Satellite systems

Abstract

Conventional Earth observation satellites cannot simultaneously consolidate multiple satellites within a predetermined range and observe that range without any unobserved areas. [Solution] A satellite system comprising multiple artificial satellites, wherein, at a time set as a reference, the projected position of each artificial satellite on the Earth's surface falls within a predetermined range of latitude and longitude set on a map, and as time progresses, this range moves in the longitude direction, and regardless of the passage of time, the projected position of each artificial satellite on the Earth's surface remains within this range. The satellite system is characterized in that, among the projection positions of all artificial satellites onto the Earth's surface, any two artificial satellites have a projection position on the Earth's surface between them in the latitudinal direction, and the latitudinal range between the projection positions of those two artificial satellites, between which there are no other artificial satellite projection positions, lies within the range of the Earth's surface observed by the sensors of either of those two artificial satellites.

Description

Technical Field

[0006]

[0001] The present invention relates to a satellite system for observing the Earth.

Background Art

[0002] In Earth observation by artificial satellites, observation by a single Earth observation satellite has been conventionally carried out. In recent years, satellite systems that use multiple artificial satellites as a system for observation have also been implemented. Since these artificial satellites have improved observation resolution the closer they are to the Earth's surface, they are often put into low orbits.

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Non-Patent Documents

[0004]

Non-Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0007] A satellite system comprising multiple artificial satellites, wherein, at a predetermined time, the projected position of each of the multiple artificial satellites, which is the point where a line drawn from each artificial satellite toward the Earth's center intersects the Earth's surface, falls within a predetermined range of one or more latitudes and longitudes set on a map, and as time progresses, the predetermined range moves in the longitude direction, and regardless of the passage of time, the projected position of each artificial satellite toward the Earth's surface remains within the predetermined range, and the predetermined range is defined as the latitude range where the maximum absolute value of the orbital inclination angle of the constituent artificial satellites is the North and South latitudes at the predetermined time, and from the predetermined time onward, all The satellite system is characterized in that, up until the time the artificial satellite completes one orbit of the Earth, the maximum difference between the projected positions of any two artificial satellites on the Earth's surface in the longitude range of the possible longitudes of each artificial satellite's projected position on the Earth's surface is defined as the longitude difference range, and all artificial satellites' projected positions on the Earth's surface are positioned within the range enclosed by this latitude range and the longitude difference range, and for any two artificial satellites' projected positions on the Earth's surface, the latitudinal range between the projected positions of any two artificial satellites that do not have any other artificial satellites' projected positions on the Earth's surface in the latitudinal direction of the Earth's surface observed by the sensor of either of the two artificial satellites is within the range in the latitudinal direction of the Earth's surface. More preferably, the satellite system is characterized in that the projection positions of each artificial satellite on the Earth's surface within the predetermined range are arranged on a figure-eight shaped line that has one intersection near the equator and forms a pair of roughly circular lines running north-south. More preferably, at a time set as a reference, if the angles between the direction vectors perpendicular to the orbital planes of multiple satellites are 1° or less, the multiple satellites are considered to be in the same orbit. In non-identical orbits, the right ascension of each satellite's ascending node is set such that the difference in the interval between all adjacent ascending node right ascensions between any two satellites' ascending nodes is within 0.1° or less. The interval of the latitude argument is set to an integer multiple of the average value of the intervals between all adjacent ascending node right ascensions. One satellite is selected as a reference satellite from among all satellites, and the reference satellite's... The satellite system is characterized by setting the latitude argument of all orbits by repeatedly adding or subtracting a constant positive or negative interval between the latitude arguments to the latitude argument of the original orbit, starting from the orbit, for non-identical orbits, and ensuring that the difference in the interval between the latitude arguments of all satellite orbits is 0.5° or less, and by selecting the interval between the latitude arguments and the right ascension of the ascending node of each satellite so that the arrangement of the projected positions of each satellite on the Earth's surface within the predetermined range lies on a figure-eight shaped line with one intersection near the equator and a pair of roughly circular lines running north-south. [Effects of the Invention]

[0008] The satellite system of the present invention simultaneously aggregates multiple artificial satellites within a predetermined range and moves this predetermined range with a period of one day or less. As a result, the predetermined range orbits the Earth several times a day in the longitude direction, which has the effect of allowing observation of the target observation range without any unobserved areas multiple times a day at the desired time intervals. [Brief explanation of the drawing]

