: 12934.3349km.

[0165] After continuous adjustments to the transition orbit period, when the semi-major axis of the transfer orbit is 12934.3349 km, the phase difference is 0 when the shadowing time is shortest. The shadowing durations for different phases under this transition orbit are as follows: Figure 6 As shown. Using this transition orbit to transfer to the lunar target orbit can effectively reduce the time the satellite is in shadow.

[0166] Example 2

[0167] This embodiment discloses a phasing system that utilizes orbital transfer to reduce the shadowing time in the lunar orbit, specifically including:

[0168] Orbit Parameter Definition Module: Defines the lunar-centered inertial coordinate system, obtains the start time of phasing and orbital parameters, satellite position, satellite velocity, solar position and Earth position, as well as the end time of orbit phasing and the parameters of the target orbit.

[0169] Step 1.1: Define the lunar inertial frame and obtain the orbit transfer time and target orbit parameters.

[0170] In this example, the orbit transfer takes 3 days, the target orbit period is 12 hours, and the orbital altitude is 200 kilometers.

[0171] Step 1.2: On a day when a long shadow may occur, obtain the satellite position, satellite velocity, sun position, moon position, and earth position in the lunar inertial frame at each time interval Δt.

[0172] The possible duration of a long Earth shadow is from 00:00:00.000 on March 25, 2024 to 00:00:00.000 on March 26, 2024, with a time interval of 120 seconds. At the start of the first time interval, the satellite's three-axis coordinates are [4589.8554, 3865.0253, -2172.2422] km, and its three-axis velocities are [0.3918, 0.01416, -0.7650] km / s. The solar three-axis coordinates are [1.4912764188×10 8 1.0751191304×10 7 4.65014724×10 6 ]km, the Earth's three axes coordinates are [4.05471×10 5 1.220403×10 4 -0.453686×10 4 ]km.

[0173] Judgment module: Based on the data obtained in step one, determine whether the satellite is in the shadow of the moon or the shadow of the earth.

[0174] Step 2.1: Given the radius and position of the Sun, the radius and position of the central celestial body, and a point in space, the following method can be used to determine whether the point is located in the penumbra or umbra of the central celestial body.

[0175] The radius of the central celestial body is denoted as R. C The location is denoted as the origin; the radius of the sun is denoted as R. S Its position vector is denoted as r. S The points where the tangents of the Sun and the central celestial body intersect are denoted as U and P, respectively, as follows: Figure 1 As shown.

[0176] The position vectors of U and P can then be calculated using the following formula:

[0177]

[0178]

[0179] If we calculate the lunar shadow, with the Moon as the central celestial body, the Sun's radius is 695,508 km, and the Earth's radius is 6,378.14 km. U The vector is [-1.38022828×10 6 -0.09950602×10 6 -0.04303873×10 6 ], r P The vector is [1.355143×10 6 0.097697×10 60.042256×10 6 ].

[0180] Step 2.2: Determine whether the detector is located within the cone of the penumbra and umbra, such as... Figure 2 As shown in the figure, point A represents the penumbra point P or the umbra point U, and point SC represents the detector.

[0181] Let α be the semi-cone angle of the cone, then...

[0182]

[0183] Let β be the angle between the detector and the axis of the cone.

[0184]

[0185] If β is less than α, it means that the detector is located inside the cone.

[0186] If point A represents the umbra point U, r A Indicates r U Calculations show that α = 0.5263 and β = 0.0030. Since β is less than α, it indicates that the detector is located inside the cone.

[0187] If point A represents point P of the penumbra, r A Indicates r P Calculations show that α = 0.5371 and β = 0.0031. Since β is less than α, it indicates that the detector is located inside the cone.

[0188] Step 2.3: Determine whether the detector and the cone apex are on the same side of the obscuring celestial body. As shown in the figure, if the angle formed by the cone apex, the detector, and the center of the obscuring celestial body is obtuse, then they are on the same side; if the angle is acute, then they are on opposite sides.

[0189] The specific method for determining this can be calculated using the following formula:

[0190] (r SC -r A )·r SC (32)

[0191] If the above expression is less than zero, it means that the expression is on the same side; if the above expression is greater than zero, it means that the expression is on the opposite side.

[0192] Or calculate:

[0193] (r A -r SC )·r SC (33)

[0194] If the above expression is greater than zero, it means that the expression is on the same side; if the above expression is less than zero, it means that the expression is on the opposite side.

