Method of holding spacecraft in geosynchronous 24-hour orbit

FIELD: transport.

SUBSTANCE: invention relates to control over spacecraft, particularly, to holding of geosynchronous spacecraft in preset are of stay and collocation with the other geostationary spacecraft. Proposed method comprises determination and correction of initial inclinations and longitude of injection orbit ascending node with allowance for epoch of spacecraft placing in orbit and term of its active existence. Note here that the time of beginning of operation in geostationary orbit when spacecraft orbit inclination reaches maximum permissible value i_per. area. The latter corresponds to permissible reach in latitude at the boundary of nominal spacecraft stay area in altitude. Stable and minimum eccentricity magnitudes are defined. Eccentricity vector is corrected so that it equals the nominal value for spacecraft collocation and spacecraft orbit apse line is aligned with that of nodes. Spacecraft active collocation is executed at changing the inclination from 0 to i_per without interaction with adjacent spacecraft control centres. At inclination larger than i_per , eccentricity is increased to minimum with setting of Laplace vector in direction from the Sun. Note here that eccentricity vector is not corrected unless the end of spacecraft active existence term termination. At inclinations larger than i_per, eccentricity vector equals modulo and is spaced apart relative to eccentricity vectors of the other spacecraft.

EFFECT: decreased power consumption for stay area and collocation of geostationary spacecraft.

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The present invention relates to the field of space technology and can be used to keep the SPACECRAFT) longitude of the ascending node geosynchronous 24-hour orbit to keep the SPACECRAFT in a geostationary orbit, when the regulations retain the breadth and Greenwich longitude does not exceed ±0,05° relative to the working point of standing. It is considered that since Pets active existence SPACECRAFT into geosynchronous (inclined) 24-hour orbits, for such as fluctuations in longitude outside the scope of ±0,05° latitude, which are the regulations and goings of latitude beyond ±0,05° do not contradict international standards.

In the book [1] ,M. Chernyavsky, B. A. Bartenev, V. A. Malyshev, "Control of stationary orbit satellite, M., engineering, 1984, pages 42, 43, 134-136 provides a method of using the gravitational fields of the moon and Sun for purposeful change of the inclination of the orbital plane of the satellite (KA), taken as a prototype. The essence of the method is that by orbit SPACECRAFT in geostationary otolarngology orbit, in a certain way located relative to the Sun and the moon, we can provide almost twice shorter change interval inclination orbit than taking it to a strictly Equatorial orbit. The same applies to the removal of on orbit and on what anenemy, measured in degrees, correct to assume that geosynchronous 24-hour orbits.

According to this method:

1. Define initial parameters inclination i₀and longitude of ascending node of orbit launch Ω₀taking into account the age of the launch of KA D₀the orbit and the period of its active existence (CAC) t_a.with.

Selected taking into account the specific locations of the orbits of the moon and the Sun at the epoch of the D₀the initial parameter Ω₀provides for$$i_0=\frac{1}{2}\Delta i$$(Δi is the maximum change of the inclination of the orbit plane at the end of the CAC to the plane of the orbit at the beginning CAC) first reducing the inclination down to zero, and then his monotonous increase again to values of i₀. According to Δi=ƒ(D₀, t_a.c.) and Ω₀=ƒ(D₀, t_a.c.) is known by calculation, an example of such dependencies is given in [1] on page 136. Reading [1], it should be understood that the change in CAC inclination i₀=0 is equivalent to the maximum a monotonic change in the slope Δi plane of the orbit of the SPACECRAFT at the end of the CAC to the plane of the orbit at the beginning of the CAC.

2. Determine the new value of i₀decreasing the previous value of i₀the value of the maximum error of deducing the inclination δi.

3. Predicted settlement is by the orbital inclination KA at the end of CAC with a maximum error of deducing the inclination and the longitude of the ascending node of the orbit ±δi, ±δΩ.

4. From the obtained variants of the calculation, given the option [δi=0; δΩ=0], define such initial values of i₀and Ω₀when implemented maximum initial inclination is equal to the maximum target inclination at the end of the SAS.

The method involves no active correction of inclination. The optimal value for Ω₀about 270°, the end is always about 90°.