[0009] [Figure 1] This is a diagram showing the configuration of the satellite system 100 in Embodiment 1. [Figure 2] This is a diagram showing the projection of the artificial satellite onto the Earth's surface (initial time) in Embodiment 1. [Figure 3] This diagram shows the latitude and longitude (initial time) of the projection point of each artificial satellite in Embodiment 1. [Figure 4]It is a diagram of the projection of the artificial satellite onto the earth's surface (at time 1795 seconds) in Embodiment 1. [Figure 5] It is a diagram of the latitude and longitude of the projection points of each artificial satellite (at time 1795 seconds) in Embodiment 1. [Figure 6] It is a diagram of the longitude difference range according to the absolute value of the orbital inclination angle in Embodiment 1. [Figure 7] It is a diagram of the relationship between the half-angle of the sensor's field of view, the altitude of the artificial satellite, and the observation range. [Figure 8] It is a diagram of the relationship between the half-angle of the sensor's field of view θs and the altitude of the artificial satellite. [Figure 9] It is a diagram of the projection of the artificial satellite onto the earth's surface (initial time) in Embodiment 2. [Figure 10] It is a diagram of the latitude and longitude of the projection points of each artificial satellite (initial time) in Embodiment 2. [Figure 11] It is a diagram of the arrangement on the figure-eight-shaped line including satellite number 1 in the diagram of the latitude and longitude of the projection points of each artificial satellite (initial time) in Embodiment 2. [Figure 12] It is a diagram of the arrangement on the figure-eight-shaped line including satellite number 2 in the diagram of the latitude and longitude of the projection points of each artificial satellite (initial time) in Embodiment 2. [Figure 13] It is a diagram of the arrangement on the figure-eight-shaped line including satellite number 3 in the diagram of the latitude and longitude of the projection points of each artificial satellite (initial time) in Embodiment 2. [Figure 14] It is a diagram of the satellite arrangement (figure-eight) according to the number of satellites. [Figure 15] It is a diagram of the satellite arrangement (figure-eight) according to N. [Figure 16] It is a diagram of the projection of the artificial satellite onto the earth's surface (initial time) in Embodiment 3. [Figure 17] It is a diagram of the latitude and longitude of the projection points of each artificial satellite (initial time) in Embodiment 3.

Modes for Carrying Out the Invention

[0010] In the embodiments and the drawings, the same elements or corresponding elements are denoted by the same reference numerals. The description of elements denoted by the same reference numerals as those already described will be omitted or simplified as appropriate.

[0011] [Embodiment 1] The satellite system 100 will be described based on FIG. 1.

[0012] [Description of Configuration] First, the notations in FIG. 1 will be described. The notations in the subsequent figures are basically the same as those first shown in the figures. The central circle 117 represents the Earth. The ellipse surrounding the Earth represents the orbit of the artificial satellite. The black circles represent the artificial satellites. The satellite system 100 of Embodiment 1 includes a total of 16 artificial satellites (101 to 116), one each on these orbits. The artificial satellites are distinguished as the first satellite 101, the second satellite 102, and so on.

[0013] [Satellite Arrangement (Initial Time)] In Embodiment 1, the time is defined based on the initial time. It is possible to install a plurality of artificial satellites on the same orbit by changing only the latitude argument. Here, the "orbit" refers to the path (line) along which the artificial satellite moves, not the position of the artificial satellite. The position of the artificial satellite is a point on the orbit. Hereinafter, unless otherwise specified, for all embodiments, the orbits of the artificial satellites are set using the inertial coordinate system centered on the Earth. That is, it is a right-handed coordinate system including the direction from the center of the Earth to the vernal equinox point and the north pole direction. The plane including the two axes that are not the north pole direction includes the equatorial plane. Here, even if we say "the same orbit", physical errors will occur. Therefore, when the angle formed by the direction vectors perpendicular to the orbital planes (planes including the orbits) of the respective artificial satellites is 1° or less, it is considered to be the same orbit. The orbits in FIG. 1 are not the same orbit in this sense. In Embodiment 1, the orbits of the respective artificial satellites are not the same orbit. A reference satellite is selected from among several satellites and designated as satellite number 1. In Embodiment 1, the first satellite 101 is this satellite, satellite number 1. The second satellite 102, the third satellite 103, and so on are numbered sequentially from satellite number 2 to 16, corresponding to the number of satellites. The orbits of each satellite are set based on mission requirements, etc. In Embodiment 1, as shown in Figure 1, the number of satellites is 16, which is a multiple of 4, and different orbits with different ascending node right ascensions are set for each satellite. The reason for setting the number of satellites as a multiple of 4 is explained later in Figure 14, etc. In Embodiment 1, the orbit of each satellite is a nearly circular orbit with an eccentricity of 0.0002 or less, and the orbital altitude of each satellite is a low Earth orbit of approximately 500 kilometers. Therefore, the orbital periods of each satellite are approximately the same, but the difference between the maximum and minimum orbital periods of all satellites is set to be 0.1% or less of the average orbital period of all satellites. The orbital inclination (i) is determined based on mission requirements, etc., but in Embodiment 1 it is set to 45°. The difference in orbital inclination of all satellite orbits shall be 0.1° or less. The orbital inclination corresponds to the range of latitudes that an artificial satellite's orbit can reach. In other words, if the orbital inclination is 45°, the orbit will not reach a range beyond ±45° of latitude.

[0014] Let Ωn0 be the right ascension of the ascending node and νn0 be the latitude argument of satellite number n (where n is a natural number, 1 to 16) at the initial time. The subscript 0 indicates that it is the initial time. In Embodiment 1, the initial position of the first satellite 101 in orbit is projected onto the Earth's surface (latitude λ10 = 36°N, longitude φ10 = 140°E). From this value, the right ascension of the ascending node (Ω10) and the latitude argument (ν10) of the first satellite 101's orbit are calculated. From the latitude and longitude (λ10, φ10) of the first satellite 101, Ω10 and ν10 can be obtained using spherical trigonometry with the following formula 1. [Mathematics 1] ν10 = Asin(sin(λ10) / sin(i)) Ω10=φ10 -Acos(cos(ν10) / cos(λ10))

[0015] The right ascension of the ascending node for each satellite is set based on the orbit derived from mission requirements, etc. However, in Embodiment 1, the orbit of each satellite is set starting from the right ascension of the ascending node (Ω10) of the reference first satellite 101 (satellite number 1). That is, 22.5°, which is the Earth's orbit of 360° divided equally by 16 satellites, is set as the interval ΔΩ between adjacent ascending nodes, and the right ascension of the ascending node of each satellite's orbit is set by shifting sequentially in the same direction by ΔΩ from the starting point. Here, two ascending nodes of any two satellites are defined as "adjacent" ascending nodes if there are no other ascending nodes between them. ΔΩ is the average value of the interval between the right ascensions of adjacent ascending nodes for all orbits, taking tolerances into account. The tolerance for ΔΩ is set such that the difference in the interval between the right ascensions of adjacent ascending nodes for all orbits is within 0.1° or less when setting the right ascension of each satellite's ascending node.

