CN106184818A - Geostationary satellite Actuator failure operating mode lower railway position keeping method - Google Patents

Abstract

The present invention relates to a kind of geostationary satellite Actuator failure operating mode lower railway position keeping method, belong to field of aerospace technology.The invention aims to solve the problem that any thruster in four thrusters cannot ensure in the case of breaking down that satellite position keeps control accuracy.Described method includes: calculate orbit inclination angle drift value and the longitude drift amount of next orbital period；Calculate satellite and carry out the speed increment that position keeps needing to provide；Calculate thirdly flame range field parameter；The speed increment provided is needed to calculate described each electric thruster igniting duration in each ignition zone according to described each electric thruster.Compared with original orbital position keeping method, the present invention can efficiently accomplish the orbital position under Actuator failure operating mode and keep task, the increase of suppression orbital eccentricity, it is ensured that orbital position keeps control accuracy.

Description

Geostationary satellite Actuator failure operating mode lower railway position keeping method

Technical field

The present invention relates to a kind of geostationary satellite Actuator failure operating mode lower railway position keeping method, particularly to one Plant and use the geostationary satellite orbit position of electric thruster to keep method for designing, it is adaptable to the earth under Actuator failure operating mode Geostationary-satellite orbit position keeps task, belongs to field of aerospace technology.

Background technology

Geostationary satellite be the orbit inclination angle orbited the earth be 0 degree, orbital eccentricity be 0, heading and the earth The class satellite that sense of rotation is identical and airborne period is equal with earth rotation period, in communications, television broadcasting and meteorology The numerous areas such as forecast have important using value.Geostationary satellite in orbit time, owing to being affected by perturbative force, meeting Gradually drift about and deviate nominal and run track, cause it normally to work.Therefore, geostationary satellite needs to carry out track position Put holding to ensure service behaviour.Electric thruster, because having the ratio feature leapt high, keeps task effectively to drop for orbital position The fuel consumption of low geostationary satellite, improve the payload ratio of satellite and increase the service life of satellite.But, by space The impact of the factor such as environment or satellite components and parts performance, electric thruster is it may happen that fault.Quiet for the earth using electric thruster How only satellite, carry out orbital position holding under Actuator failure operating mode and reach intended position holding effect, being current One of hot issue that scientific and technical personnel pay close attention to.

In the geostationary satellite orbit position keeping method using electric thruster developed, in first technology [1] (Bernard M Anzel.Method for Satellite Station Keeping [P] .US5020746A, 1989), pin Geostationary satellite orbit position is kept task, it is proposed that two electric thruster of a kind of employing carry out the side of orbital position holding Method.Two thrusters are installed on the plate privately of satellite, and orbital position is 90 degree and 270 degree at right ascension RA respectively during keeping Igniting.The thruster layout using the method contains electric thruster and the electric thruster of a backup of two normal work, when Two electric thruster of normal work any one when breaking down, backup electric thruster work is protected to proceed orbital position Hold task.The advantage of the method is that satellite can carry out north and south simultaneously and thing position keeps, and simplifies orbital position and keeps task, Shortcoming is by thruster placement constraint, and the thruster of backup can not substitute the thruster broken down completely, thus fault condition Under be difficult to ensure that the control accuracy that thing orbital position keeps and north and south orbital position keeps.

At first technology [2] (Bernard M Anzel.Method and Apparatus for a Satellite Station Keeping [P] .US 5443231A, 1993), for geostationary satellite orbit position Preserving problems, give A kind of orbital position keeping method based on four electric thruster layouts.Within each orbital period, four electric thruster are red Through RA be 90 degree and 270 degree of each igniting once, complete north and south simultaneously and thing position keep task.When any one thruster is sent out During raw fault, quitting work with this thruster thruster on same diagonal, orbital position keeps task by other two Individual electric thruster continues executing with and increases thirdly flame range territory right ascension 0 degree or 180 degree.The advantage of the method is that satellite need not Backup electric thruster also can complete orbital position under single electric thruster fault condition and keep task, and shortcoming is under fault condition Increasing thirdly flame range territory right ascension 0 degree or 180 degree can not effectively suppress orbital eccentricity to drift about, and ultimately results in position and keeps control Precision processed can not meet mission requirements.