[0195] If point A represents the umbra point U, r A Indicates r U After calculation, (r) A -r SC )·r SC = -6.667 × 10 9 Therefore, the starting point of the first time interval is located on the opposite side of the umbra.

[0196] If point A represents point P of the penumbra, r A Indicates r P After calculation, (r) A -r SC )·r SC =6.464×10 9 Therefore, the starting point of the first time interval is located on the same side as the penumbra.

[0197] Step 2.4: If the detector and the vertex of the umbra cone are on the same side of the occluding celestial body, then the detector is in the umbra; if the detector and the vertex of the penumbra cone are on opposite sides of the occluding celestial body, then the detector is in the penumbra.

[0198] The judgment result of step 2.3 indicates that the starting point of the first time interval is located on the opposite side of the umbra point, therefore the satellite is not in shadow during the first time interval.

[0199] Calculation module: Calculates the period and semi-major axis of the intermediate orbit based on the orbit transfer time, and uses the intermediate orbit as a transition orbit to calculate the total time the satellite is in shadow.

[0200] Step 3.1: The period of the transition orbit is selected as half of the sum of the period of the target orbit and the transfer time. The semi-major axis of the transition orbit is calculated based on the period.

[0201] Let the period of the transition orbit be T0, and the period of the target orbit be T. H The transfer time is T. r The period of the transition orbit can be calculated by the following formula:

[0202]

[0203] In this example, the transfer to the lunar orbit takes 3 days, the period of the target lunar orbit is 12 hours, so the period of the transition orbit is 42 hours.

[0204] The semi-major axis of the transition orbit can be calculated based on the orbital period, in the following formula, where 'a' represents the semi-major axis of the orbit, and 'μ' represents the gravitational constant of the central celestial body, here representing the lunar gravitational constant:

[0205]

[0206] Given the lunar gravitational constant μ = 4902.800066, the semi-major axis of the transition orbit is a = 14160 km.

[0207] Step 3.2: Calculate the total time the satellite is in shadow, starting from the initial time, during a day when a long shadow will appear.

[0208] Divide a day into equal intervals Δt and obtain the satellite position, satellite velocity, sun position, moon position, and earth position of each node in the lunar inertial frame. Assume there are L sets of data. The process for calculating the total shadow time is shown in the figure below.

[0209] The system determines whether the satellite is in shadow for each time interval. If it is in shadow, the total shadow time is increased by 120 seconds. After determining each time interval, the total time the satellite is in shadow throughout the day can be obtained.

[0210] Transition orbit parameter adjustment module: Make the phases differ sequentially from 1 to 360 degrees, calculate the shadow time for each phase difference, select the phase with the shortest shadow time, if the phase difference is not 0 when the shadow time is shortest, adjust the period of the transition orbit according to the phase difference, and calculate the new transition orbit period and the semi-major axis of the orbit.

[0211] Step 4.1: Select the phases of the lunar orbit to be 1-360 degrees, and calculate the shadow time of each phase in a day according to Step 3.

[0212] Figure 5 Based on the transition orbit selected in step three, after transferring to the lunar mission orbit, with an initial phase of 1-360 degrees, it can be seen that the satellite experiences the shortest Earth shadow time when the phase is 56 degrees.

[0213] Step 4.2: Select the phase with the shortest shadow time. If the phase difference is not less than 0.5 degrees when the shadow time is shortest, adjust the period of the transition orbit according to the phase difference and calculate the adjusted period of the transition orbit.

[0214] Let the minimum phase be α, the transition orbit period be T0, and the adjusted transition orbit period be T1. The process for adjusting the transition orbit period based on the phase difference is as follows. Figure 4 In this example, the minimum phase is 56 degrees, dt = 6.53 hours, and the adjusted orbital period is 35.47 hours.

[0215] Step 4.3: Calculate the semi-major axis of the orbit based on the adjusted transition orbit period. In the following formula, 'a' represents the semi-major axis of the orbit, and 'μ' represents the gravitational constant of the central celestial body, which here represents the gravitational constant of the Moon:

[0216]

[0217] Using the above formula, the semi-major axis of the adjusted transition track is 12651 km.

[0218] Iterative module: Using the new transition orbit as the standard, repeat step four until the shadow time is the shortest and the phase difference is less than 0.5 degrees. After the transition orbit of this cycle is transferred to the target orbit, the influence of the Earth shadow and the Moon shadow can be avoided.