[0016] From the ascending node right ascension (Ω10) and latitude argument (ν10) of the first satellite 101 obtained in this way, the ascending node right ascension (Ωn0) and latitude argument (νn0) of the orbit of satellite number n at the initial time are set by the following equation 2. Here, the subscript 0 written at the end of Ωn0, Ωn-10, νn0, and νn-10 indicates the initial time. [Math 2] Ωn0 = Ωn - 10 + (n-1)ΔΩ Δν = N * ΔΩ νn0 = νn-10 - (n-1)Δν Ωn0: Right ascension of the ascending node of the nth satellite (°), Ωn-10: Right ascension of the ascending node of the (n-1)th satellite (°) ΔΩ: The average value of the distance between the right ascensions of adjacent ascending nodes (°) Δν: Latitude argument interval (°) N: Integer value νn0: Latitude argument of the nth satellite (°), νn-10: Latitude argument of the (n-1)th satellite (°) n: Natural number, 2~16 The first formula shows how to set the right ascension of the ascending node of an artificial satellite. Starting from the orbit of satellite number 1, which serves as the reference satellite, the right ascension of the ascending node of the next orbit (Ωn0) is set by adding the average value (ΔΩ) of the interval between adjacent right ascensions of all the aforementioned orbits to the right ascension of the ascending node of the original orbit (Ωn-10). The second formula shows that the interval of the latitude argument (Δν) is an integer multiple (N times) of the average value (ΔΩ) of the intervals between all adjacent ascending node right ascensions. (Hereafter, "N" refers to this integer value.) The third formula shows how to set the latitude argument. Starting from the orbit of the reference satellite number 1, the latitude argument of the next orbit (νn0) is set by adding the interval (Δν) of the latitude argument to the original orbit's latitude argument (νn-10). This process is repeated until the latitude argument of all orbits is set. Note that this includes adding ΔΩ and Δν with their signs reversed, but the signs are considered to be the same for all n. Ultimately, the tolerance of the spacing between the latitude argument νn of all satellite orbits will be adjusted to 0.5° or less through satellite orbit control. The point where a line drawn from a satellite toward the Earth's center intersects the Earth's surface (expressed in latitude and longitude) is called the projection position onto the Earth's surface. As will be described later in Figure 6, the above integer value (N) is selected so that the projection positions of each artificial satellite onto the Earth's surface are arranged on a figure-eight shaped line. In Embodiment 1, N=15. The "figure-eight" refers to a shape with one intersection near the equator and two roughly circular shapes running north-south.

[0017] From the right ascension of the nth satellite's ascending node (Ωn0) and latitude argument (νn0) obtained in this way, the projected position (latitude and longitude (λn0, φn0)) of the nth satellite (n is a natural number, 2 to 16) (102 to 116) onto the Earth's surface is given by the following equation 3. [Math 3] λn0 = Asin(sin(νn0)sin(i)) φn0=Acos(cos(νn0) / cos(λn0)) +Ωn0 This means that the projected position (latitude and longitude) of the first satellite's orbital position at the initial reference time, along with its orbital inclination, has been used to determine the projected position (latitude and longitude) of each satellite's orbital position on the Earth's surface.

[0018] Figure 2 shows the projected position of each satellite onto the Earth's surface at the initial time set in this manner. Based on Figures 2 and 3, the projection position of the satellite system 100 onto the Earth's surface at the initial time is explained.

[0019] Let's explain the notation in Figure 2. 118 shows a world map. The black dots represent artificial satellites (101-116). 119 (dotted quadrilateral) shows the distribution range of the projection positions of artificial satellites onto the Earth's surface.

[0020] As shown in Figure 2, the projection position falls within a predetermined range of one or more (in the case of multiple, as shown in Embodiment 2) latitude and longitude coordinates set on the map, which is within the arrangement range 119 for the projection position of the artificial satellite onto the Earth's surface. The placement range 119 for the projection position of this satellite onto the Earth's surface is set as follows.

[0021] First, let's explain how to set the latitudinal range. The "latitude range" is defined as the range within which the maximum absolute value of the orbital inclination angle of the constituent satellites at a predetermined reference time (initial time) corresponds to the north and south latitudes of the projected position of each satellite on the Earth's surface. For example, the latitude range is from 45° south (-45°) to 45° north (+45°). The absolute values ​​of north and south latitude are equal. Since the orbital inclination corresponds to the northernmost and southernmost range reached by the satellite's orbit, the latitude range of the satellite's projected position on the Earth's surface (119) is determined by the satellite's orbital inclination. Since there are multiple satellites, we will use the maximum absolute value of the orbital inclination of each satellite.