Summary of the invention

The invention aims to solve any thruster in four thrusters cannot ensure in the case of breaking down The problem that satellite position keeps control accuracy, it is provided that a kind of geostationary satellite Actuator failure operating mode lower railway position holding side Method.

It is an object of the invention to be achieved through the following technical solutions.

Geostationary satellite Actuator failure operating mode lower railway position keeping method, specifically comprises the following steps that

Step one, the present invention use the layout of four electric thruster, four thrusters to be respectively NW, NE, SW, SE.Determine The established angle of thruster thrust direction is θ and α.When any thruster breaks down, the current orbit cycle is until satellite transit To right ascension 0 degree, thruster no longer carries out position and keeps task.Orbital position is restarted from the right ascension 0 degree of next orbital period Keeping, thruster is lighted a fire at ascending node, the 3rd region and southbound node.

Step 2, the orbit inclination angle drift value calculating next orbital period and longitude drift amount；

By orbit inclination angle i of prediction in next orbital period described_PWith longitude λ_PPoor with the desired value of mission requirements, meter Calculate inclination angle drift value Δ i and longitude drift amount Δ λ, described inclination angle drift value Δ i and the computing formula of longitude drift amount Δ λ For:

$\left\{\begin{array}{c}\mathrm{\Δ}i=i_P-i_T\\ \mathrm{\Δ}\mathrm{\λ}={\mathrm{\λ}}_P-{\mathrm{\λ}}_T\end{array}\right.$

Wherein: described i_TWith described λ_TIt is respectively orbit inclination angle and the longitude desired value of mission requirements；

Step 3, calculating satellite carry out the speed increment that position keeps needing to provide；

Calculate satellite according to described orbit inclination angle drift value and described longitude drift amount and carry out what position holding needs provided Normal velocity increment Delta V_IWith tangential velocity increment Delta V_T, described normal velocity increment Delta V_IWith tangential velocity increment Delta V_TMeter Calculation formula is:

Wherein: described V_SFor satellite flight speed on geostationary orbit；

Step 4, calculate thirdly flame range field parameter；

According to electric thruster layout, by described normal velocity increment Delta V_IWith described tangential velocity increment Delta V_TDistribution is to two On individual thruster, its distribution formula is:

$\left\{\begin{array}{c}{\mathrm{\ΔV}}_{T1}=\frac{1}{2}({\mathrm{\ΔV}}_{I}tan\mathrm{\θ}tan\mathrm{\α}+{\mathrm{\ΔV}}_T)\\ {\mathrm{\ΔV}}_{T2}=\frac{1}{2}({\mathrm{\ΔV}}_{I}tan\mathrm{\θ}tan\mathrm{\α}-{\mathrm{\ΔV}}_T)\end{array}\right.$

Wherein: described Δ V_T1The tangential velocity increment provided for north electric thruster, described Δ V_T2For electric thruster in the south The tangential velocity increment provided；

Calculate the eccentricity variable quantity that orbital eccentricity is caused by tangential velocity increment, wherein, described eccentricity variable quantity Computing formula be:

$\left\{\begin{array}{c}{\mathrm{\Δe}}_X=\frac{2\left({\mathrm{\ΔV}}_{T1}+{\mathrm{\ΔV}}_{T2}\right)}{V_S}\\ {\mathrm{\Δe}}_Y=\frac{\left({\mathrm{\ΔV}}_{T1}-{\mathrm{\ΔV}}_{T2}\right)\·\cot \left(\mathrm{\α}\right)}{V_S}\end{array}\right.$

Wherein: described Δ e_XWith described Δ e_YIt is respectively described eccentricity variable quantity X and Y side in geocentric inertial coordinate system To component；

