A method for calculating optimal orbit inclination to achieve a specified latitude high revisit rate

Abstract

The present application belongs to the technical field of satellite remote sensing, and particularly relates to a kind of orbit inclination design method.The technical scheme is a kind of optimal orbit inclination calculation method for realizing high revisit rate of specified latitude range, and the features are as follows: when the satellite is at the intersection point of ascending orbit and descending orbit, the edge of scanning strip close to the earth's poles coincides with the highest coverage latitude of the remote sensing area; and the edge of scanning strip close to the earth's equator coincides with the most coverage times latitude of the remote sensing area, at this time the orbit inclination is optimal, and the calculation formula of optimal orbit inclination i is: ∠AOa is the most coverage times latitude, which is a known value; and φ is the corresponding earth center angle of satellite scanning strip width.The present application studies the law that the orbit inclination has optimal solution with the orbit inclination of the most coverage times latitude ∠AOa, provides a kind of optimal orbit inclination calculation method for realizing high revisit rate of specified latitude, so that the optimal orbit inclination is obtained by calculation, and the satellite satisfies the most single-day coverage times at the most coverage times latitude.

Description

Technical Field

[0001] This invention belongs to the field of satellite remote sensing orbit design technology, specifically relating to an orbit inclination design method. Background Technology

[0002] Since the orbital inclination *i* determines the latitude at which each satellite achieves the most repeated coverage per day, maximizing the number of overpass coverages at a given latitude can be achieved by selecting a specific orbital inclination *i*. Furthermore, the orbital inclination, along with the instantaneous coverage spherical cap arc length, determines the highest coverage latitude. Currently, satellite orbital inclination is primarily determined through simulation, which suffers from numerous simulations, high time consumption, and the resulting orbital inclination may not be the optimal solution. Determining the optimal orbital inclination to maximize the daily coverage of a given latitude is a key technical problem that needs to be solved in satellite orbit design. Summary of the Invention

[0003] The purpose of this invention is to address the shortcomings of the prior art by providing an optimal orbital inclination calculation method for achieving a high revisit rate at a specified latitude. This method calculates the optimal orbital inclination to ensure that the satellite achieves the maximum number of daily coverages at the latitude requiring the most coverages.

[0004] This invention employs the following technical solution: an optimal orbital inclination calculation method for achieving a high revisit rate at a specified latitude. Its characteristic is that when the satellite is at the intersection of its ascending and descending orbits, the edge of the scanning strip closest to the Earth's pole coincides with the latitude of the highest coverage area in the remote sensing region; and the edge of the scanning strip closest to the Earth's equator coincides with the latitude of the region with the most coverage times. At this point, the orbital inclination satisfies the requirement of having the most daily coverage times at the latitude with the most required coverage times, thus achieving the optimal orbital inclination. This solution enables the satellite to have the most daily coverage times at the latitude with the most required coverage times, thereby achieving a high revisit rate at the specified latitude.

[0005] In other words, in the Northern Hemisphere, at the intersection of the satellite's ascending and descending orbits, the southern edge of the scan strip coincides with the latitude ∠AOa with the highest coverage frequency, and the northern edge coincides with the latitude ∠AOB with the highest coverage frequency; in the Southern Hemisphere, at the intersection of the satellite's ascending and descending orbits, the northern edge of the scan strip coincides with the latitude ∠AOa with the highest coverage frequency, and the southern edge coincides with the latitude ∠AOB with the highest coverage frequency.

[0006] It should be noted that the highest latitude value in the latitude range corresponding to the remote sensing area is the highest coverage latitude, and the latitude that needs to be revisited the most times in the latitude range is the latitude with the most coverage times. These are known values ​​determined by the needs of remote sensing applications.

[0007] Furthermore, the optimal orbital inclination angle i is: "the latitude ∠AOa with the most coverage times" + "half of the geocentric angle φ corresponding to the width of the satellite scan strip", that is:

[0008]

[0009] ∠AOa is a known value determined by the characteristics of the satellite sensor and the satellite's orbital altitude; φ is the geocentric angle φ corresponding to the width of the satellite scan strip, which is also known. As a special case, φ is also equal to the difference between the latitude with the highest coverage, ∠AOB, and the latitude with the most coverage times, ∠AOa, where ∠AOa is a known value.

