CN108614575A - A kind of satellite stationary orbit fixed position method of adjustment - Google Patents

A kind of satellite stationary orbit fixed position method of adjustment Download PDF

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CN108614575A
CN108614575A CN201810634252.8A CN201810634252A CN108614575A CN 108614575 A CN108614575 A CN 108614575A CN 201810634252 A CN201810634252 A CN 201810634252A CN 108614575 A CN108614575 A CN 108614575A
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major axis
orbit
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subpulse
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赵书阁
向开恒
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Beijing Institute of Electronic System Engineering
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Beijing Institute of Electronic System Engineering
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B64—AIRCRAFT; AVIATION; COSMONAUTICS
    • B64G—COSMONAUTICS; VEHICLES OR EQUIPMENT THEREFOR
    • B64G1/00—Cosmonautic vehicles
    • B64G1/22—Parts of, or equipment specially adapted for fitting in or to, cosmonautic vehicles
    • B64G1/24—Guiding or controlling apparatus, e.g. for attitude control
    • B64G1/244—Spacecraft control systems

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Abstract

The present invention discloses a kind of satellite stationary orbit fixed position method of adjustment, including S1：The inter-orbital transfer time of satellite is calculated according to transfer initial point, distal point and maximum transfer time；S2：Calculate the semi-major axis variable quantity of the satellite second pulse of zonal harmonics perturbation；S3：Calculate the second pulse for considering tesseral harmonics perturbation；S4：Three subpulses for considering tesseral harmonics perturbation are calculated, solve the problems, such as that satellite fixed position Adjustment precision is relatively low.

Description

A kind of satellite stationary orbit fixed position method of adjustment
Technical field
The present invention relates to satellite orbit control technology fields.More particularly, to a kind of satellite stationary orbit fixed position Method of adjustment.
Background technology
Currently, with the increase of stationary orbit (GEO) number of satellite, the in-orbit maintenance of satellite mainly face with Lower problem：The consumables such as the portable propellant of satellite launch are limited and are difficult to realize feed；Scrap the track including spacecraft Rubbish occupies orbital position for a long time, it is difficult to remove.In-orbit service technology will provide completely new mould for the in-orbit maintenance of stationary orbit Formula, by maintainable technology on-orbit, module replacing, fuel adding and it is in-orbit rescue etc. in-orbit services technology can reduce space mission at Originally, extend the service life of in-orbit spacecraft.In order to reduce task cost, one in-orbit service satellite of generally use is more static rails Road satellite provides in-orbit filling or maintenance service.
When the fixed point difference of longitude between more target satellites is larger, in-orbit service satellite needs to carry out a wide range of stationary orbit Position adjustment approaches the remote of target satellite to realize.The adjustment of stationary orbit position is usually real by applying tangential thrust It is existing, but the influence of perturbation is usually ignored in existing research.For the stationary orbit position adjustment that difference of longitude is larger, need longer Inter-orbital transfer time is to reduce the fuel consumption of mobile process.In long-time transfer process, perturbation of earths gravitational field, especially Tesseral harmonics perturbation has large effect to stationary orbit position Adjustment precision, causes satellite positioning precision low.
Invention content
It is an object of the present invention to provide a kind of satellite stationary orbit fixed position methods of adjustment, solve stationary orbit The relatively low problem of satellite positioning position Adjustment precision.
In order to achieve the above objectives, the present invention uses following technical proposals：
One aspect of the present invention discloses a kind of satellite stationary orbit fixed position method of adjustment, including
S1：The inter-orbital transfer time of satellite is calculated according to transfer initial point, distal point and maximum transfer time；
S2：Calculate the semi-major axis variable quantity of the satellite second pulse of zonal harmonics perturbation；
S3：Calculate the second pulse for considering tesseral harmonics perturbation；
S4：Calculate three subpulses for considering tesseral harmonics perturbation.
Preferably, the inter-orbital transfer time is
Tz=czPz
Wherein, czThe maximum track number of turns during transfer, PzFor the orbital period.