According to described eccentricity variable quantity, calculate thirdly flame range field parameter, the most thirdly flame range territory and right ascension 0 degree or The angle γ of 180 degree, and thirdly each electric thruster needs the speed increment Δ V provided in flame range territory_R:

$\left\{\begin{array}{c}\mathrm{\γ}=\arctan \left(\frac{{\mathrm{\Δe}}_Y}{{\mathrm{\Δe}}_X}\right)\\ {\mathrm{\ΔV}}_R=\frac{V_S}{2}\·\sqrt{{{\mathrm{\Δe}}_X}^2+{{\mathrm{\Δe}}_Y}^2}\end{array}\right.$

Step 5, according to described each electric thruster need provide speed increment calculate described each electric thruster rise Igniting duration at intersection point, thirdly flame range territory and southbound node, the computing formula of described igniting duration T is:

$T=\frac{2}{{\mathrm{\ω}}_E}\mathrm{arc}sin\[\frac{{\mathrm{\ω}}_E}{2}\left(\frac{{\mathrm{m\ΔV}}_i}{Fcos\mathrm{\θ}\cos \mathrm{\α}}\right)\]$

Wherein: described ω_EFor rotational-angular velocity of the earth, described m is geostationary satellite quality, described Δ V_iFor electricity thrust Need the speed increment provided at different ignition zones, described F is electric thruster thrust size.

Beneficial effect

The invention provides a kind of geostationary satellite Actuator failure operating mode lower railway position keeping method.With original rail Position, road keeping method is compared, and under Actuator failure operating mode, normal ignition region is in ascending, descending point of intersection in the present invention, thirdly Flame range territory adds location parameter γ, and this angle is calculated by orbital eccentricity drift bearing and obtains, thus position of the present invention Keeping method can effectively suppress orbital eccentricity to drift about, it is ensured that orbital position keeps control accuracy.

Accompanying drawing explanation

Fig. 1 is four electric thruster schematic layout patterns that the embodiment of the present invention provides；

Fig. 2 is the first kind fault condition electric thruster ignition zone schematic diagram that the embodiment of the present invention provides；

Fig. 3 is the Equations of The Second Kind fault condition electric thruster ignition zone schematic diagram that the embodiment of the present invention provides；

Fig. 4 is that under the first kind fault condition that the embodiment of the present invention provides, latitude keeps effect schematic diagram；

Fig. 5 is that under the first kind fault condition that the embodiment of the present invention provides, longitude keeps effect schematic diagram；

Fig. 6 is that the first kind fault condition lower railway inclination angle that the embodiment of the present invention provides keeps effect schematic diagram；

Fig. 7 is that under the first kind fault condition that the embodiment of the present invention provides, eccentricity keeps effect schematic diagram；

Fig. 8 is the geostationary satellite Actuator failure operating mode lower railway position keeping method stream that the embodiment of the present invention provides Cheng Tu.

Detailed description of the invention

Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is carried out clear, complete Explanation is described wholely

As it is shown in figure 1, four electric thruster schematic layout patterns based on quarter sawing normal coordinates.Four thrusters are symmetrically installed On satellite privately plate, thrust vectoring points to centroid of satellite.Four electric thruster be respectively NW, the NE on north and the SW of the south, SE.Each thruster is equipped with a thrust vectoring and changes device, controls thrust direction through centroid of satellite.Thruster NW and NE Thrust vectoring constitute a plane, the thrust vectoring of thruster SW and SE constitutes another plane, satellite north and south axle to this two The angle of individual plane is θ.Electric thruster initial position, afterwards can be around north and south in the plane of north barycenter earth center Axle rotates, NW and SW westwards rotates, NE and SE rotates eastwards, and the anglec of rotation is α.α and θ is defined as the installation of thruster layout Angle.