A method of using the gravitational fields of the moon and Sun for purposeful change of the inclination of the plane of the orbit should be considered the optimal helper method, which, coupled with practical tactics hold geostationary satellites longitude and latitude based on the data obtained by the trajectory measurements, is the strategy of keeping the SPACECRAFT in a given area standing (field of the operating point of standing). When calculating corrections retention geostationary satellites vector changes indicative Δi is directed into the center of the small area ε of radius r, if the vector inclination i is out of scope, and is directed in the opposite direction secular changes of mood, if i is inside this area. In the coordinates [i, Ω] i_ε=i_opt; Ω_ε=270°, where i_optoptimal value of the "aiming point" is for example equal to half the area of standing on inclination. In cases of interruption of corrections NAC is onania this strategy ensures stay SPACECRAFT in a given narrow range of latitude [±(0,05 - 0,1)°] relative to the point of standing for 30 days or more. Hereinafter, for brevity, the expression "relative to the point of standing (orbital position)" is omitted. The method has none of the disadvantages.

This paper describes a method of using a cyclic change of eccentricity within SAS using in full the above method is the passive control inclination of the orbit.

Currently, in addition to actually hold geosynchronous SPACECRAFT in the specified area of longitudes, requires work on collocation (safe coexistence) spacecraft are in the same area standing. The collocation should be considered as a method of restraint. There is a method of cluster management are in geostationary orbit satellites (EN 2284950 C2). According to this method, including the measurement of the parameters of the orbit of each SPACECRAFT, determining them to the current values of the orbital elements of each KA, comparing them with the required and carrying out correction of the orbital period, inclination and eccentricity of the orbit maneuvers on each of the SPACECRAFT performed using thrusters, translating vectors indicative KA in spaced relation to each other [ring] the field of the allowable changes so that the angle between the line connecting the current position of the end of each vector with the center line is adequate to him annular area, and the Sun was equal increased by 180° the value of the right ascension of the Sun, at the same time carry out correction of the eccentricity vectors to translate these vectors are spaced from each other, the annular area of their allowable changes so that the line connecting the current position of each vector from the center of the annular region (hereinafter options):

1 - lagged from the direction to the Sun at half the angular distance when the motion vector of eccentricity around the circumference of natural drift within the annular area, then the entire flight produce a change in the relative distance between the SPACECRAFT in the required limits at the expense of compensation quasivector increment vector indicative of each SPACECRAFT in combination with correction of the eccentricity vector, in which at the moment of passing the vector eccentricity of the middle of the interval between the entry point of the circumference of natural drift in the annular region of permissible variation of the eccentricity vector and the exit point of the line connecting the center of the circle natural drift and the center of the annular region of permissible variation of the eccentricity vector, coincides with the direction of the Sun, thereby leading to the constancy of the relative vectors mood and eccentric is ricetta between the SPACECRAFT;

2 is coincided with the direction to the Sun, then the entire flight produce a change in the relative distance between the SPACECRAFT in the required limits at the expense of compensation quasivector increment vector indicative of each SPACECRAFT without correction of the eccentricity vector, thereby leading to the constancy of the relative vectors inclination and eccentricity between the SPACECRAFT.

Here the circle of natural drift" - the circle of radius sustainable eccentricity (definition and derivation of the formula (14'), see below).

The essence of this method is to synchronize the motion of the SPACECRAFT in the phase planes [i_x; i_y] and [e_x; e_y] where i_x=i·cosΩ; i_y=i·sinΩ; e_x=e·cos(Ω+ω); e_y=e·sin(Ω+ω); ω is the argument of latitude of perigee, and synchronize the motion of the SPACECRAFT in both planes, considering that the mutual orientation of the relative vectors of the eccentricity and inclination of ΔΕ and ΔI 2-3 KA is saved if you use the annual cycles of the natural drift of the vector of eccentricity and semi-annual periodicity vector indicative provided compensation secular component of the natural drift vector inclination. Both cycles owe their existence exclusively to the Sun, for the initial and ongoing orientation vectors inclination and eccentricity relative to the Sun is essential DOS is to achieve a technical result.