Preferably, the S2 includes：
Longitude drift speed in transfer process should be
Δ λ=λn-λ0
Wherein, TzInitial longitude for inter-orbital transfer time, satellite is λ0, target longitude is λn。
After applying first pulse, the orbit angular velocity of transfer orbit is：
In formula, ΩEFor rotational-angular velocity of the earth, J2It is 2 ranks with humorous term coefficient, n is mean orbit angular speed, be a is track Radius, ReqIt is the mean equatorial radius of the earth.
The semi-major axis of T moment transfer orbits is
aT=(μe/nT 2)1/3
So the first moment in Orbit Transformation and last moment, semi-major axis knots modification is respectively caused by two Impulse maneuvers：
Wherein, Δ a0For the semi-major axis knots modification at first moment, Δ anFor the semi-major axis knots modification at last moment；ac(λ0) it is first The semi-major axis at moment, ac(λn) be the last moment semi-major axis.
Preferably, consider that the Orbit Transformation of tesseral harmonics perturbation first moment and last moment tangential second pulse are respectively：
g1(λ)=sin2 (λ-λ22)
g2(λ)=cos2 (λ-λ22)
In formula,For the first second pulse,For second secondary pulse, ΩEFor rotational-angular velocity of the earth, ac For the relationship of the stationary orbit semi-major axis and longitude of the aspherical major event perturbation of the earth, J22It is 2 rank, 2 humorous term coefficients in field, aJTo examine Consider J22Semi-major axis after first time tangential Impulse maneuver afterwards.
Preferably, three subpulses for considering tesseral harmonics perturbation：
Wherein,For the first second pulse,For second secondary pulse, Δ V1For first in three subpulses Subpulse, Δ V2For the second subpulse in three subpulses, Δ V3For the third subpulse in three subpulses.
Preferably, the application position of three subpulse is as follows：First subpulse and third subpulse and right ascension phase Tongfang To on the contrary, being respectively applied to first moment and last moment, the second subpulse right ascension and the first subpulse or the third time of Orbit Transformation The right ascension of pulse differs 180 °.
Preferably,
WhenWhen, the second subpulse is applied to the first subpulse later half a orbital period, direction with First time pulsion phase is same；
WhenWhen, the second subpulse is applied to the third subpulse first half orbital period, direction with Third time pulsion phase is same.
Preferably, the relationship of three subpulse is
Beneficial effects of the present invention are as follows：
The present invention separates a kind of high-precision stationary orbit fixed position method of adjustment, in the case where considering to perturb, obtains It obtains higher stationary orbit and pinpoints Adjustment precision, large-scale stationary orbit fixed position for a long time is adjusted, using consideration The control error of the correction strategy of perturbation, longitude can be decreased within 1 °.Two Impulse maneuver strategies are extended to three arteries and veins by the present invention Maneuver strategy is rushed, while realizing the control of longitude, semi-major axis and eccentricity, it can be by the control of longitude, semi-major axis and eccentricity Precision is down to 1 °, 1000m and 2 × 10 respectively-4Within.
Description of the drawings
Specific embodiments of the present invention will be described in further detail below in conjunction with the accompanying drawings.
Fig. 1 shows a kind of schematic diagram of one specific embodiment of satellite stationary orbit fixed position method of adjustment of the invention.
Fig. 2 shows the application schemes of second pulse in the prior art.
Fig. 3 shows to consider the application scheme of three subpulses of tesseral harmonics perturbation in the present invention.
Fig. 4 shows not use the time history of tesseral harmonics perturbation amendment and the satellite longitude using tesseral harmonics perturbation.
Fig. 5 shows time history of the present invention using longitude in tesseral harmonics perturbation transfer process.
Fig. 6 shows time of the present invention using semi-major axis and stationary orbit semi-major axis deviation in tesseral harmonics perturbation transfer process Course.
Fig. 7 shows time history of the present invention using eccentricity in tesseral harmonics perturbation transfer process.