The design principle of the present invention is: fault condition is divided into two classes: (1) thruster NE or SW breaks down；(2) push away Power device NW or SE breaks down.If there is first kind fault condition, orbital position keeps task will be total to by NW and SE electric thruster With performing.If there is Equations of The Second Kind fault condition, orbital position keeps task jointly will be performed by NE and SW electric thruster.First will The orbit inclination angle of prediction in following a day and longitude are poor with the desired value of mission requirements, calculate inclination angle drift value and longitude drift Amount；Then, calculate satellite according to above two track element drift value and carry out the speed increment that orbital position keeps needing to provide； Calculate the igniting duration of two electric thruster finally according to speed increment and determine ignition zone.

Embodiment 1

For first kind fault condition, electric thruster has three ignition zones, is that NW normal ignition region, SE are normal respectively The thirdly flame range territory that ignition zone and NW, SE light a fire in succession.Under geocentric inertial coordinate system, electric thruster working region is illustrated Figure is as shown in Figure 2.Electric thruster NW normal ignition region is in ascending node of orbit position, and electric thruster SE normal operation region is in-orbit Southbound node position, road, thirdly flame range territory is γ with the angle of right ascension 180 degree.

Below by geostationary satellite as a example by fixed point longitude east longitude 120 degree and NE thruster break down, in conjunction with accompanying drawing Embodiments of the present invention are elaborated.Satellite quality is 2000 kilograms, and thruster thrust is 200 person of outstanding talent cattle, electric thruster Established angle θ and α is respectively 40 degree and 18 degree.The orbit inclination angle desired value of mission requirements is 0.01 degree, and longitude desired value is east longitude 120 degree, orbital position keeps control accuracy to be ± 0.05 degree.

Specifically comprising the following steps that of the present embodiment

Step one, the orbit inclination angle drift value calculating next orbital period and longitude drift amount

By orbit inclination angle i of prediction in next orbital period_PWith longitude λ_pPoor with the desired value of mission requirements, calculate Inclination angle drift value Δ i and longitude drift amount Δ λ:

$\left\{\begin{array}{c}\mathrm{\Δ}i=i_P-i_T\\ \mathrm{\Δ}\mathrm{\λ}={\mathrm{\λ}}_P-{\mathrm{\λ}}_T\end{array}\right.$

Wherein: orbit inclination angle desired value i of mission requirements_TWith longitude desired value λ_FIt is respectively 0.01 degree and east longitude 120 degree.

Step 2, calculating satellite carry out the speed increment that position keeps needing to provide

Calculate satellite according to track element drift value and carry out normal velocity increment Delta V that position keeps needing to provide_IWith cut To speed increment Δ V_T:

Wherein: geostationary orbit speed V_SIt is 3074.7 meter per seconds.

Step 3, calculate thirdly flame range field parameter

According to electric thruster layout, by normal velocity increment Delta V_IWith tangential velocity increment Delta V_TDistribution is to two thrusters Upper:

$\left\{\begin{array}{c}{\mathrm{\ΔV}}_{T1}=\frac{1}{2}({\mathrm{\ΔV}}_{I}tan\mathrm{\θ}tan\mathrm{\α}+{\mathrm{\ΔV}}_T)\\ {\mathrm{\ΔV}}_{T2}=\frac{1}{2}({\mathrm{\ΔV}}_{I}tan\mathrm{\θ}tan\mathrm{\α}-{\mathrm{\ΔV}}_T)\end{array}\right.$

Wherein: Δ V_T1The tangential velocity increment provided for electric thruster NW, Δ V_T2The tangential speed provided for electric thruster SE Degree increment.

The impact that orbital eccentricity is caused by tangential velocity increment is calculated by following formula:

$\left\{\begin{array}{c}{\mathrm{\Δe}}_X=\frac{2\left({\mathrm{\ΔV}}_{T1}+{\mathrm{\ΔV}}_{T2}\right)}{V_S}\\ {\mathrm{\Δe}}_Y=\frac{\left({\mathrm{\ΔV}}_{T1}-{\mathrm{\ΔV}}_{T2}\right)\·\cot \left(\mathrm{\α}\right)}{V_S}\end{array}\right.$

