CN111177948A - Typical Walker constellation mathematical model described by using orbit elements - Google Patents
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Abstract
The invention relates to the technical field of internet constellation design of space satellites, in particular to a typical Walker constellation mathematical model described by using orbital elements, which comprises (a)j,k，ej,k，ij,k，Ωj,k，ωj,k，fj,k) Six track elements; the Walker constellation types comprise a star constellation, a delta constellation, a rose constellation and a sigma constellation; in the six elements of the track, aj,k，ej,k，ij,k，Ωj,k，ωj,kConstellation configuration, f, which together describe the Walker constellationj,kDescribing the constellation operation state of the Walker constellation. When the satellite internet constellation is simulated, the simulation environment which takes the six orbital elements as input can be set up, the performance of the constellation system is further analyzed, and the realization of general design is facilitated.
Description
Technical Field
The invention belongs to the technical field of aerospace satellite internet constellation design, and particularly relates to a typical Walker constellation mathematical model described by using orbital elements.
Background
The constellation generally comprises one or more types of orbit satellites, the Walker constellation is the constellation which is most effective in global and latitudinal coverage, and comprises a star constellation, a delta constellation, a rose constellation, a sigma constellation and the like, wherein the delta constellation is widely used, and the sigma constellation and the rose constellation are special cases of the delta constellation. At present, the parameter description models of the typical Walker constellations have research bases, and can provide references for constellation design, constellation simulation analysis and optimization design analysis.
The star constellation with the orbit height of h, P orbit planes have a common intersection point on an orbit plane, the right ascension of the intersection point is omega, S satellites are arranged on each orbit, the total number N of the satellites is PS, the phase factor is F, and the parameter description model is N/P/F: omega, h.
The method comprises the following steps of obtaining a delta constellation with an orbit height of h, wherein the orbit inclination angles of P orbit surfaces are i, each orbit is provided with S satellites, the total number N of the satellites is PS, a phase factor is F, and a parameter description model is N/P/F: i, h.
The total number of the satellites is N, the orbital plane P is N, the orbital inclination angle is i, the phase factor is m, and the parameter description model is N/m: i, h.
The sigma constellation with the orbit height h is a quasi-regression orbit which runs for (M +1) circles in M days, the orbit inclination angles of P orbit surfaces are i, each orbit is provided with S satellites, the total number N of the satellites is PS, and the parameter description model is N/M: i, h.
In the above-mentioned parameter description model, different types of constellation configurations correspond to different structural parameters or feature codes, and the parameter description model has the following disadvantages:
(1) when the constellation is simulated, the constellation performance of different configurations needs to be analyzed, and when a simulation environment is established, corresponding interfaces need to be developed aiming at different constellation configurations, which is not beneficial to general design;
(2) the constellation operation state needs to be analyzed in real time during constellation simulation, and the parameter description model can only describe the constellation configuration state and cannot represent the constellation operation state;
(3) the constellation parametric model only includes partial orbit elements, even no orbit elements, and it is difficult for a designer unfamiliar with the parametric model to quickly know the orbit characteristics of the configuration.
Disclosure of Invention
The invention aims to solve the technical problem of providing a typical Walker constellation mathematical model which is described by using orbital elements, overcoming the defects of a Walker constellation parameter model at the present stage, and the mathematical model provided by the invention can describe a plurality of typical Walker constellations by using consistent elements, thereby facilitating the orbital analysis, providing uniform orbital design input for satellite internet constellation simulation, forming a uniform simulation interface, avoiding redundancy of a simulation program, facilitating inheritance and use and providing uniform design input.
In order to solve the technical problems, the invention adopts the following technical scheme:
a rail using deviceA typical Walker constellation mathematical model described by elements includes (a)j,k，ej,k，ij,k，Ωj,k，ωj,k，fj,k) Six orbital elements, wherein aj,kRepresenting the semi-major axis, e, of the satellite orbit at each node in the constellationj,kRepresenting the satellite orbit eccentricity i of each node in the constellationj,kRepresents the orbital inclination angle of each node satellite in the constellation, omegaj,kRepresenting the right ascension, omega, of each node satellite in the constellationj,kRepresenting the argument of each node satellite in the constellation, fj,kRepresenting the real near point angle of each node satellite in the constellation to describe the real-time running state of each node satellite in the constellation; the Walker constellation types comprise a star constellation, a delta constellation, a rose constellation and a sigma constellation; in the six elements of the track, aj,k，ej,k，ij,k，Ωj,k，ωj,kConstellation configuration, f, which together describe the Walker constellationj,kDescribing the constellation operation state of the Walker constellation.