[0022] Next, we will explain how to set the range in the longitude direction. The "longitude difference range" is defined as the maximum difference between the projected positions of any two satellites on the Earth's surface, considering the longitudes that each satellite can take from a predetermined time until the time when all satellites have completed one orbit of the Earth. The area enclosed by the quadrilateral, with the latitude range defined as the latitude direction and the longitude difference range defined as the longitude direction, is the range 119 for the projection position of the artificial satellite onto the Earth's surface.

[0023] As shown in Figure 2, the projection positions of all artificial satellites onto the Earth's surface are located within the arrangement range 119 of the projection positions of the artificial satellites onto the Earth's surface, and moreover, they lie on a figure-eight shaped line.

[0024] Figure 3 shows the latitude and longitude (initial time) of the projected position of each satellite onto the Earth's surface. As a result, as can be seen in Figure 3, the positional range 119 of the projection position of the artificial satellite onto the Earth's surface at the initial time is the following value (tolerance 10%). Latitude range -45° to 45° (center 0°, width 90°) (because the orbital inclination is 45°) Longitude 140°~159° (center 149.5°, width (longitude difference range) 19°) A smaller range of longitude differences results in a smaller maximum difference in the time when each satellite passes through the same longitude. This has the effect of reducing the maximum difference in observation times for observation target points at the same longitude on a given map. In this embodiment, the difference in the longitude direction is 19°, and the time difference is 19 / 360 of the time it takes for the satellite's projection position range 119 onto the Earth's surface to complete one revolution on the map.

[0025] [Satellite configuration (time elapsed)] Taking the initial time as t=0, the right ascension of the nth satellite's ascending node and the latitude arguments (Ωnt, νnt) at time t are given by the following equation 4. Here, the subscript t at the end of Ωnt and νnt indicates that it is time t. [Math 4] Ωnt = Ωn0 (independent of time) νnt=νn0+ωS·t ωS=2π / Ts Ts: Orbital period ωS is the orbital angular velocity determined from the orbital period of the artificial satellite, and in Embodiment 1, it is the same value for each artificial satellite. The first equation shows that the right ascension of the ascending node for each satellite is the same as the initial value. The second equation shows that the latitude argument of each satellite changes with time by the orbital angular velocity ωS.

[0026] The projected position of the nth satellite onto the Earth's surface at time t (latitude and longitude (λnt, φnt)) is given by the following equation 5. [Number 5] λnt = Asin(sin(νnt)sin(i)) φnt=Acos(cos(νnt) / cos(λnt)) +Ωnt This means we have now determined the projected position (latitude and longitude) of each satellite on the Earth's surface at time t.

[0027] Figure 4 shows the projected position of the artificial satellite onto the Earth's surface at t = 1795 seconds (= 1 / 16th of a sidereal day, one example). Based on Figure 4, the projected position of satellite system 100 on the Earth's surface at t=1795 seconds is explained.

[0028] First, let's explain the notation in Figure 4. The 120 (figure-eight shaped curve) represents the moving line of the satellite's projection position onto the Earth's surface. 121 (the arrow near line 120, which represents the moving projection of the satellite onto the Earth's surface) indicates the direction of the satellite as it moves on the map over time. 122 (circular) indicates the observation range of the Earth's surface observed by the sensors of each satellite.

[0029] As shown in Figure 4, the projection positions of all artificial satellites onto the Earth's surface are located within the arrangement range 119 of the projection positions of the artificial satellites onto the Earth's surface, and moreover, they lie on a figure-eight shaped line.

[0030] Figure 5 shows the latitude and longitude of each satellite's projected position on the Earth's surface (time 1795 seconds). The size of the projection position of the artificial satellite onto the Earth's surface (119 (t=1795 seconds) (latitude range, longitude difference range)) is as shown in Figure 5, with the following values ​​(tolerance 10%), and remains unchanged from the initial time. Latitude range -45° to 45° (center 0°, width 90°) (because the orbital inclination is 45°) Longitude 245°~264° (center 254.5°, width (longitude difference range) 19°) The longitude center of the 119-point projection range of the artificial satellite onto the Earth's surface has shifted eastward by 105° in the longitude direction, from 149.5° to 254.5°. In other words, even as time passes, the projected positions of all artificial satellites on the Earth's surface remain within the arrangement range 119 of artificial satellites of the same size (latitude range, longitude difference range). Furthermore, the shape of the moving line 120, which represents the projection position of the artificial satellite onto the Earth's surface, remains unchanged.

[0031] The range of longitude differences in the figure-eight arrangement is determined by the maximum absolute value of the orbital inclination of all satellites. Figure 6 shows the range of longitude differences when the absolute value of the orbital inclination is varied. (For the purpose of calculating for all orbital inclinations, the projection position of the first satellite 101 onto the Earth's surface at the initial time was set to 0°N latitude and 0°E longitude.) When the absolute value of the orbital inclination falls within the range of the values ​​shown in Figure 6, the range of longitude difference can be approximately determined by interpolating it as a linear function of the absolute values ​​of both orbital inclinations that are closest to that value.