Wherein: Δ e_XWith Δ e_YIt is respectively eccentricity variable quantity X and component of Y-direction in geocentric inertial coordinate system.According to Eccentricity variable quantity, calculates thirdly flame range field parameter, the most thirdly flame range territory and the angle γ of right ascension 180 degree and thirdly fiery In region, each electric thruster needs the speed increment Δ V provided_R:

$\left\{\begin{array}{c}\mathrm{\γ}=\arctan \left(\frac{{\mathrm{\Δe}}_Y}{{\mathrm{\Δe}}_X}\right)\\ {\mathrm{\ΔV}}_R=\frac{V_S}{2}\·\sqrt{{{\mathrm{\Δe}}_X}^2+{{\mathrm{\Δe}}_Y}^2}\end{array}\right.$

Step 4, finally according to each electric thruster need provide speed increment calculate electric thruster in each ignition zone Igniting duration

$T=\frac{2}{{\mathrm{\ω}}_E}\mathrm{arc}sin\[\frac{{\mathrm{\ω}}_E}{2}\left(\frac{{\mathrm{m\ΔV}}_i}{Fcos\mathrm{\θ}\cos \mathrm{\α}}\right)\]$

Wherein: rotational-angular velocity of the earth ω_EBeing 0.00417 degrees second, satellite quality m is 2000 kilograms, electric thruster thrust Size F is 200 person of outstanding talent cattle.

Step 5, complete the position holding task in current orbit cycle after, it was predicted that the orbit inclination angle in next orbital period With longitude drift amount, then repeat step one to step 4 and continue orbital position holding task.

Geostationary satellite position under fixed point longitude east longitude 120 degree and NE thruster break down keeps effect such as figure Shown in 4 to Fig. 7.As it can be seen, the latitude of geostationary satellite be effectively controlled ± 0.01 degree within, longitude controls 119.99 Spending～within 120.04 degree, orbit inclination angle is effectively controlled and is controlling near target 0.01 degree, and eccentrically connecting change is also had Effect suppression is 2.5 × 10^-4Below.

Embodiment 2

For Equations of The Second Kind fault condition, electric thruster has three ignition zones, is that NE normal ignition region, SW are normal respectively The thirdly flame range territory that ignition zone and NE, SW light a fire in succession.Under geocentric inertial coordinate system, electric thruster working region is illustrated Figure is as shown in Figure 3.Electric thruster NE normal ignition region is in ascending node of orbit position, and electric thruster SW normal operation region is in-orbit Southbound node position, road, thirdly flame range territory is γ with the angle of right ascension 0 degree.Electric thruster igniting duration under this type of fault condition Computational methods are identical with first kind situation principle.

Orbital position keeps concretely comprising the following steps:

Step one, the orbit inclination angle drift value calculating next orbital period and longitude drift amount

By orbit inclination angle i of prediction in next orbital period_PWith longitude λ_PPoor with the desired value of mission requirements, calculate Inclination angle drift value Δ i and longitude drift amount Δ λ:

$\left\{\begin{array}{c}\mathrm{\Δ}i=i_p-i_T\\ \mathrm{\Δ}\mathrm{\λ}={\mathrm{\λ}}_P-{\mathrm{\λ}}_T\end{array}\right.$

Wherein: i_TAnd λ_TIt is respectively orbit inclination angle and the longitude desired value of mission requirements.

Step 2, calculating satellite carry out the speed increment that position keeps needing to provide

Calculate satellite according to track element drift value and carry out normal velocity increment Delta V that position keeps needing to provide_IWith cut To speed increment Δ V_T:

Wherein: V_SFor satellite flight speed on geostationary orbit.

Step 3, calculate thirdly flame range field parameter

According to electric thruster layout, by normal velocity increment Delta V_IWith tangential velocity increment Delta V_TDistribution is to two thrusters Upper:

$\left\{\begin{array}{c}{\mathrm{\ΔV}}_{T1}=\frac{1}{2}({\mathrm{\ΔV}}_{I}tan\mathrm{\θ}tan\mathrm{\α}+{\mathrm{\ΔV}}_T)\\ {\mathrm{\ΔV}}_{T2}=\frac{1}{2}({\mathrm{\ΔV}}_{I}tan\mathrm{\θ}tan\mathrm{\α}-{\mathrm{\ΔV}}_T)\end{array}\right.$

Wherein: Δ V_T1The tangential velocity increment provided for electric thruster NE, Δ V_T2The tangential speed provided for electric thruster SW Degree increment.