We propose a method that does not require synchronization of the change vectors indicative (which is very important for geosynchronous SPACECRAFT without adequate energy supply) and does not require concerted action to control the movement of the SPACECRAFT.

The aim of the invention is:

a) in the absence of collocation - guaranteed retention of geosynchronous SPACECRAFT in the field of ±(0,1-0,05)° in longitude of the ascending node of the orbit without constraints on the inclination (variations in latitude from ballistics;

b) guaranteed collocation KA with other SPACECRAFT in a narrow region;

C) multiple fuel savings on hold in comparison with the cost of fuel on geostationary satellites, without loss of solution quality targets in orbit.

Last may, when on Board the SPACECRAFT is the antenna drive system. But it is always there even on geostationary satellites for narrow beam antennas. The same in principle, the system features and tools, ground control and communications. You want only certain way to program it work turn on the motion of the SPACECRAFT. As for global antennas, each antenna drive system is not required in principle.

Fuel on Board never never too much, the launch mass of the SPACECRAFT at altitudes of ~36,000 km tends to increase, therefore, the claimed method of deduction KA is relevant is diversified and even alternative in the choice of the existence of KA - or geosynchronous 24-hour orbit, or geostationary orbit.

This objective is achieved in that in the method of keeping the SPACECRAFT in geosynchronous 24-hour orbit, including the definition of initial parameters inclination and longitude of ascending node of orbit launch taking into account the age of the launch SPACECRAFT into orbit and the period of its active existence, defining a new value of the initial inclination decreasing the previous value to the value of the maximum error of deducing the inclination, the prediction calculation, the values of the orbital inclination of the SPACECRAFT at the end of the active lifetime with a maximum error of deducing the inclination and the longitude of the ascending node of the orbit determination of the initial values of the inclination and longitude of ascending node, when implemented maximum initial inclination is equal to the maximum target inclination at the end of the active lifetime of the new transactions that determine the amount of sustainable eccentricity e_mouthfor AC output; determine a preliminary value of the minimum eccentricity e_minas the sum of the maximum permissible eccentricity while keeping the SPACECRAFT longitude at zero inclination (geostationary orbit) and the relationship of the radius of the exclusion zone between the SPACECRAFT, occupying the same working the th position in orbit, to the radius of the geostationary orbit; determine the locus of the change of the eccentricity vector under the action of radiation pressure in the polar coordinate system [f, θ], where θ is the angle between the directions of the sun in the initial period (the end date of bringing into the area of standing) and perigee orbit, the polar axis is directed from the center of the Earth to the Sun and includes a radius-vector of e_minwhere θ is zero, the polar distance equal to the eccentricity vector polar distances during the year, describes a circle of radius e_mouthand, knowing the amplitude of the oscillation angle θ, specify the value of e_minand hodograph in General; after the SPACECRAFT at geosynchronous 24-hour orbit and determine the actual motion parameters define the term, "0", during which the actual initial inclination is reduced to zero; to determine the locus of the optimal value of the vector of initial eccentricity e₀at the initial epoch at which the line of apses is aligned with the radius vector of the Sun, and annual cyclic evolution of the vector e [f,θ], in the absence of a negative impact on them active forces guarantee at maturity "0", the minimum difference between the vectors e and e_min; at the stage of bringing the SPACECRAFT into the specified area of standing simultaneous correction of the orbital period and eccentricity bring the actual current C is Uchenie vector to the calculated eccentricity e ₀; on stage, hold, closer to the deadline "0" conduct clarification-time mode of operation in geostationary orbit, when the inclination of the orbit of the SPACECRAFT will reach the maximum allowable inclination of i_beforeat which the output of latitude for the limit value for geostationary satellites is on the border of the nominal area of standing in longitude; correction of the eccentricity vector so that it was rated for collocation KA in the specified area of standing, and the line of apsides of the orbit of geosynchronous SPACECRAFT coincided with the line of nodes of the orbit; over time, while the inclination produces the evolution in the range [0-i_before], are actively collocation KA without interaction with the control centers of adjacent SATELLITES; when greater inclination i_beforeincrease the eccentricity to e_minwith the installation of the Laplace vector in the direction from the Sun and in the remaining time before the end of the active lifetime correction of the eccentricity vector is not carried out; in the absence of collocation at the stage of bringing the conduct simultaneous correction of the orbital period and eccentricity, so that the current eccentricity equal sustainable; smaller inclination to the value of i_beforespend correction of eccentricity to e_techwas not more acceptable excentrica the ETA while keeping the SPACECRAFT longitude (≡PL.min longitude for areas of standing ±0,05°), with increasing inclination to the value of i_beforerestore the eccentricity to e_mouthwith the installation of the Laplace vector in the direction of the Sun and in the remaining time before the end of the active lifetime correction of the eccentricity vector is not performed.