Specific implementation mode
In order to illustrate more clearly of the present invention, the present invention is done further with reference to preferred embodiments and drawings It is bright.Similar component is indicated with identical reference numeral in attached drawing.It will be appreciated by those skilled in the art that institute is specific below The content of description is illustrative and be not restrictive, and should not be limited the scope of the invention with this.
In the prior art, two Impulse maneuvers for only applying lateral thrust are usually used in the adjustment of stationary orbit fixed position, along rail First transverse pulse of road transverse direction can change semi-major axis, for reducing difference of longitude；Second pulse is in fixed position tune The whole end moment applies, for eliminating longitude drift rate.During long-term stationary orbit fixed position adjustment, the humorous item in field is taken the photograph It is dynamic to change semi-major axis, fixed position Adjustment precision is influenced, causes positioning accuracy low.The present invention considers tesseral harmonics perturbation first Influence devises two Impulse maneuver strategies, since initial time and end moment are for changing the transverse pulse no longer phase of semi-major axis Deng so that the final value of eccentricity is no longer zero, in order to match eccentricity, under the premise of not increasing fuel consumption, by two pulses Maneuver strategy is expanded into three Impulse maneuver strategies, improves the orbit injection accuracy of stationary orbit fixed position adjustment.
According to an aspect of the present invention, the one of a kind of satellite stationary orbit fixed position method of adjustment of the present invention is disclosed A specific embodiment.As shown in Figure 1, in the present embodiment, for giving the long-time stationary orbit of initial point and distal point longitude Transfer task devises the two pulse transition strategies for considering perturbation of earths gravitational field first, and in transfer, just moment and last moment apply Add two tangential velocity increments for controlling longitude and semi-major axis.Due to the influence of the aspherical humorous item in gravitation field of the earth, transfer is just Two speed increments at moment and last moment are no longer equal, so the eccentricity at last moment can be influenced, then by two pulse strategies It is extended to three pulse strategies while realizing the control of longitude, semi-major axis and eccentricity, and the speed that three Impulse maneuver strategies need It is identical as two Impulse maneuver strategies to spend increment
Specifically, the method for adjustment includes：
S1：The inter-orbital transfer time of satellite is calculated according to transfer initial point, distal point and maximum transfer time.
For two pulse-orbit transition strategies, the first subpulse and last time pulse are applied to the first moment that position adjusts With the last moment, in order to make the eccentricity of terminal juncture be zero, two subpulses apply right ascension answer it is identical, so inter-orbital transfer time It must be the integral multiple in transfer orbit period.
First, satellite longitude is calculated.The satellite for running on stationary orbit is usually controlled in the longitude zone of permission, satellite Longitude can characterize satellite in the position in space as independent, can be expressed as by clas sical orbit element
λ=Ω+ω+M- θG (1)
Wherein, Ω, ω and M are respectively the right ascension of ascending node, argument of perigee and mean anomaly of satellite, θGFor moment epoch Greenwich sidereal time.
Since the longitude drift of stationary orbit is mainly caused by perturbation of earths gravitational field, the present invention only considers that the earth is non- The influence that spherical shape perturbation adjusts stationary orbit position.For circular orbit, the major event of Earth nonspherical gravitation perturbation potential function is
In formula, n is mean orbit angular speed,μeIt is the gravitational constant of the earth, μe=3.986 × 1014m3/s2, a is the semi-major axis of orbit of satellite, and i is the orbit inclination angle of satellite, ReqIt is the mean equatorial radius of the earth, J2It is 2 ranks With humorous term coefficient, J22It is 2 rank, 2 humorous term coefficients in field, λ22It is the humorous item longitude in 2 rank, 2 fields.
Track is usually assumed to be ideal stationary orbit, i.e. i=0, e=0 during determining stationary orbit radius.From And Earth nonspherical gravitation perturbation major event potential function can be reduced to
Using lagrange equation of motion, it can obtain and consider J2Perturbation and J22The differential side of the longitude and semi-major axis of perturbation Journey.