The impact that orbital eccentricity is caused by tangential velocity increment is calculated by following formula:

$\left\{\begin{array}{c}{\mathrm{\Δe}}_X=\frac{2\left({\mathrm{\ΔV}}_{T1}+{\mathrm{\ΔV}}_{T2}\right)}{V_S}\\ {\mathrm{\Δe}}_Y=\frac{\left({\mathrm{\ΔV}}_{T1}-{\mathrm{\ΔV}}_{T2}\right)\·\cot \left(\mathrm{\α}\right)}{V_S}\end{array}\right.$

Wherein: Δ e_XWith Δ e_YIt is respectively eccentricity variable quantity X and component of Y-direction in geocentric inertial coordinate system.According to Eccentricity variable quantity, calculates thirdly flame range field parameter, the most thirdly the angle γ of flame range territory and right ascension 0 degree and thirdly flame range In territory, each electric thruster needs the speed increment Δ V provided_R:

$\left\{\begin{array}{c}\mathrm{\γ}=\arctan \left(\frac{{\mathrm{\Δe}}_Y}{{\mathrm{\Δe}}_X}\right)\\ {\mathrm{\ΔV}}_R=\frac{V_S}{2}\·\sqrt{{{\mathrm{\Δe}}_X}^2+{{\mathrm{\Δe}}_Y}^2}\end{array}\right.$

Step 4, finally according to each electric thruster need provide speed increment calculate electric thruster in each ignition zone Igniting duration

$T=\frac{2}{{\mathrm{\ω}}_E}\mathrm{arc}sin\[\frac{{\mathrm{\ω}}_E}{2}\left(\frac{{\mathrm{m\ΔV}}_i}{Fcos\mathrm{\θ}\cos \mathrm{\α}}\right)\]$

Wherein: ω_EFor rotational-angular velocity of the earth, m is geostationary satellite quality, Δ V_iFor electricity thrust in difference flame range Territory needs the speed increment provided, and F is electric thruster thrust size.

Step 5, complete the position holding task in current orbit cycle after, it was predicted that the orbit inclination angle in next orbital period With longitude drift amount, then repeat step one to step 4 and continue orbital position holding task.

Wherein, the geostationary satellite Actuator failure operating mode lower railway position keeping method that the embodiment of the present invention is provided Flow chart is with reference to shown in Fig. 8.

It should be understood that one of ordinary skill in the art will appreciate that all or part of step realizing above-described embodiment Can be completed by hardware, it is also possible to instructing relevant hardware by program and complete, described program can be stored in one Planting in computer-readable recording medium, storage medium mentioned above can be read only memory, disk or CD etc..

The foregoing is only presently preferred embodiments of the present invention, not in order to limit the present invention, all spirit in the present invention and Within principle, any modification, equivalent substitution and improvement etc. made, should be included within the scope of the present invention.

Claims (1)

1. geostationary satellite Actuator failure operating mode lower railway position keeping method, specifically comprises the following steps that

Step one, the layout of four electric thruster of employing, four thrusters are respectively NW, NE, SW, SE；Determine thruster thrust The established angle in direction is θ and α；When any thruster breaks down, the current orbit cycle until satellite transit is to right ascension 0 degree, Thruster no longer carries out position and keeps task；Restart orbital position from the right ascension 0 degree of next orbital period to keep, thruster Light a fire at ascending node, the 3rd region and southbound node；

Step 2, the orbit inclination angle drift value calculating next orbital period and longitude drift amount；