As an optimization, with ReRepresenting the mean radius of the earth, i1Is the track inclination of the reference track, u1The index j represents the jth orbital plane (j is 1, 2. cndot. cndot., P), the index k represents the number k of the satellites on the jth orbital plane (k is 1, 2. cndot., S), P is the number of orbital planes, S is the number of the satellites, h is the orbital height, omega is the elevation declination, F is the phase factor, and the operation time is t0The single-layer circular orbit star constellation of (a) can be described as:
aj,k＝Re+h
ej,k＝0
Ωj,k＝Ω
ωj,k＝0
asOptimized in omega1For the right ascension of the elevation point of the reference satellite in the reference orbit, the single-layer circular orbit δ constellation can be described as:
aj,k＝Re+h
ej,k＝0
ij,k＝i
ωj,k＝0
wherein P is the number of track surfaces, i is the track inclination angle, t0For the running time of a single-layer circular orbit delta constellation, u1The index j indicates the amplitude of the intersection point of the reference satellite in the reference orbit, the index k indicates the number k of the satellites (k 1, 2. cndot., S) in the jth orbital plane, P is the number of orbital planes, S is the number of satellites, h is the orbital height, F is the phase factor, R is the phase factor, and j is 1, 2. cndot., P is the jth orbital planeeRepresenting the mean radius of the earth.
As an optimization, the rose constellation k is 1, and a single-layer circular orbit rose constellation can be described as:
aj,k＝Re+h
ej,k＝0
ij,k＝i
ωj,k＝0
where m denotes a phase factor, P is the number of track surfaces, i is the track inclination, t0For the running time of a single-layer circular orbital rose constellation, u1As a reference on a reference trackThe argument of the intersection point of the satellite, the subscript j representing the jth orbital plane (j ═ 1,2 ·, P), the subscript k representing the satellite with the number k on the jth orbital plane, P the number of orbital planes, h the orbital height, ReRepresenting the mean radius of the earth. And k is 1, which means that each orbital plane of the single-layer circular orbital rose constellation only has one satellite.
As an optimization, the single-layer circular orbit σ constellation can be described as:
aj,k＝Re+h
ej,k＝0
ij,k＝i
ωj,k＝0
wherein M is the number of days of a single-layer circular orbit sigma constellation quasi-regression orbit, M +1 circles are operated in M days, P is the number of orbital planes, i is an orbital inclination angle, t is0For the running time of a single-layer circular-orbit sigma constellation1The index j indicates the amplitude of the intersection point of the reference satellite in the reference orbit, the index k indicates the number k of the satellites (k 1, 2. cndot., S) in the jth orbital plane, P is the number of orbital planes, S is the number of satellites, h is the orbital altitude, R is the orbital altitude, and j is the jth orbital plane (j 1, 2. cndot., P), k is the number of orbital planeseRepresenting the mean radius of the earth.
As an optimization, n is the satellite average operating angular rate:
wherein mu is a gravitational constant, and mu is 398600.44km3/s2。
The invention has the beneficial effects that:
compared with the prior art, the typical Walker constellation mathematical model method described by utilizing the orbit elements has the following technical effects by adopting the technical scheme:
(1) the invention describes constellations with different configurations by using the six orbital elements, and can build a simulation environment which takes the six orbital elements as input when the satellite internet constellation is simulated, thereby analyzing the performance of a constellation system and being beneficial to realizing general design;
(2) the method not only considers the mathematical description of the constellation configuration, but also introduces the time parameter, builds the constellation dynamic operation mathematical model, and is beneficial to analyzing the constellation operation state in the real-time satellite internet constellation simulation;
(3) the invention describes a typical Walker constellation by using the orbit elements, thereby facilitating the orbit designer to quickly know the orbit characteristics of the corresponding Walker constellation.