[0032] The positional range 119 of the satellite's projection onto the Earth's surface shifts eastward in the longitude direction over time. The time T required to complete one revolution along the longitude of a map is calculated by taking into account the Earth's rotation speed. This is given by equation 6 below. For example, in a circular orbit at an altitude of 500 kilometers, it takes approximately 100 minutes. [Number 6] T = Ts(1 + Ts / Td) Ts: orbital period, Td: sidereal day

[0033] On the map, each satellite moves along a moving line 120 representing the satellite's projection position onto the Earth's surface, in the direction 121 of the satellite as time progresses. Even though the satellites move over time, they remain within the range 119 of the satellite's projection position onto the Earth's surface, and the shape of the moving line 120 representing the satellite's projection position onto the Earth's surface remains unchanged.

[0034] When each artificial satellite is equipped with sensors such as synthetic aperture radar to observe the Earth's surface, the corresponding area of ​​the Earth's surface is determined once the sensor's field of view and the satellite's altitude are set, as shown in Figure 4, where the observation range 122 of the Earth's surface observed by the satellite's sensors is determined. The projection position of the artificial satellite onto the Earth's surface, within the range 119, moves eastward in the longitude direction, so observation is possible without any unobserved areas in the longitude direction. While synthetic aperture radar (SIRA) scans perpendicular to the satellite's direction of motion in other Earth observation satellites, in this case, the scan direction is perpendicular to the longitude. Satellites and SIRAs are controlled to maintain this scan direction, but the scan direction is fixed in an inertial coordinate system with the Earth at its center and the equatorial plane and the North Pole as coordinate axes.

[0035] Hereinafter, "adjacent projection positions" refers to any two projection positions of any two artificial satellites on the Earth's surface that do not have any other satellite projection positions between them in the latitudinal direction. If the latitudinal distance between adjacent projection positions is within the range of the Earth's surface observed by the sensors of either of the two satellites, then the area between adjacent projection positions can be observed without any unobserved areas in the latitudinal direction. In Embodiment 1, the maximum latitudinal interval between adjacent projection positions of the satellite onto the Earth's surface is 16°, as shown in Figures 3 and 5.

[0036] Figure 7 shows the relationship between the sensor's field of view half-angle, the satellite's altitude, and the observation range. First, let's explain the notation in Figure 7. 123 represents the half-angle of the field of view θs of the sensor mounted on satellite 101. 124 represents the angle θ between the line from the Earth's surface to satellite 101 and the line to the edge of the area of ​​the Earth observable by the sensor mounted on satellite 101. 125 represents the latitudinal interval between adjacent projection positions of the satellite's projection position onto the Earth's surface. In Embodiment 1, the half-angle of the sensor's field of view is set to the same value in both positive and negative (north-south) directions in the latitudinal direction relative to the straight line from the Earth's center to the satellite 101. This is the case, for example, when the sensor's field of view is conical.

[0037] These relationships can be determined geometrically. This relationship holds true not only for satellite 101 but for all satellites 101-116. As shown in Figure 7, if the angle θ124 formed by the line from the Earth's surface to satellite 101 and the line to the edge of the area on Earth observable by the sensors on satellite 101 is smaller than half the latitudinal interval 125 between adjacent projection positions of the satellites on the Earth's surface, then there is no unobserved area between the observation ranges of satellite 101 and satellite 102. In other words, if the latitudinal distance between adjacent projection positions is within the range of the latitudinal direction of the Earth's surface observed by the sensors of either of the two satellites, then it becomes possible to observe the area between adjacent projection positions without any unobserved areas in the latitudinal direction. The latitudinal spacing of 125 between adjacent projection positions of artificial satellites onto the Earth's surface is 17°, taking a 1° margin from the maximum value of 16° shown in Figure 5, and θ124 must be at least half of that, or 8.5°.

[0038] Figure 8 shows the field of view half-angle θs123 of the sensors mounted on satellite 101 when the altitude of satellite 101 is changed. For example, if the altitude is 500 kilometers and the sensor field of view half-angle is 59° or more, the latitudinal interval covered by the sensor field of view half-angle will be greater than the latitudinal interval between adjacent projection positions of the satellite onto the Earth's surface. This means that observations can be made in the latitudinal direction without any unobserved areas. The arrangement of the satellites along a figure-eight line allows them to orbit the Earth once in the longitude direction, making it possible to perform a sweep observation around the Earth with no unobserved areas within the latitude range.

[0039] The arrangement of the satellites along the figure-eight line shown in Embodiment 1 remains within the same size range 119 as the projection position of the satellites onto the Earth's surface at the initial time, not only at the initial time but also as time progresses. Only the position on the map has shifted in the longitude direction. The projected positions of all artificial satellites onto the Earth's surface move over time along a moving line 120 representing the projected positions of the satellites. Even though the position of each satellite changes, the shape of this moving line 120 remains unchanged. Therefore, the latitudinal interval between adjacent projection positions of artificial satellites on the Earth's surface is less than or equal to 122, which is the observation range of the Earth's surface observed by each satellite's sensor.

[0040] The range of longitude difference is determined by the orbital inclination of the artificial satellite, and a smaller range is generally considered advantageous. This is because even if the latitudinal direction can be observed without any unobserved areas, a large difference in the time the satellite passes over the target point latitude can be disadvantageous for observations of the target point and its vicinity. To minimize the difference in observation times between each satellite, it is necessary to minimize the difference in longitude between them, which is achieved by arranging the satellites on a figure-eight shape to keep the longitude difference range to a minimum.