The differential equation of semi-major axis is
The differential equation of longitude is
In formula, ΩEFor rotational-angular velocity of the earth.
Using Taylor series expansion, the first-order expression that orbit averaging angular speed changes with semi-major axis can be obtained：
In formula, aeNot consider the stationary orbit semi-major axis of perturbation,
It brings formula (6) into formula (5), and enablesIt is hereby achieved that considering the static rail of the aspherical major event perturbation of the earth The relationship of road semi-major axis and longitude is
Assuming that the initial longitude of satellite is λ0, target longitude be λn, task allow the maximum transfer time be Tmax, so as to To obtain the minimum average B configuration longitude drift speed of Orbit Transformation needs：
In formula, Δ λ=λn-λ0。
It can obtain the minimum orbit angular speed needed during Orbit Transformation：
In formula, aJIt is to consider J22Semi-major axis after first time tangential Impulse maneuver afterwards, nJBe semi-major axis be aJCorresponding track Angular speed.
Since inter-orbital transfer time must be the integral multiple of transfer orbit orbital period, the maximum track number of turns during transfer For：
In formula, floor indicates downward bracket function, thus during Orbit Transformation in an orbital period longitude change Amount is：
It is to obtain the orbital period after the downward rounding of the track number of turns
It is to obtain the inter-orbital transfer time after the downward rounding of the track number of turns
Tz=czPz (13)
S2：Calculate the semi-major axis variable quantity of satellite second pulse.Motor-driven two pulse tangential thrusts are Satellite Phase adjustment Common strategy.Apply tangential thrust first and change semi-major axis of orbit (orbit angular velocity), after one section of flight time, satellite arrives Up to target location, applies second of thrust and eliminate semi-major axis (orbit angular velocity) deviation.
Longitude drift speed in transfer process should be
After applying first pulse, the orbit angular velocity of transfer orbit is：
The semi-major axis of transfer orbit is
aT=(μe/nT 2)1/3 (16)
So the first moment in Orbit Transformation and last moment, semi-major axis knots modification is respectively caused by two Impulse maneuvers：
Wherein, Δ a0For the semi-major axis knots modification at first moment, Δ anFor the semi-major axis knots modification at last moment；ac(λ0) it is first The semi-major axis at moment, ac(λn) be the last moment semi-major axis.
S3：Calculate the second pulse for considering perturbation.Stationary orbit fixed position adjustment for the short time, two pulse of satellite Tangential thrust can obtain higher fixed point adjustment orbit injection accuracy, still, for prolonged Orbit Transformation, J22Perturbation will be right Longitude causes larger change, it is therefore desirable to consider J22The influence that long-time stationary orbit is shifted in perturbation.The earth is aspherical to be taken the photograph It moves, especially tesseral harmonics perturbation, it will cause longitude and semi-major axis to deviate desired value in long-time transfer process, it is therefore, quiet Only the adjustment of track long-time precise phase needs to consider the influence of perturbation of earths gravitational field.
Wherein, considering J22When perturbation, it is assumed that longitude at the uniform velocity changes in transfer process, i.e.,
By formula (4) divided by formula (18), thus：
g1(λ)=sin2 (λ-λ22)
Consider J22The semi-major axis for the first time after tangential Impulse maneuver is denoted as a afterwardsJ, orbit angular velocity is denoted asThe J in transfer process22Semi-major axis variation caused by perturbation is smaller, in transfer process：a≈aJ, n ≈nJ, then above formula both ends are integrated with the expression formula that can be obtained semi-major axis and change with longitude simultaneously：
Function g in formula2(λ)=cos2 (λ-λ22)。
Longitude drift speed is segmented into following three parts：First part is J22Semi-major axis caused by perturbation changes indirect shadow It rings；Second part is J22It is directly affected caused by perturbation；Part III depends on the initial semi-major axis after first time Impulse maneuver aJ。
The first part that subscript " 1 " indicates can be expressed as the function of semi-major axis.