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Detailed Description
A typical Walker constellation mathematical model described by orbital elements comprises (a)j,k，ej,k，ij,k，Ωj,k，ωj,k，fj,k) Six orbital elements, wherein aj,kRepresenting the semi-major axis, e, of the satellite orbit at each node in the constellationj,kRepresenting the satellite orbit eccentricity i of each node in the constellationj,kRepresents the orbital inclination angle of each node satellite in the constellation, omegaj,kRepresenting the right ascension, omega, of each node satellite in the constellationj,kRepresenting the argument of each node satellite in the constellation, fj,kRepresenting the real near point angle of each node satellite in the constellation to describe the real-time running state of each node satellite in the constellation; the Walker constellation types comprise a star constellation, a delta constellation, a rose constellation and a sigma constellation; in the six elements of the track, aj,k，ej,k，ij,k，Ωj,k，ωj,kConstellation configuration, f, which together describe the Walker constellationj,kDescribing the constellation operation state of the Walker constellation.
In this example, R iseRepresenting the mean radius of the earth, i1Is the track inclination of the reference track, u1The index j indicates the jth orbital plane (j ═ 1,2 ·, P), and the index k indicates the jth orbital plane, for the amplitude of the lift-off point of the reference satellite in the reference orbitThe upper serial number k of the satellite (k is 1, 2. cndot., S), P is the number of orbital planes, S is the number of satellites, h is the orbital height, Ω is the right ascension of the intersection, F is the phase factor, and the operation time is t0The single-layer circular orbit star constellation of (a) can be described as:
aj,k＝Re+h
ej,k＝0
Ωj,k＝Ω
ωj,k＝0
in this example, the reference Ω1For the right ascension of the elevation point of the reference satellite in the reference orbit, the single-layer circular orbit δ constellation can be described as:
aj,k＝Re+h
ej,k＝0
ij,k＝i
ωj,k＝0
wherein P is the number of track surfaces, i is the track inclination angle, t0For the running time of a single-layer circular orbit delta constellation, u1The index j indicates the amplitude of the intersection point of the reference satellite in the reference orbit, the index k indicates the number k of the satellites (k 1, 2. cndot., S) in the jth orbital plane, P is the number of orbital planes, S is the number of satellites, h is the orbital height, F is the phase factor, R is the phase factor, and j is 1, 2. cndot., P is the jth orbital planeeRepresenting the mean radius of the earth.
In this embodiment, the rose constellation k is 1, and the single-layer circular orbit rose constellation may be described as:
aj,k＝Re+h
ej,k＝0
ij,k＝i
ωj,k＝0
where m denotes a phase factor, P is the number of track surfaces, i is the track inclination, t0For the running time of a single-layer circular orbital rose constellation, u1The index j indicates the amplitude of the intersection point of the reference satellite in the reference orbit, the index k indicates the number k of the satellites in the jth orbital plane (j is 1, 2. cndot., P), P is the number of orbital planes, h is the orbital height, R is the orbital height, and j indicates the jth orbital planeeRepresenting the mean radius of the earth. And k is 1, which means that each orbital plane of the single-layer circular orbital rose constellation only has one satellite.
In this embodiment, the single-layer circular orbit σ constellation may be described as:
aj,k＝Re+h
ej,k＝0
ij,k＝i
ωj,k＝0
wherein M is the number of days of a single-layer circular orbit sigma constellation quasi-regression orbit, M +1 circles are operated in M days, P is the number of orbital planes, i is an orbital inclination angle, t is0For the running time of a single-layer circular-orbit sigma constellation1Is taken as a referenceThe amplitude of the intersection point of a reference satellite on the orbit, the subscript j denotes the jth orbital plane (j ═ 1,2 ·, P), the subscript k denotes the satellite with the sequence number k on the jth orbital plane (k ═ 1,2 ·, S), P denotes the number of orbital planes, S denotes the number of satellites, h denotes the orbital altitude, R denotes the orbital altitudeeRepresenting the mean radius of the earth.
In this embodiment, n is the satellite average operating angular rate:
wherein mu is a gravitational constant, and mu is 398600.44km3/s2。
While the embodiments of the present invention have been described in detail, the present invention is not limited to the above embodiments, and various modifications can be made without departing from the spirit of the present invention within the knowledge of those skilled in the art.
Finally, it should be noted that: various modifications and alterations of this invention may be made by those skilled in the art without departing from the spirit and scope of this invention. Thus, it is intended that the present invention cover the modifications and variations of this invention provided they come within the scope of the appended claims and their equivalents.