[0041] As shown in Embodiment 1, with 16 satellites, they were arranged along a single figure-eight line. Embodiment 2 shows how this arrangement would look with other numbers of satellites.

[0042] [Embodiment 2] The details of the case where there are 48 artificial satellites are shown as Embodiment 2. The Earth's orbit of 360° is divided equally among 48 satellites, and 7.5° is set as the distance ΔΩ between adjacent ascending nodes. ΔΩ is the average value of the distance between adjacent ascending node right ascensions across all orbits, taking tolerances into account. The tolerance for ΔΩ is set so that the difference in the distance between adjacent ascending node right ascensions across all orbits is within 0.1° or less when setting the ascending node right ascension of each satellite. The initial position of the first satellite 101 (satellite number 1), which is used as the reference, projected onto the Earth's surface, is latitude λ10 = 36°N and longitude φ10 = 140°E, which are the same values ​​as in Embodiment 1. The interval of the latitude argument (Δν) is set to an integer multiple (N times) of the average value (ΔΩ) of the intervals between the right ascensions of all adjacent ascending nodes, where the value of N is 15, the same value as in Embodiment 1. Under these conditions, using the same method as in Embodiment 1, 48 units can be arranged on a figure-eight pattern at three locations on the map, with the three figure-eights being equally spaced on the equator. This means that the observation period for target points on Earth can be reduced to one-third of that for a single figure-eight.

[0043] Figure 9 shows the projected position of the satellite onto the Earth's surface at the initial time. Figure 10 shows the latitude and longitude (λn0, φn0) of the projected position of each satellite onto the Earth's surface. Figures 11, 12, and 13 are three divisions of Figure 10. Since the satellites can be arranged along a figure-eight pattern at three locations on the map, Figure 11 shows the arrangement along the figure-eight pattern including satellite number 1, Figure 12 shows the arrangement along the figure-eight pattern including satellite number 2, and Figure 13 shows the arrangement along the figure-eight pattern including satellite number 3. As a result, the positional range 119 of the projection position of the artificial satellite onto the Earth's surface at the initial time is as follows (tolerance 10%). Arrangement along a figure-eight shaped line including satellite number 1 (Figure 11) Latitude range -45° to 45° (center 0°, width 90°) (because the orbital inclination is 45°) Longitude 140°~159° (center 149.5°, width (longitude difference range) 19°) (same as Embodiment 1) Arrangement along a figure-eight shaped line including satellite number 2 (Figure 12) Latitude range -45° to 45° (center 0°, width 90°) (because the orbital inclination is 45°) Longitude 260°~279° (center 269.5°, width (longitude difference range) 19°) Arrangement along a figure-eight shaped line including satellite number 3 (Figure 13) Latitude range -45° to 45° (center 0°, width 90°) (because the orbital inclination is 45°) Longitude 20°~39° (center 29.5°, width (longitude difference range) 19°) The latitude range and longitude difference range for the arrangement of each satellite along the figure-eight lines are the same as in Embodiment 1, and the centers of longitude are spaced at 120° intervals.

[0044] In Embodiments 1 and 2, the number of satellites was 16 and 48, respectively. However, Figure 14 shows a case where the number of satellites ranges from 8 to 64, and the projection positions of the satellites onto the Earth's surface are arranged along a figure-eight shaped line. Figure 11 shows the satellite arrangement by the number of satellites (number of satellites in the figure eight × number of figures eight) only when eight or more satellites are included in the arrangement along a single figure eight-shaped line (N=15). If the number of satellites is a multiple of 16, 16 satellites will be arranged in a figure-eight shape, with the number of eights equal to the multiple. If the number of satellites is a multiple of 8 but not a multiple of 16, 8 satellites will be arranged in a figure-eight shape, with the number of eights equal to the multiple. If the number of satellites is a multiple of 4 but not a multiple of 8, 4 satellites will be arranged in a figure-eight shape, with the number of eights equal to the multiple.

[0045] For any given N, the satellites will not be positioned along a figure-eight shape; this can be achieved by selecting the correct N. In embodiments 1 and 2, N was 15, but Figure 15 shows the case where the absolute value of N is 15 or less, and the projected positions of the satellites on the Earth's surface are arranged on a figure-eight shape. Figure 15 shows the values ​​of N, the number of satellites included in one figure-eight, and the number of figure-eights when 16 and 48 satellites are arranged in a figure-eight shape. Here, when N is negative, Δν is set to a negative value to define νn0.