Bring the expression formula (20) that semi-major axis changes with longitude into formula (23).
Based on longitude even variation it is assumed that by formula (24) divided by formula (4), and longitude λ integrals can be obtained at formula both ends J22It perturbs on the indirect relationship for influencing knots modification and longitude of longitude.
Based on longitude even variation it is assumed that the relationship of Part III and longitude that subscript " 2 " indicates can also determine, to Integral can obtain J22The longitude amount of being directly changed caused by perturbation.
So in long-time transfer process, the longitude knots modification caused by the first subpulse is total longitude knots modification and J22 The difference (including directly or indirectly changing) of longitude knots modification caused by perturbation：
To which the longitude drift speed during Orbit Transformation is：
Composite type (6) and (28) can obtain and consider J22The semi-major axis that the first time tangential Impulse maneuver of perturbation needs changes Variable：
Meanwhile aJ, acWithThere is also following relationships.
Composite type (29) and (30) can calculateAnd aJ.Due to aJ≈aT, can be by aJ=aTBring formula (29) into Directly calculateIt, can be by a in order to further increase precisionTAs aJInitial value, utilize formula (29) and (30) iteration Calculate aJ。
After determination, it can be obtained using formula (20) and consider J22What second of tangential Impulse maneuver of perturbation needed Semi-major axis knots modification：
Consider J22Just moment and last moment tangential pulse are respectively the Orbit Transformation of perturbation：
S4：Calculate three subpulses for considering perturbation.
The above two Impulse maneuvers strategy only controls longitude and semi-major axis, will be in the case where not increasing general speed increment Two Impulse maneuver strategies of upper proposition are extended to three Impulse maneuver strategies, to realize while control longitude, semi-major axis and eccentricity.
Due to J22The impulse magnitude twice of the influence of perturbation, two Impulse maneuvers is no longer equal, even if two subpulses are applied to Same right ascension, as shown in Fig. 2, in terminal juncture, eccentricity is also no longer equal to zero.In the general speed increment of two pulse tangential maneuvers On the basis of, it is proposed that three tangential Impulse maneuver strategies, as shown in figure 3, be used for while controlling longitude, semi-major axis and eccentricity.
The speed increment of three pulses is respectively：
The application position of three Impulse maneuver strategies is as follows：First pulse Δ V1With third pulse Δ V3Right ascension it is identical Direction is on the contrary, be respectively applied to the first moment of Orbit Transformation and last moment, second pulse Δ V2Right ascension and first (or third It is a) right ascension of pulse differs 180 °.WhenWhen, second pulse Δ V2It is applied to first pulse Δ V1 Half of orbital period afterwards, direction and first pulse Δ V1It is identical；WhenWhen, second pulse Δ V2It applies It is added in third pulse Δ V3Preceding half of orbital period, direction and third pulse Δ V3It is identical.
Since the size of the second subpulse is much smaller than first time and third subpulse, caused by within half of orbital period Longitude accumulation can be ignored, so three Impulse maneuver strategies are identical as the general speed increment of two Impulse maneuver strategies.
The above three Impulse maneuvers strategy is equivalent to dismantle to be divided by pulse larger in two pulse strategies and execute twice, so The increment that will not increase speed consumes.
Below by a specific example, the invention will be further described, a kind of high-precision stationary orbit of the invention The initial longitude of fixed position method of adjustment, satellite is 0 °, and target longitude is 90 °, and the maximum transfer time is 100 It.
S1：Inter-orbital transfer time is calculated according to transfer initial point and distal point.
Maximum longitude knots modification during Orbit Transformation is -0 ° of Δ λ=90 °=90 °, when the maximum transfer that task allows Between be Tmax=100day, it is hereby achieved that the minimum average B configuration longitude drift speed that Orbit Transformation needs：
It can obtain the minimum orbit angular speed needed during Orbit Transformation
The maximum track number of turns during transfer is
So the knots modification of longitude is in an orbital period during Orbit Transformation
Δλz=Δ λ/cz=0.90 °.