[0219] Step 5.1: Using the orbital period and semi-major axis adjusted in Step 4 as the new transitional orbit, repeat Step 4.1 and Step 4.2 until the phase difference is less than 0.5 when the shadow time is the smallest. The transitional orbit at this time is the final transitional orbit. After the transitional orbit of this period is transferred to the target orbit, the influence of the Earth shadow and the Moon shadow can be avoided.

[0220] First time: Shortest shadow time phase difference: 56, recommended phase adjustment orbit semi-major axis: 13737.2553km.

[0221] Second time: Shortest shadow time phase difference: 30, recommended phase adjustment orbit semi-major axis: 13508.1034km.

[0222] Third time: Shortest shadow time phase difference: 21, recommended phase adjustment orbit semi-major axis: 13346.5346km.

[0223] Fourth time: Shortest shadow time phase difference: 15, recommended phase adjustment orbit semi-major axis: 13230.5273km.

[0224] 5th time: Shortest shadow time phase difference: 11, recommended phase adjustment orbit semi-major axis: 13145.1312km.

[0225] 6th time: Shortest shadow time phase difference: 8, recommended phase adjustment orbit semi-major axis: 13082.8503km.

[0226] 7th time: Shortest shadow time phase difference: 6, recommended phase adjustment orbit semi-major axis: 13036.0421km.

[0227] 8th time: Shortest shadow time phase difference: 4, recommended phase adjustment orbit semi-major axis: 13004.79km.

[0228] 9th time: Shortest shadow time phase difference: 3, recommended phase adjustment orbit semi-major axis: 12981.3262km.

[0229] 10th time: Shortest shadow time, phase difference: 2, recommended phase adjustment orbit semi-major axis: 12965.6719km.

[0230] 11th time: Shortest shadow time phase difference: 2, recommended phase adjustment orbit semi-major axis: 12950.0082km.

[0231] 12th time: Shortest shadow time phase difference: 1, recommended phase adjustment orbit semi-major axis: 12942.1727km.

[0232] 13th time: Shortest shadow time, phase difference: 0, recommended phase adjustment orbit semi-major axis: 12934.3349km.

[0233] After continuous adjustments to the transition orbit period, when the semi-major axis of the transfer orbit is 12934.3349 km, the phase difference is 0 when the shadowing time is shortest. The shadowing durations for different phases under this transition orbit are as follows: Figure 6 As shown. Using this transition orbit to transfer to the lunar target orbit can effectively reduce the time the satellite is in shadow.

[0234] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A phase adjustment method for reducing the shadowing time in a lunar orbit by utilizing orbital transfer, characterized in that, Includes the following steps: Step 1: Define the lunar-centered inertial coordinate system, obtain the satellite position, satellite velocity, solar position, Earth position, orbit transfer time, and target orbit parameters; Step 2: Based on the data obtained in Step 1, determine whether the satellite is in the shadow of the moon or the earth; Step 3: Calculate the period and semi-major axis of the intermediate orbit based on the orbit transfer time, and use the intermediate orbit as the transition orbit; determine and calculate the total time the satellite is in shadow during the day based on Step 2. Step 4: Select the phases of the lunar orbit to be 1-360 degrees. Calculate the shadow time for each phase in a day according to Step 3. Select the phase with the shortest shadow time. If the phase with the shortest shadow time is not less than the set angle, adjust the period of the transition orbit according to the phase and calculate the new transition orbit period and the semi-major axis of the orbit. Step 5: Using the new transition orbit as a standard, repeat Step 4 until the shadow time is the shortest and the phase is less than the set angle. After the transition orbit of this cycle is transferred to the target orbit, the effects of the ground shadow and the moon shadow can be avoided.

2. The phase adjustment method for reducing the shadow time on the lunar orbit by utilizing orbital transfer according to claim 1, characterized in that, Orbit phasing is performed simultaneously with orbit transfer, and is executed in step one, including the following steps: Step 1.1: Define the lunar inertial frame of reference, and obtain the orbit transfer time and the parameters of the target orbit; Step 1.2: On a day when a long shadow is likely to occur, with For each time interval, obtain the satellite position, satellite velocity, sun position, moon position, and earth position in the lunar inertial frame at each different moment.