[0046] [Embodiment 3] Embodiment 3 shows one method for arranging the projection position of the artificial satellite onto the Earth's surface at an initial time, which differs from that of Embodiments 1 and 2. This method involves setting the latitude and longitude at a time determined as the reference for the projection position of each satellite onto the Earth's surface using the methods of Embodiments 1 and 2, changing the longitude to the desired value, and then recalculating and setting the right ascension of the ascending node without changing the latitude argument from the original latitude and the changed longitude. In Embodiment 3, first, the latitude and longitude at the time (initial time) defined as the reference for the projection position of each satellite onto the Earth's surface are set, using the same orbital conditions and arrangement method as in Embodiment 1. The results are shown in Figures 2 and 3. Next, the longitude of each satellite is changed to the target value of 140° East, and the right ascension of the ascending node (Ωn0) is recalculated from that latitude and longitude. Since the latitude does not change, the latitude argument (νn0) is the value from Embodiment 1. The latitude argument can also be calculated from only the latitude and orbital inclination using spherical trigonometry, so it will be the same value. The right ascension of the ascending node (Ωn0) is calculated using spherical trigonometry with the following formula 7 from the latitude and longitude (λn0, φn0) of the projection position onto the Earth's surface of the nth satellite (101-116) (where n is a natural number, 1-16; the assignment of satellite number n remains the same as in Embodiment 1). [Number 7] Ωn0=φn0-Acos(cos(νn0) / cos(λn0)) Or Ωno=φn0+Acos(cos(νn0) / cos(λn0))+π The latitude argument (νn0) and the right ascension of the ascending node (Ωn0) are set to either increase monotonically or decrease as n increases. By using the same arrangement method as in Embodiment 1, the maximum latitudinal distance between adjacent projection positions can be reduced in the same way as in Embodiment 1, increasing the likelihood of observation without any unobserved areas in the latitudinal direction. Whether observation is possible depends on the sensor's field of view, as in Embodiment 1.

[0047] Figure 16 shows the projection of the satellites onto the Earth's surface at the initial time, and Figure 17 shows the latitude and longitude (λn0, φn0) of the projection position of each satellite onto the Earth's surface.

[0048] As time passes, this orbit changes from a straight line to a figure-eight shape, and then back to a straight line. It becomes a straight line twice during one orbit around the Earth, and at this point, observation times at the same latitude occur simultaneously. The range of longitude difference is approximately 40°, which is larger than that of Embodiment 1.

[0049] In embodiments 1 to 3, a coordinate system is assumed with the Earth at its center, with the North Pole, equator, and vernal equinox as reference points. The right ascension of the ascending node, which is the angle between the direction of the vernal equinox and the ascending node (the point where the orbit intersects the equatorial plane from south to north), is determined along the equator. One method that is not constrained by this coordinate system is to define a pseudo-equator as a circle with the same radius as the equator, rotated around an axis representing the direction of advancement to a predetermined longitude on the equator. A pseudo-north pole is set perpendicular to the equatorial plane. By implementing embodiments 1 to 3 in this coordinate system, the figure-eight satellite arrangement will be located not on the equator, but in a direction and position inclined toward the equator.

[0050] In embodiments 1 to 3, by setting the orbits of each satellite to a recurring orbit or quasi-revolving orbit, observations can be made periodically at the same longitude as the initial time and with the same satellite configuration.

[0051] [Supplement to the embodiment] Each embodiment is an example of a preferred form and is not intended to limit the technical scope of the present invention. Each embodiment may be carried out in part or in combination with other embodiments. [Explanation of symbols]

[0052] 100 Satellite system, 101-116 Artificial satellite, 117 Earth, 118 World map, 119 Range of satellite projections onto the Earth's surface, 120 Moving line of satellite projections onto the Earth's surface, 121 Direction of satellite as time progresses on the map, 122 Observation range of the Earth's surface observed by satellite sensors, 123 Half-angle of field of view of sensor on satellite 101, 124 Angle between the line from the Earth's center to satellite 101 and the line to the edge of the area on Earth observable by the sensor on satellite 101, 125 Latitude interval between adjacent satellite projections onto the Earth's surface.

Claims

1. A satellite system comprising multiple artificial satellites, wherein, at a time set as a reference, the projected position of each of the multiple artificial satellites, which is the point where a line drawn from each artificial satellite toward the Earth's center intersects the Earth's surface, falls within a predetermined range of one or more latitudes and longitudes set on a map, and as time progresses, the predetermined range moves in the longitude direction, and regardless of the passage of time, the projected position of each artificial satellite toward the Earth's surface remains within the predetermined range.

2. The satellite system according to claim 1 is characterized in that the predetermined range is defined as the latitude range, where the maximum absolute value of the orbital inclination angle of the constituent satellites at a predetermined reference time is the range between north and south latitudes; the longitude difference range is defined as the maximum difference between the projected positions of any two satellites on the Earth's surface in the longitudes that each satellite can take from the predetermined reference time until the time when all satellites have completed one orbit around the Earth; and the projected positions of all satellites on the Earth's surface are positioned within the range enclosed by the latitude range in the latitudinal direction and the longitude difference range in the longitude direction.

3. The satellite system according to claim 2, characterized in that the projection positions of each artificial satellite onto the Earth's surface within the predetermined range are arranged on a figure-eight shaped line that has one intersection near the equator and forms a pair of roughly circular lines running north-south.