It is to obtain the orbital period after the downward rounding of the track number of turns
It is to obtain the inter-orbital transfer time after the downward rounding of the track number of turns
Tz=czPz=8595510sec=99.485day
S2：Calculate the semi-major axis variable quantity of satellite second pulse.Do not consider J22Two Impulse maneuver strategies of perturbation, were shifted Longitude drift speed in journey is
After applying first pulse, the orbit angular velocity of transfer orbit is：
The semi-major axis of transfer orbit is
aT=(μe/nT 2)1/3=42095.966 × 103km
So the first moment in Orbit Transformation and last moment, semi-major axis knots modification is respectively caused by two Impulse maneuvers：
S3：Calculate the second pulse for considering perturbation.
Due to aJ≈aT, during calculating, by aJ=aTBring correlate equation calculating intoOrbit Transformation mistake Longitude knots modification in journey is made of three parts, first part J22Semi-major axis variation caused by perturbation influences indirectly, Ke Yili It is calculated with equation (25), a in equationJUse aTIt is approximate.
Δλ(90°)1=0.1104rad=6.327 °
Second part is J22It is directly affected caused by perturbation, equation (26) can be utilized to calculate, a in equationJUse aT It is approximate.
Δλ(90°)2=-1.448 × 10-4Rad=-0.00830 °
Part III is total longitude knots modification and J22The difference of longitude knots modification caused by perturbation (including directly or indirectly changes Become)：
Part III determines the semi-major axis knots modification of first time Impulse maneuver, so as to be calculated using equation (29) The semi-major axis knots modification that tangential Impulse maneuver needs for the first time：
After determination, it can be obtained using equation (31) and consider J22Second of tangential Impulse maneuver of perturbation The semi-major axis knots modification needed：
Consider J22Just moment and last moment tangential pulse are respectively the Orbit Transformation of perturbation：
S4：Calculate three subpulses for considering perturbation.
The above two Impulse maneuvers strategy only controls longitude and semi-major axis, will be in the case where not increasing general speed increment Two Impulse maneuver strategies of upper proposition are extended to three Impulse maneuver strategies, to realize while control longitude, semi-major axis and eccentricity. Due in this example,Three pulses, which can be calculated, according to equation (33)-(35) is respectively：
The speed increment of three pulses is respectively：
ΔV1=-2.3884m/s
ΔV2=0.1334m/s
ΔV3=2.5218m/s
The application position of three Impulse maneuver strategies is as follows：The right ascension same direction of first and third pulse is on the contrary, divide It is not applied to the first moment of Orbit Transformation and last moment, the right ascension phase of second pulse right ascension and first (or third) pulse Poor 180 °, as shown in Figure 3.
In this example,Second pulse is applied to half of track week before third pulse Phase, the direction of pulse and third pulsion phase are same.
Fig. 4 is not use J22Correct and use J22Modified longitude time history, the longitude time by comparing the two are gone through Journey, it can be found that：When without J22When amendment, end moment longitude control error has reached 6 °, using J22After amendment, warp The error of degree has been reduced within 1 °, compared to not considering J22Modified pulse transition strategy, the J that this patent proposes22Correct transfer Strategy improves fixed position adjustment orbit injection accuracy.
Fig. 5, Fig. 6 and Fig. 7 are respectively to use J22Deviation (the a-a of modified longitude, semi-major axis and stationary orbit semi-major axisp) With the time history of eccentricity, can be seen that from the partial enlarged view of each figure：The control accuracy of longitude, semi-major axis and eccentricity point Not 1 °, 1000m and 2 × 10-4Within, this patent propose based on J22Modified three pulses stationary orbit transition strategy, can be with Obtain higher longitude, semi-major axis and eccentricity control accuracy.
Obviously, the above embodiment of the present invention be only to clearly illustrate example of the present invention, and not be pair The restriction of embodiments of the present invention may be used also on the basis of the above description for those of ordinary skill in the art To make other variations or changes in different ways, all embodiments can not be exhaustive here, it is every to belong to this hair Row of the obvious changes or variations that bright technical solution is extended out still in protection scope of the present invention.