[0010] Furthermore, a method for calculating the optimal orbital inclination to achieve a high revisit rate at a specified latitude is characterized by calculating the optimal orbital inclination i such that the satellite has the most daily coverages at the latitude with the most coverages; when considering the Earth's curvature, the first approximate formula for calculating the optimal orbital inclination i is:

[0011]

[0012] ∠AOa is the latitude with the most coverage, a known value determined by application requirements; D is the arc length of the spherical cap covering the instantaneous ground, a known value determined by satellite sensor characteristics and satellite orbital altitude; R is the Earth's radius, a known value.

[0013] When the Earth's surface is simplified to a plane, the second approximate formula for calculating the optimal orbital inclination angle i is:

[0014]

[0015] In the formula: ∠AOa is the latitude with the most coverage times, which is a known value; D is the arc length of the spherical cap covering the ground instantaneously by the satellite; and R is the Earth's radius.

[0016] Alternatively, the second approximate formula for calculating the optimal orbital inclination angle i is:

[0017]

[0018] In the formula: ∠AOB is the highest coverage latitude, a known value determined by the needs of remote sensing applications; D is the arc length of the spherical cap covering the ground instantaneously by the satellite, a known value determined by the characteristics of the satellite sensor and the satellite orbital altitude; R is the Earth's radius, a known value.

[0019] Although this formula is expressed using electronic remote sensing satellites as an example, it is also applicable to optical / infrared remote sensing imaging satellites and SAR two-sided imaging satellites with attitude-adjustable pushbroom imaging lenses. In this case, D is the maximum swath width that optical / infrared / SAR two-sided imaging satellites can achieve. This situation applies in the following discussion.

[0020] Furthermore, the highest coverage latitude ∠AOB is the highest latitude of the circumscribed rectangle determined by the remote sensing area, and is a known value; the latitude with the most coverage times ∠AOa refers to the latitude in the remote sensing area that requires the most coverage times, and is a known value.

[0021] Furthermore, the circumscribed rectangle is the circumscribed rectangle of the remote sensing area on the Mercator projection world map.

[0022] The technical effects of this invention are as follows: This invention proposes an optimal orbital inclination i with a specific pattern: Optimal inclination i = "latitude with the most coverage times ∠AOa" + "half of the geocentric angle φ corresponding to the width of the satellite scan strip"; In the Northern Hemisphere (or Southern Hemisphere), at the intersection of the satellite's ascending and descending orbits, the southern (or northern) edge of the scan strip coincides with the latitude with the most coverage times ∠AOa, and the northern (or southern) edge coincides with the latitude with the highest coverage times ∠AOB; This invention provides a method for calculating the optimal orbital inclination to achieve a high revisit rate at a specified latitude, ensuring that the satellite achieves the most daily coverage times at the latitude requiring the most coverage times. Attached Figure Description

[0023] Figure 1 A schematic diagram of the circumscribed rectangle of the remote sensing area and the UV line of the maximum coverage;

[0024] Figure 2 A schematic diagram of the projection of the circumscribed rectangle of the remote sensing area onto a three-dimensional Earth.

[0025] Figure 3 A schematic diagram illustrating the definition of the required remote sensing range in the northern latitude, the highest coverage latitude, the latitude with the most coverage times, and their relationship with orbital inclination.

[0026] Figure 4 A schematic diagram representing the stripe of Earth's surface covered by a satellite using a three-dimensional Earth surface;

[0027] Figure 5 This is a simulation diagram illustrating the number of times a typical low-orbit, low-inclination satellite covers different latitudes in 24 hours. Detailed Implementation

[0028] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the embodiments provided below are only for the purpose of fully and completely disclosing the present invention and fully conveying the technical concept of the present invention to those skilled in the art. The present invention can also be implemented in many different forms and is not limited to the embodiments described herein.

[0029] Example 1:

[0030] This embodiment provides a method for calculating the optimal orbital inclination angle to achieve a high revisit rate at a specified latitude. Its key feature is the calculation of the optimal orbital inclination angle *i*, which maximizes the number of daily coverages for the satellite at the latitude with the "maximum coverage count" in the remote sensing area (the latitude with the "maximum coverage count" is the latitude that requires the most coverages in the remote sensing area, and is a known value during satellite orbit design). The specific solution steps are as follows:

[0031] STEP 1: Determine the bounding rectangle of the remote sensing area and the latitude of the "maximum coverage times".

[0032] Before designing a remote sensing satellite constellation, the area to be remotely sensed is first drawn on a two-dimensional map using Mercator projection, thus obtaining the bounding rectangle of that area. This bounding rectangle is defined by the upper left L... U R in the upper right corner U , lower left L L and the bottom right R L The latitude and longitude values ​​of the four corners are determined, and the circumscribed rectangle is as follows: Figure 1 The rectangle L in U R U L L R L As shown.