The essence of the method are as follows.

1. Collocation with geostationary satellites

If we consider that in the interval between trajectory measurements 7 days the error in the determination and prediction of the position along the orbit δl is 4.5 km ([2] JSC "ECA". Scientific and technical report. The development of the technology and performance evaluation of navigation-ballistic ensure flight KA PM on the stage of flight tests, M.,2010, page 82), multiply it by two (have a bug positioning KA pairs) and add 1 km (warranty excluding any accidental), receive a guaranteed exclusion zone both KA S_z= 10 km on all key areas. The value of$$\Delta e_{z_0}$$relationship S_zto the nominal radius (r_article) geostationary orbit 42164 km is the minimum difference eccentricities when matching the directions on perigee (vector Laplace) and the minimum amount in diametrically opposite directions at Perigueux is - 0,00024 - 0,0003 that prevents geosynchronous and geostationary satellites to converge at a distance of less S_min= 10 km in areas of standing longitude ±0,05° or more for any values of i, Ω, provided that the argument of latitude of perigee (ω) geosynchronous orbit SPACECRAFT does not exceed ±(20-30)° relative to the zero or 180°, i.e., the line of apsides of the orbit of geosynchronous SPACECRAFT is in coincident position relative to the line of nodes, which is confirmed by calculations of the inter-satellite distances, shown in Fig.1-3 (Fig.1: i₁=5°, i₂=0; Ω₁=Ω₂=270°, ω₁=ω₂=0, e₁=0,0006, e₂=0,0003; Fig.2: i₁=4'30", i₂=4'30", Ω₁=0, Ω₂=90°, ω₁=0, ω₂=135°, e₁=0,0004, e₂=0,0001; Fig.3: i₁=30", i₂=30", Ω₁=Ω₂=0, ω₁=180°, ω₂=0, e₁=0,00015, e₂=0,00015; the index "1" refers to geosynchronous SPACECRAFT). If we add to this value$$(\Delta e_{z_0})$$the maximum possible eccentricity e_SSwhen holding geostationary satellites calculated by the formula (all components of the formula in radians):

$$e_{d\mathrm{about}p}=\left(\Delta {\lambda }_{n\mathrm{about}m}-\delta {\lambda }_{\mathrm{about}pp}-\delta {\lambda }_{ypp}\right),\left(1\right)$$

where Δλ_Mr.- half the width of the rated (this) area of standing in longitude;

δλ_ODA=δl/r_article- the error in the determination and prediction of the motion of the SPACECRAFT along the

orbit;

δλ_panelthe degree of freedom in managing retention in longitude, of the order of ±(0,01-0,015), get popular later minimum eccentricity e_minfor SPACECRAFT in geosynchronous 24-hour orbit. For areas of standing ±0,05° f_SS≤0,0003, and e_min≤0,0006. An important value that gives the possibility to calculate the initial eccentricity vector e₀. Up until the inclination of the orbit of geosynchronous SPACECRAFT will not fall from the initial (5-7,5)° (depending on CAC CA) to several minutes (for example - 4,5 coal.min for areas of standing longitude ±(0,1-0,05°)), it is possible not to take into account fluctuations in longitude due to the inclination and eccentricity. The latter is possible because the output of the nominal area of standing in longitude at latitudes greater than the norm for geostationary satellites, should not be considered a violation of international the underwater regulations, because at a certain time on orbit geosynchronous SPACECRAFT is unspecified by the rules of space and really doesn't hurt anyone.