Claims (8)

1. a kind of satellite stationary orbit fixed position method of adjustment, which is characterized in that including
S1：The inter-orbital transfer time of satellite is calculated according to transfer initial point, distal point and maximum transfer time；
S2：Calculate the semi-major axis variable quantity of the satellite second pulse of zonal harmonics perturbation；
S3：Calculate the second pulse for considering tesseral harmonics perturbation；
S4：Calculate three subpulses for considering tesseral harmonics perturbation.
2. according to the method described in claim 1, it is characterized in that, the inter-orbital transfer time be
Tz=czPz
Wherein, czThe maximum track number of turns during transfer, PzFor the orbital period.
3. according to the method described in claim 1, it is characterized in that, the S2 includes：
Longitude drift speed in transfer process should be
Δ λ=λn-λ0
Wherein, TzInitial longitude for inter-orbital transfer time, satellite is λ0, target longitude is λn。
After applying first pulse, the orbit angular velocity of transfer orbit is：
In formula, ΩEFor rotational-angular velocity of the earth, J2It is 2 ranks with humorous term coefficient, n is mean orbit angular speed, be a is track half Diameter, ReqIt is the mean equatorial radius of the earth.
The semi-major axis of T moment transfer orbits is
aT=(μe/nT 2)1/3
So the first moment in Orbit Transformation and last moment, semi-major axis knots modification is respectively caused by two Impulse maneuvers：
Wherein, Δ a0For the semi-major axis knots modification at first moment, Δ anFor the semi-major axis knots modification at last moment；ac(λ0) it is the first moment Semi-major axis, ac(λn) be the last moment semi-major axis.
4. according to the method described in claim 3, it is characterized in that, when considering the Orbit Transformation of tesseral harmonics perturbation first moment and end Carving tangential second pulse is respectively：
g1(λ)=sin2 (λ-λ22)
g2(λ)=cos2 (λ-λ22)
In formula,For the first second pulse,For second secondary pulse, ΩEFor rotational-angular velocity of the earth, acFor ground The relationship of the stationary orbit semi-major axis and longitude of the aspherical major event perturbation of ball, J22It is 2 rank, 2 humorous term coefficients in field, aJTo consider J22 Semi-major axis after first time tangential Impulse maneuver afterwards.
5. according to the method described in claim 1, it is characterized in that, three subpulses for considering tesseral harmonics perturbation：
Wherein,For the first second pulse,For second secondary pulse, Δ V1For the first time in three subpulses Pulse, Δ V2For the second subpulse in three subpulses, Δ V3For the third subpulse in three subpulses.
6. according to the method described in claim 5, it is characterized in that, the application position of three subpulse is as follows：First time arteries and veins Punching and third subpulse and the right ascension same direction are on the contrary, be respectively applied to the first moment of Orbit Transformation and last moment, second of arteries and veins It rushes right ascension and differs 180 ° with the right ascension of the first subpulse or third subpulse.
7. according to the method described in claim 6, it is characterized in that,
WhenWhen, the second subpulse is applied to the first subpulse later half a orbital period, direction and first Subpulse is identical；
WhenWhen, the second subpulse is applied to third subpulse first half orbital period, direction and third Subpulse is identical.
8. according to the method described in claim 1, it is characterized in that, the relationship of three subpulse is
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CN112036037A (en) * 2020-08-31 2020-12-04 北京理工大学 Long-term evolution rapid analysis method of inclined geosynchronous orbit
CN113987407A (en) * 2021-10-28 2022-01-28 中国西安卫星测控中心 Method for calculating nonspherical gravitational tangential drift acceleration of geostationary satellite
CN113985908A (en) * 2021-10-29 2022-01-28 中国西安卫星测控中心 East-west position preserving perturbation drift ring control method for geostationary satellite

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