Claims (6)
1. A typical Walker constellation mathematical model described by using orbital elements is characterized by comprising (a)j,k，ej,k，ij,k，Ωj,k，ωj,k，fj,k) Six orbital elements, wherein aj,kRepresenting the semi-major axis, e, of the satellite orbit at each node in the constellationj,kRepresenting the satellite orbit eccentricity i of each node in the constellationj,kRepresents the orbital inclination angle of each node satellite in the constellation, omegaj,kRepresenting the right ascension, omega, of each node satellite in the constellationj,kRepresenting the argument of each node satellite in the constellation, fj,kRepresenting the real near point angle of each node satellite in the constellation to describe the real-time running state of each node satellite in the constellation; the Walker constellation types comprise a star constellation, a delta constellation, a rose constellation and a sigma constellation; in the six elements of the track, aj,k，ej,k，ij,k，Ωj,k，ωj,kConstellation configuration, f, which together describe the Walker constellationj,kDescribing the constellation operation state of the Walker constellation.
2. A mathematical model of a classical Walker constellation as described by orbital elements according to claim 1, characterized by ReRepresenting the mean radius of the earth, i1Is the track inclination of the reference track, u1The index j represents the jth orbital plane (j is 1, 2. cndot. cndot., P), the index k represents the number k of the satellites on the jth orbital plane (k is 1, 2. cndot., S), P is the number of orbital planes, S is the number of the satellites, h is the orbital height, omega is the elevation declination, F is the phase factor, and the operation time is t0The single-layer circular orbit star constellation of (a) can be described as:
aj,k＝Re+h
ej,k＝0
Ωj,k＝Ω
ωj,k＝0
3. the mathematical model of a classical Walker constellation as described by orbital elements as claimed in claim 1, characterized by Ω ∑ q [ ]1For the right ascension of the elevation point of the reference satellite in the reference orbit, the single-layer circular orbit δ constellation can be described as:
aj,k＝Re+h
ej,k＝0
ij,k＝i
ωj,k＝0
wherein P is the number of track surfaces, i is the track inclination angle, t0For the running time of a single-layer circular orbit delta constellation, u1The index j indicates the amplitude of the intersection point of the reference satellite in the reference orbit, the index k indicates the number k of the satellites (k 1, 2. cndot., S) in the jth orbital plane, P is the number of orbital planes, S is the number of satellites, h is the orbital height, F is the phase factor, R is the phase factor, and j is 1, 2. cndot., P is the jth orbital planeeRepresenting the mean radius of the earth.
4. A mathematical model of a typical Walker constellation described by using orbital elements as claimed in claim 1, wherein the rose constellation k-1, and the single-layer circular orbit rose constellation can be described as:
aj,k＝Re+h
ej,k＝0
ij,k＝i
ωj,k＝0
where m denotes a phase factor, P is the number of track surfaces, i is the track inclination, t0For the running time of a single-layer circular orbital rose constellation, u1The index j indicates the amplitude of the intersection point of the reference satellite in the reference orbit, the index k indicates the number k of the satellites in the jth orbital plane (j is 1, 2. cndot., P), P is the number of orbital planes, h is the orbital height, R is the orbital height, and j is the jth orbital plane (j is 1, 2. cndot., P)eRepresenting the mean radius of the earth.
5. The mathematical model of a typical Walker constellation described by using orbital elements as claimed in claim 1 wherein the single-layer circular orbit σ constellation can be described as:
aj,k＝Re+h
ej,k＝0
ij,k＝i
ωj,k＝0
wherein M is the number of days of a single-layer circular orbit sigma constellation quasi-regression orbit, M +1 circles are operated in M days, P is the number of orbital planes, i is an orbital inclination angle, t is0For the running time of a single-layer circular-orbit sigma constellation1The index j indicates the amplitude of the intersection point of the reference satellite in the reference orbit, the index k indicates the number k of the satellites (k 1, 2. cndot., S) in the jth orbital plane, P is the number of orbital planes, S is the number of satellites, h is the orbital altitude, R is the orbital altitude, and j is the jth orbital plane (j 1, 2. cndot., P), k is the number of orbital planeseRepresenting the mean radius of the earth.
6. A mathematical model of a classical Walker constellation as described by means of orbital elements according to claims 1-5, characterized in that n is the satellite mean running angular rate:
wherein mu is a gravitational constant, and mu is 398600.44km3/s2。
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112580220A (en) * | 2020-12-28 | 2021-03-30 | 北京理工大学 | Top-level modeling of satellite internet simulation system based on node-branch coupling matrix |
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