3. The phase adjustment method for reducing the shadow time on the lunar orbit by utilizing orbital transfer according to claim 2, characterized in that, A method for determining whether a satellite is in the moon's shadow or the earth's shadow, executed in step two, includes the following steps: Step 2.1: Given the radius and position of the Sun, the radius and position of the central celestial body, and a point in space, determine whether the point is located in the penumbra or umbra of the central celestial body using the following method; The radius of the central celestial body is denoted as R C The location is denoted as the origin; the solar radius is denoted as... R S Its position vector is denoted as r S Let U and P be the points where the tangents of the Sun and the central celestial body intersect; then the position vectors of U and P can be calculated by the following formula: (1) (2) Step 2.2: Determine whether the detector is located within the cone of the penumbra and umbra. Point A represents point P in the penumbra or point U in the umbra, and point SC represents the detector; the semi-cone angle of the cone is denoted as... α ,have (3) The angle between the detector and the axis of the cone is denoted as . β ,have (4) like β Less than α This indicates that the detector is located inside the cone; Step 2.3: Determine whether the detector and the cone apex are on the same side of the occluding celestial body; if the angle formed by the cone apex, the detector, and the center of the occluding celestial body is obtuse, then they are on the same side; if the angle is acute, then they are on opposite sides. The specific determination method involves calculating the following formula: (5) If the above expression is less than zero, it means that they are on the same side; if the above expression is greater than zero, it means that they are on opposite sides. Or calculate: (6) If the above expression is greater than zero, it means that they are on the same side; if the above expression is less than zero, it means that they are on opposite sides. Step 2.4: If the detector and the vertex of the umbra cone are on the same side of the occluding celestial body, then the detector is in the umbra; if the detector and the vertex of the penumbra cone are on opposite sides of the occluding celestial body, then the detector is in the penumbra.

4. The phase adjustment method for reducing the shadow time on the lunar orbit by utilizing orbital transfer according to claim 3, characterized in that, Selecting a transition orbit and calculating the total time the satellite is in shadow are performed in step three, including the following steps: Step 3.1: The period of the transition orbit is selected as half of the sum of the period of the target orbit and the transfer time. The semi-major axis of the transition orbit is calculated based on the period. Let the period of the transition orbit be... The period of the target orbit is The transfer time is The period of the transition orbit can be calculated by the following formula: (7) The semi-major axis of the transition track can be calculated based on the track period, as shown in the following formula: Indicates the semi-major axis of the track. The gravitational constant of the central celestial body is represented here, and the gravitational constant of the Moon is also represented here. (8) Step 3.2: Calculate the total time the satellite is in shadow, starting from the initial time, during a day when a long shadow may occur; Divide the day into equal intervals Separate and obtain the satellite position, satellite velocity, sun position, moon position, and earth position of each node in the lunar inertial frame. Assume there are L sets of data in total, and calculate the total shadow time.

5. A phase adjustment method for reducing the shadow time on the lunar orbit by utilizing orbital transfer according to claim 4, characterized in that, Calculate the shadowing time under different phase differences, and adjust the period of the transition orbit according to the phase with the smallest shadowing time. This is performed in step four and includes the following steps: Step 4.1: Select the phases of the lunar orbit to be 1-360 degrees, and calculate the shadow time of each phase in a day according to Step 3; Step 4.2: Select the phase with the shortest shadow time. If the phase difference is not less than 0.5 degrees when the shadow time is shortest, adjust the period of the transition orbit according to the phase difference and calculate the adjusted period of the transition orbit. Let the minimum phase be The transition orbit period is The adjusted transition orbit period is The transition orbit period is adjusted according to the phase difference; Step 4.3: Calculate the semi-major axis of the orbit based on the adjusted transition orbit period, as shown in the following formula: Indicates the semi-major axis of the track. The gravitational constant of the central celestial body is represented here, and the gravitational constant of the Moon is also represented here. (9)。 6. A phasing system that utilizes orbital transfer to reduce the shadowing time in a lunar orbit, characterized in that, include: Orbit parameter definition module: used to define the lunar inertial coordinate system, obtain satellite position, satellite velocity, solar position and Earth position, as well as the parameters of orbit transfer time and target orbit; Judgment module: Used to determine whether the satellite is in the shadow of the moon or the shadow of the earth based on the acquired data; Calculation module: used to calculate the period and semi-major axis of the intermediate orbit based on the orbit transfer time, using the intermediate orbit as a transition orbit; and to determine and calculate the total time the satellite is in shadow during the day. Transition orbit parameter adjustment module: Select the phases of the lunar orbit to arrive at the lunar orbit in sequence from 1 to 360 degrees, calculate the shadow time of each phase in a day, select the phase with the shortest shadow time, if the phase with the shortest shadow time is not less than the set angle, then adjust the period of the transition orbit according to the phase, and calculate the new transition orbit period and the semi-major axis of the orbit. Iteration module: Used to repeatedly execute the transition track parameter adjustment module with the new transition track as the standard until the phase is less than the set angle when the shadow time is the shortest.