By orbit inclination angle i of prediction in next orbital period described_PWith longitude λ_PPoor with the desired value of mission requirements, calculate Inclination angle drift value Δ i and longitude drift amount Δ λ, the computing formula of described inclination angle drift value Δ i and longitude drift amount Δ λ is:

$\left\{\begin{array}{c}\mathrm{\Δ}i=i_P-i_T\\ \mathrm{\Δ}\mathrm{\λ}={\mathrm{\λ}}_P-{\mathrm{\λ}}_T\end{array}\right.$

Wherein: described i_TWith described λ_TIt is respectively orbit inclination angle and the longitude desired value of mission requirements；

Step 3, calculating satellite carry out the speed increment that position keeps needing to provide；

Calculate satellite according to described orbit inclination angle drift value and described longitude drift amount and carry out the normal direction that position keeps needing to provide Speed increment Δ V_IWith tangential velocity increment Delta V_T, described normal velocity increment Delta V_IWith tangential velocity increment Delta V_TCalculating public Formula is:

Wherein: described V_SFor satellite flight speed on geostationary orbit；

Step 4, calculate thirdly flame range field parameter；

According to electric thruster layout, by described normal velocity increment Delta V_IWith described tangential velocity increment Delta V_TDistribution pushes away to two On power device, its distribution formula is:

$\left\{\begin{array}{c}{\mathrm{\ΔV}}_{T1}=\frac{1}{2}({\mathrm{\ΔV}}_{I}tan\mathrm{\θ}tan\mathrm{\α}+{\mathrm{\ΔV}}_T)\\ {\mathrm{\ΔV}}_{T2}=\frac{1}{2}({\mathrm{\ΔV}}_{I}tan\mathrm{\θ}tan\mathrm{\α}-{\mathrm{\ΔV}}_T)\end{array}\right.$

Wherein: described Δ V_T1The tangential velocity increment provided for north electric thruster, described Δ V_T2There is provided for electric thruster in the south Tangential velocity increment；

Calculate the eccentricity variable quantity that orbital eccentricity is caused by tangential velocity increment, wherein, the meter of described eccentricity variable quantity Calculation formula is:

$\left\{\begin{array}{c}{\mathrm{\Δe}}_X=\frac{2\left({\mathrm{\ΔV}}_{T1}+{\mathrm{\ΔV}}_{T2}\right)}{V_S}\\ {\mathrm{\Δe}}_Y=\frac{\left({\mathrm{\ΔV}}_{T1}-{\mathrm{\ΔV}}_{T2}\right)\·\cot \left(\mathrm{\α}\right)}{V_S}\end{array}\right.$

Wherein: described Δ e_XWith described Δ e_YIt is respectively described eccentricity variable quantity X and Y-direction in geocentric inertial coordinate system Component；

According to described eccentricity variable quantity, calculate thirdly flame range field parameter, the most thirdly flame range territory and right ascension 0 degree or 180 degree Angle γ, and thirdly each electric thruster needs the speed increment Δ V provided in flame range territory_R:

$\left\{\begin{array}{c}\mathrm{\γ}=\arctan \left(\frac{{\mathrm{\Δe}}_Y}{{\mathrm{\Δe}}_X}\right)\\ {\mathrm{\ΔV}}_R=\frac{V_S}{2}\·\sqrt{{{\mathrm{\Δe}}_X}^2+{{\mathrm{\Δe}}_Y}^2}\end{array}\right.$

Step 5, according to described each electric thruster need provide speed increment calculate described each electric thruster liter hand over Igniting duration at point, thirdly flame range territory and southbound node, the computing formula of described igniting duration T is:

$T=\frac{2}{{\mathrm{\ω}}_E}\mathrm{arc}sin\[\frac{{\mathrm{\ω}}_E}{2}\left(\frac{{\mathrm{m\ΔV}}_i}{Fcos\mathrm{\θ}\cos \mathrm{\α}}\right)\]$

Wherein: described ω_EFor rotational-angular velocity of the earth, described m is geostationary satellite quality, described Δ V_iFor electricity thrust not Need the speed increment provided with ignition zone, described F is electric thruster thrust size.