[0033] exist Figure 1 Draw a horizontal line pq (pq corresponds to the circumference of the spherical cap at the corresponding latitude on the Earth's sphere), such that pq passes through the latitude of the "maximum coverage," and intersects the two sides (the two sides perpendicular to the latitude) of the circumscribed rectangle at points u and v. The line segment uv is called the latitude of the "maximum coverage" of the remote sensing area (uv is a segment of the circumference of the spherical cap at the latitude of the "maximum coverage" on the Earth's sphere). If... Figure 1 When drawn on a three-dimensional Earth, its meaning is as follows: Figure 2 As shown. Figure 3 This diagram illustrates the definition of the required remote sensing range in the northern latitude, the highest coverage latitude ∠AOB, the latitude ∠AOa with the most coverage times, and their relationship with the orbital inclination i.

[0034] STEP2: Solve for the optimal orbital inclination angle i

[0035] Research approach: Since the orbital inclination i determines the specified latitude that is covered most frequently by each satellite every day, the maximum number of times a specified latitude can be covered by crossing over can be achieved by selecting a specific orbital inclination i; at the same time, the orbital inclination i, together with the instantaneous coverage spherical cap arc length D, determines the highest coverage latitude.

[0036] Assuming a circular orbit and simplifying the Earth to a sphere, and neglecting Earth's rotation, regardless of the orbital inclination *i*, the surface area of ​​the Earth covered by the scanned satellite is the same within the same satellite orbital period. As the satellite moves around its orbit, a satellite with an orbital inclination *i* and an instantaneous coverage arc length *D* sweeps across a strip of Earth's surface, as shown below. Figure 4 As shown, the satellite's coverage strip across the Earth's surface is represented by a three-dimensional Earth surface. In the figure, D is the arc length of the spherical cap of the instantaneous satellite remote sensing coverage of the ground. The closed area formed by aebcfd represents the satellite's coverage strip across the Earth's surface. AA is the equator; O is the Earth's center; B is the highest coverage latitude; ∠AOB is the highest coverage latitude angle; uv is called the latitude of the remote sensing area with the "most coverage times"; the four corners of the circumscribed rectangle are L... U R U L L R L i is the orbital inclination angle = AOe; the geocentric angle corresponding to the maximum coverage zone is φ = ∠aOb, φ = the latitude of the highest coverage zone ∠AOB - the latitude of the maximum number of coverages ∠AOa.

[0037] The proof for why ∠AOa is exactly equal to the dimension with the maximum number of coverages is as follows:

[0038] Conclusion 1: The latitude of the maximum number of coverages, ∠AOa, is exactly equal to the latitude of the uv line.

[0039] The proof is as follows:

[0040] First, because when the instantaneous arc length of the satellite's nadir is covered by the spherical cap is D, and the orbit is circular, if we simplify the Earth to a sphere and disregard its rotation, regardless of the orbital inclination i, the surface area of ​​the Earth covered by the scanned satellite within the same orbital period is the same. Since the circumference of the Earth's equator (0° latitude) is greater than the circumference of any other latitude (the Earth's spherical cap), and the higher the latitude, the shorter the circumference of the Earth's spherical cap, when considering the Earth's rotation around its north-south axis from west to east, the arc length traversed by the equator per unit time is always greater than the arc length traversed by non-equatorial regions, and the higher the latitude, the shorter the arc length traversed. Furthermore, under normal circumstances, the direction of the satellite's orbital plane normal is essentially constant (the precession is very small). Therefore, after a low-Earth orbit satellite completes one rotation (approximately 90-110 minutes) in its orbit, its nadir trajectory shifts a certain distance from east to west (called the westward retreat distance, a technical term). When the width of the strip formed by the instantaneous coverage circular scan is limited, the current scan strip does not overlap with the previous scan strip, but rather merges with it by a certain distance ΔL. The higher the latitude, the smaller ΔL becomes. When the latitude reaches a certain level, ΔL = 0. When the latitude is even higher, ΔL becomes negative. That is to say, when ΔL is negative, the current scan strip overlaps with the previous scan strip. In other words, the higher the latitude, the more times it is covered. Therefore, the maximum number of coverages is not at the equator, but rather, as the latitude increases from 0 degrees to 90 degrees, it gets closer and closer to the latitude with the maximum number of coverages.