At the stage of bringing the SPACECRAFT into the specified area of standing in the very sparing mode, when only extinguished passive drift in this area (~2°/day), produces the pulse velocity increment of about 17 m/s For the creation of eccentricity from zero to (e_min+2e_mouth)≈0,00150 required, based on the formula [3], Erica K. "Space flight", T. II, part 1, page 388, the velocity increment

$$\Delta V_T=\frac{\Delta e\cdot V}{2+2\Delta e}=\mathrm{2,38}m/\mathrm{with\; a},\left(2\right)$$

where Δε=e_max=(e_min+2E_mouth)=0,0015;

V is the velocity of the motion of the SPACECRAFT in a circular orbit, 3074 m/S.

Correction of eccentricity, of necessity, combined with correction of the orbital period, so the energy consumption for the implementation of the initial eccentricity are not independent and the total energy consumption for conversion do not increase.

2. Hold geosynchronous SPACECRAFT relative to a given point of standing on the same terms on which the UD is Givaudan geostationary satellites, without correction of the inclination in General and with minimal correction of the eccentricity during the active lifetime. Due to the inclination, already 5 more coal.min, you can have a large orbital eccentricity, which gives the opportunity not to carry out correction of the eccentricity (see item 10, Fig.8).

The energy consumption for the correction of eccentricity are not significant in the overall fuel budget and, if not urgency of implementation of these corrections, can be combined with the correction of the orbital period of the SPACECRAFT.

We introduce the notion of sustainable eccentricity.

The influence of small pulse velocity (velocity increment per second)$${\stackrel{}{\vartheta }}_0$$the eccentricity e and argument of latitude of perigee ω is described by the formulae [3], page 388 (see Fig.6, numerals showing: 1 - Sun; 2 - Ground; 3 - KA; 4 - orbit SPACECRAFT at the current epoch; 5 - perigee orbit; 6 - orbit SPACECRAFT in an era when the center of the Earth, perigee and the Sun are on the same line; 7 - the radius of the big circle e_mouth), taking into account the tangential and normal perturbations in the orbit plane:

$$\frac{de}{dt}=2\cdot \left(e+\cos \eta \right)\frac{{\stackrel{}{\vartheta }}_0}{\vartheta }\cdot \sin \alpha -\frac{{\stackrel{}{\vartheta }}_0}{\vartheta }\cdot \sin \eta \cdot \cos \alpha ;\left(3\right)$$

$$\frac{d\omega }{dt}=\frac{2\sin \eta }{e}\cdot \frac{{\stackrel{}{\vartheta }}_0}{\vartheta }\cdot \sin \alpha +\frac{2e+\cos \eta }{e}\cdot \cos \alpha ,\left(4\right)$$

where ϑ is the average speed of motion of the SPACECRAFT, 3074 m/s;

η = α - θ is the true anomaly;

θ is the angle between the direction of the Sun and the perigee of the orbit of the SPACECRAFT.

Then, substituting the expression for η in (3) and using the formula for the difference of two angles, we obtain:

The first component, at least two orders of magnitude smaller than the rest and is not a permanent member, then

$$\frac{de}{dt}=\frac{{\stackrel{}{\vartheta }}_0}{\vartheta }\cdot \left(\frac{1}{2}\cdot \sin 2\alpha \cdot \cos \theta +{\sin }^2\alpha \cdot \sin \theta +\sin \theta \right).\left(6\right)$$

When θ = 0

$$\frac{de}{dt}=\frac{1}{2}\cdot \sin 2\eta \cdot \frac{{\stackrel{}{\vartheta }}_0}{\vartheta }.\left(7\right)$$

Similar reasoning, we will have to speed (argument of latitude of perigee:

$$\frac{d\omega }{dt}=\frac{1}{e}\cdot \frac{{\stackrel{}{\vartheta }}_0}{\vartheta }\cdot \left(-\frac{1}{2}\cdot \sin 2\alpha \cdot \sin \theta +{\sin }^2\alpha \cdot \cos \theta +\cos \theta \right).\left(8\right)$$

When θ = 0

$$\frac{d\omega }{dt}=\frac{{\stackrel{}{\vartheta }}_0}{e\cdot \vartheta }\cdot \left(1+{\sin }^2\eta \right).\left(9\right)$$

Next,

$$dt=\frac{d\alpha }{n-n},\left(10\right)$$

where- the average motion of the SPACECRAFT, with^-1;

then

Integrate on the day (on the circuit):

Will assess$${\stackrel{}{\vartheta }}_0$$. Light pressure is described by the formula

$$P=\frac{S\left(1+A\right)}{c},\left(15\right)$$

where S is the power of the light wave incident on a 1 m²body surface, W/m²;

And the reflection coefficient (A=0 for absolute black body);

C - light speed, km/S.