4. In the satellite system described in claim 3, the arrangement of the projected positions of each artificial satellite on the Earth's surface within a predetermined range is such that the arrangement is on a figure-eight shaped line with one intersection near the equator and a pair of roughly circular lines running north-south, and the range of longitude difference is based on the maximum value of the absolute value of the orbital inclination angle of all artificial satellites. The absolute value of the orbital inclination angle is between 0° and 10°, and the longitude difference range is 2° or less. The absolute value of the orbital inclination angle is 20° and the longitude difference range is 5° or less, and the value between the absolute value of the orbital inclination angle and 10° is less than or equal to the value obtained by interpolating the longitude difference range as a linear function of the orbital inclination angle. The absolute value of the orbital inclination angle is 30° and the longitude difference range is 9° or less, and between the orbital inclination angle and 20°, the value is less than or equal to the value obtained by interpolating the longitude difference range as a linear function of the absolute value of the orbital inclination angle. The absolute value of the orbital inclination angle is 40°, the longitude difference range is 17° or less, and between the orbital inclination angle and 30°, the value is less than or equal to the value obtained by interpolating the longitude difference range as a linear function of the absolute value of the orbital inclination angle. The absolute value of the orbital inclination angle is 50° and the longitude difference range is 28° or less, and between the orbital inclination angle and 40°, the value is less than or equal to the value obtained by interpolating the longitude difference range as a linear function of the absolute value of the orbital inclination angle. The absolute value of the orbital inclination angle is 60°, the longitude difference range is 41° or less, and the value between the orbital inclination angle and 50° is less than or equal to the value obtained by interpolating the longitude difference range as a linear function of the absolute value of the orbital inclination angle. The absolute value of the orbital inclination angle is 70°, the longitude difference range is 62° or less, and the value between the orbital inclination angle and 60° is less than or equal to the value obtained by interpolating the longitude difference range as a linear function of the absolute value of the orbital inclination angle. The absolute value of the orbital inclination angle is 80°, the longitude difference range is 100° or less, and the value between the orbital inclination angle and 70° is less than or equal to the value obtained by interpolating the longitude difference range as a linear function of the absolute value of the orbital inclination angle. The absolute value of the orbital inclination angle is 90°, the longitude difference range is 180° or less, and the value between the orbital inclination angle and 80° is less than or equal to the value obtained by interpolating the longitude difference range as a linear function of the absolute value of the orbital inclination angle. A satellite system characterized by arranging artificial satellites in such a manner.

5. In the satellite system according to either claim 3 or claim 4, at a time designated as a reference, If the angles between the direction vectors perpendicular to the orbital planes of multiple satellites are 1° or less, the multiple satellites are considered to be in the same orbit. In non-identical orbits, the right ascension of each satellite's ascending node is set to be equal such that the difference in the spacing between all adjacent ascending node right ascensions between any two satellites' ascending nodes, where there are no other ascending nodes between them, is within a range of 0.1° or less. The interval of the latitude argument is set to an integer multiple of the average value of the intervals between the right ascensions of all adjacent ascending nodes. Select one satellite from all artificial satellites to serve as a reference satellite, and starting from the orbit of that reference satellite, set the latitude argument of the next orbit by adding or subtracting an interval of the latitude argument, while maintaining a constant positive or negative sign, to the latitude argument of the original orbit, repeating this process until all orbits have been set. The difference in the latitude argument intervals of all artificial satellite orbits should be 0.5° or less. A satellite system characterized in that the spacing of the latitude arguments and the right ascension of the ascending node of each artificial satellite is selected such that the arrangement of the projected positions of each artificial satellite on the Earth's surface within the predetermined range is on a figure-eight shaped line with one intersection point near the equator and a pair of roughly circular lines running north-south.

6. The satellite system according to claim 5, characterized in that the difference between the maximum and minimum orbital periods of all artificial satellites is 0.1% or less of the average value of the orbital periods of all artificial satellites, the number of satellites is a multiple of 4, orbits with different ascending node right ascensions are set for the number of satellites, and the orbits of all artificial satellites have an orbital inclination difference of 0.1° or less and an eccentricity of 0.0002 or less.

7. In the satellite system described in claim 2, if, at a time set as a reference, the difference between the maximum and minimum values ​​of the orbital periods of all artificial satellites is 0.1% or less of the average value of the orbital periods of all artificial satellites, and the angles between the direction vectors perpendicular to the orbital planes of multiple artificial satellites are 1° or less, then the multiple artificial satellites are considered to be in the same orbit. In non-identical orbits, the right ascension of each artificial satellite's ascending node is set to be equal in size such that the difference in the interval between all adjacent right ascensions of ascending nodes of any two artificial satellites whose orbits do not have other ascending nodes is within the range of 0.1° or less. In non-identical orbits, all adjacent latitude arguments between any two artificial satellites whose orbits do not have other latitude arguments A satellite system characterized by setting the interval between the right ascensions of all adjacent ascending nodes as an integer multiple of the average value of the intervals between all adjacent ascending node right ascensions, setting the difference in the intervals between the latitude arguments of the orbits of all artificial satellites to 0.5° or less, selecting the intervals between the latitude arguments and the right ascension of each artificial satellite so that the arrangement of the projected positions of each artificial satellite on the Earth's surface within the predetermined range is on a figure-eight shaped line with one intersection near the equator and a pair of roughly circular lines running north-south, setting the latitude and longitude at a time determined as the reference for the projected position of each artificial satellite on the Earth's surface, changing the longitude to a predetermined target value, and recalculating and setting the right ascension of the ascending node without changing the latitude argument from the original latitude and the changed longitude.

8. A satellite system according to any one of claims 1 to 7, characterized in that, among the projection positions of all satellites onto the Earth's surface, the latitudinal range between any two projection positions of satellites onto the Earth's surface, where there are no other satellite projection positions between them in the latitudinal direction, is within the range observed by the sensor of either of the two satellites in the latitudinal direction of the Earth's surface.

9. A satellite system according to any one of claims 1 to 8, characterized in that the orbital elements of each artificial satellite are set in a coordinate system defined in a direction perpendicular to the plane containing a circle with the same radius as the equator, which is rotated around an axis in the direction of moving from the Earth's center to a predetermined longitude on the equator.

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