[0041] Second, a satellite crosses the same latitude line twice during its orbit: once during an ascending orbit (for low-inclination satellites, flying from southwest to northeast) and once during a descending orbit (flying from northwest to southeast). However, at high latitudes, the satellite's instantaneous coverage circle only crosses the line once, or even just barely at the highest coverage latitude. Therefore, in the Northern Hemisphere (or Southern Hemisphere), the coverage circle only crosses the line once at latitudes lower than the southern edge of the coverage strip. Figure 4 Point a) (or north edge, Figure 4 Only at point c) will the conditions for two crossings be met. Therefore, the maximum number of coverages should be close to but less than the southern edge a (or northern edge c) of the coverage strip.

[0042] Conclusion: The maximum coverage count is located at Figure 4 On the UV latitude line. Q.E.D.

[0043] As a verification of this proof, Figure 5 This paper presents STK simulations of a single satellite passing over different latitudes within 24 hours in a typical low-Earth orbit with a low inclination (35° inclination as an example). Figure 5 It can be seen that along the southern edge of the coverage strip ( Figure 5 A line near mid-north latitude N20 is the dividing line for the maximum number of coverages, and this conclusion is correct for different orbital inclinations.

[0044] The relationship between the orbital inclination angle i and the highest coverage latitude and the instantaneous coverage spherical crown arc length D is derived below.

[0045] Let the instantaneous arc length of the covered spherical cap be D, then from Figure 4 It can be seen that the relationship between the geocentric angle ∠aOb (abbreviated as φ) corresponding to the cover zone and the arc length D of the spherical cap is as follows:

[0046]

[0047] or

[0048] Where R is the Earth's radius.

[0049] The formula for calculating the geocentric angle φ corresponding to the satellite's instantaneous maximum coverage is:

[0050] φ = Latitude with the highest coverage (∠AOB) - Latitude with the most coverage times (∠AOa)

[0051] Given φ, the instantaneous arc length D of the spherical crown covering the ground can be calculated, as shown below:

[0052]

[0053] The above calculation is the minimum required value of the instantaneous ground coverage spherical crown arc length D. However, in the actual satellite development process, the instantaneous ground coverage spherical crown arc length may be greater than this value, and the effect will be better than the theoretical calculation value.

[0054] Conclusion 2: Let the instantaneous coverage arc length be D (km). If the highest coverage latitude ∠AOB (°) and the geocentric angle corresponding to the coverage zone is ∠aOb (°), then the method for calculating the orbital inclination angle i (°) is as follows: or

[0055] Proof: From Figure 4 It can be seen that the formula for calculating ∠AOa is:

[0056]

[0057] so:

[0058]

[0059] Similarly, it can be proven that:

[0060]

[0061] Q.E.D.

Claims

1. A method for calculating the optimal orbital inclination angle to achieve a high revisit rate at a specified latitude, characterized by: When the satellite is at the intersection of its ascending and descending orbits, the edge of the scan strip closest to the Earth's pole coincides with the latitude of the highest coverage area in the remote sensing region; and the edge of the scan strip closest to the Earth's equator coincides with the latitude of the region with the most coverage times. At this point, the orbital inclination satisfies the condition that the latitude with the most coverage times has the most daily coverage times, and the orbital inclination is optimal. The first approximate formula for calculating the optimal orbital inclination angle i is: Wherein, ∠AOa is the latitude with the most coverage times, a known value determined by application requirements; D is the arc length of the spherical cap covering the instantaneous ground, a known value determined by satellite sensor characteristics and satellite orbital altitude; R is the Earth's radius, a known value. Alternatively, the second approximate formula for calculating the optimal orbital inclination angle i is: In the formula: ∠AOa is the latitude of the maximum number of coverages, which is a known value; D is the arc length of the spherical cap of the ground instantaneously covered by the satellite; and R is the Earth's radius. Alternatively, the second approximate formula for calculating the optimal orbital inclination angle i is: In the formula: ∠AOB is the highest coverage latitude, which is a known value; D is the arc length of the spherical cap covering the ground instantaneously by the satellite; and R is the Earth's radius.

2. The method for calculating the optimal orbital inclination angle to achieve a high revisit rate at a specified latitude as described in claim 1, characterized in that: The highest coverage latitude ∠AOB is the highest latitude of the circumscribed rectangle determined by the remote sensing area; the latitude ∠A0a with the most coverage times refers to the latitude in the remote sensing area that needs to be covered the most times, which is a known value determined by application requirements.

3. The method for calculating the optimal orbital inclination angle to achieve a high revisit rate at a specified latitude as described in claim 2, characterized in that: The circumscribed rectangle refers to the circumscribed rectangle of the remote sensing area on a Mercator projection world map.

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