7. A phasing system for reducing shadow time in lunar orbit by utilizing orbital transfer as described in claim 6, characterized in that, Track phasing is performed simultaneously with track transfer, and is executed in the track parameter definition module, including the following steps: Step 1.1: Define the lunar inertial frame of reference, and obtain the orbit transfer time and the parameters of the target orbit; Step 1.2: On a day when a long shadow is likely to occur, with For each time interval, obtain the satellite position, satellite velocity, sun position, moon position, and earth position in the lunar inertial frame at each different moment.

8. A phasing system for reducing shadow time in lunar orbit by utilizing orbital transfer according to claim 7, characterized in that, A method for determining whether a satellite is within the moon's shadow or the earth's shadow, executed in a determination module, includes the following steps: Step 2.1: Given the radius and position of the Sun, the radius and position of the central celestial body, and a point in space, determine whether the point is located in the penumbra or umbra of the central celestial body using the following method; The radius of the central celestial body is denoted as R C The location is denoted as the origin; the solar radius is denoted as... R S Its position vector is denoted as r S Let U and P be the points where the tangents of the Sun and the central celestial body intersect; then the position vectors of U and P can be calculated by the following formula: (1) (2) Step 2.2: Determine whether the detector is located within the cone of the penumbra and umbra. Point A represents point P in the penumbra or point U in the umbra, and point SC represents the detector; the semi-cone angle of the cone is denoted as... α ,have (3) The angle between the detector and the axis of the cone is denoted as . β ,have (4) like β Less than α This indicates that the detector is located inside the cone; Step 2.3: Determine whether the detector and the cone apex are on the same side of the occluding celestial body; if the angle formed by the cone apex, the detector, and the center of the occluding celestial body is obtuse, then they are on the same side; if the angle is acute, then they are on opposite sides. The specific determination method involves calculating the following formula: (5) If the above expression is less than zero, it means that they are on the same side; if the above expression is greater than zero, it means that they are on opposite sides. Or calculate: (6) If the above expression is greater than zero, it means that they are on the same side; if the above expression is less than zero, it means that they are on opposite sides. Step 2.4: If the detector and the vertex of the umbra cone are on the same side of the occluding celestial body, then the detector is in the umbra; if the detector and the vertex of the penumbra cone are on opposite sides of the occluding celestial body, then the detector is in the penumbra.

9. A phasing system for reducing shadow time in lunar orbit by utilizing orbital transfer, as described in claim 8, is characterized in that, Selecting a transition orbit and calculating the total time the satellite is in shadow are performed in the calculation module, including the following steps: Step 3.1: The period of the transition orbit is selected as half of the sum of the period of the target orbit and the transfer time. The semi-major axis of the transition orbit is calculated based on the period. Let the period of the transition orbit be... The period of the target orbit is The transfer time is The period of the transition orbit can be calculated by the following formula: (7) The semi-major axis of the transition track can be calculated based on the track period, as shown in the following formula: Indicates the semi-major axis of the track. The gravitational constant of the central celestial body is represented here, and the gravitational constant of the Moon is also represented here. (8) Step 3.2: Calculate the total time the satellite is in shadow, starting from the initial time, during a day when a long shadow may occur; Divide the day into equal intervals Separate and obtain the satellite position, satellite velocity, sun position, moon position, and earth position of each node in the lunar inertial frame. Assume there are L sets of data in total, and calculate the total shadow time.

10. A phasing system for reducing shadow time in lunar orbit by utilizing orbital transfer according to claim 9, characterized in that, The shadowing time under different phase differences is calculated, and the period of the transition orbit is adjusted according to the phase with the smallest shadowing time. This is performed in the transition orbit parameter adjustment module, including the following steps: Step 4.1: Select the phases of the lunar orbit to be 1-360 degrees, and calculate the shadow time of each phase in a day according to Step 3; Step 4.2: Select the phase with the shortest shadow time. If the phase difference is not less than 0.5 degrees when the shadow time is shortest, adjust the period of the transition orbit according to the phase difference and calculate the adjusted period of the transition orbit. Let the minimum phase be The transition orbit period is The adjusted transition orbit period is The transition orbit period is adjusted according to the phase difference; Step 4.3: Calculate the semi-major axis of the orbit based on the adjusted transition orbit period, as shown in the following formula: Indicates the semi-major axis of the track. The gravitational constant of the central celestial body is represented here, and the gravitational constant of the Moon is also represented here. (9)。

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