S=1,4·10³W/m².

The value of a depends on the reflectivity of the details in the design of SPACECRAFT and in the context of this technical solution must include (conditionally) the gravitational influence of the Sun as "±" position, when the vector Laplace aimed at the Sun. For real KA at the height of the stationary orbit values And are within [of 0.28 to 0.44]. On the basis of A = 0,44, we will have R, R the main 6,72·10 ^-6n/m². Because the force of radiation pressure F=S'·P, where S' is the area of the fuselage mid-section, then

$${\stackrel{}{\vartheta }}_0=a=\frac{S\text{'}}{m}\cdot P.\left(16\right)$$

The ratio of$$k=\frac{S\text{'}}{m}$$for modern domestic geostationary satellites more or less constant and equal order (2,3-2,6)·10^-2. Then, for example, when k=0,0259$${\stackrel{}{\vartheta }}_0\mathrm{0,174}\cdot {10}^{-6}m/{\mathrm{with\; a}}^2.$$As shown by numerical integration, the period of recurrence for eccentricity is a few more years about 390 days. This is due to the fact that perturbations of the motion of the perigee at sustainable eccentricity from the gravitational field of the Sun are not annual and semi-annual period with the amplitude of the oscillations, as shown by separate integration, order 0,00005. Substitution$${\stackrel{}{\vartheta }}_0$$in equation (14') gives if$$\frac{2\pi }{390}$$the value e = e_mouthorder 0,00045, i.e. to the speed of movement of perigee equal to the velocity of movement of the Sun, you must have a stable eccentricity. The original formulas (13-14') provides for the disclosure of the essence of the concept of sustainable eccentricity.

The energy consumption for maintaining the e_mouthpractically absent: each year it is necessary to perform correction of the eccentricity on the value of its old care Δe = 0,000052 by decentralist the Earth's gravitational field. This is a very small value, commensurate with the daily care of the eccentricity due to the combined effect of all passive disturbing factors, however, if the age-old care not to compensate, the current eccentricity by the end of the CAC will be far from sustainable.

Implementation of the proposed method involves the following sequence of operations:

1. Determine the initial values of the inclination and longitude of ascending node of orbit launch.

This operation is similar to the total sequence of operations 1-4 prototype.

2. Determine the amount of sustainable eccentricity to be displayed on the orbit geesin the electronic KA.

The operation is the calculation of e_mouthon the basis of the formulas (14', 15, 16) taking into account the real data on the reflectivity of the details of the construction of KA (mainly solar panels), the average square fuselage mid-section and mass of the SPACECRAFT. The influence of the gravitational effects on the SPACECRAFT, the Sun can not be considered at the annual interval, but at the end of the yearly period to adjust the position of the perigee in the direction of the Sun. To adjust will have no more than (4-5)°, which will require no more than to 0.055 m/s, which does not exceed 2% annual fuel budget restraint in longitude in the functioning of the AC for the intended purpose and 0.09% of the fuel of the annual budget when compared with geostationary satellites, held in latitude (inclination).

3. Determine a first approximation of minimum eccentricity, which is implemented on an annual interval.

The minimum value of the eccentricity e_mindetermined from the relationship:

$$e_{\min }=e_{d\mathrm{about}p}+\frac{S_Z}{r_{cm}},\left(17\right)$$

as the sum of the maximum is about allowable eccentricity e _SSwhen holding the SPACECRAFT longitude when the orbital inclination is close to zero, calculated by the formula (1), and the relationship of the radius of the exclusion zone between the SPACECRAFT in the state of collocation to the radius of the geostationary orbit. Since e_min>e_mouththe center of the polar coordinate system made for great circle hodograph (see item 5).

4. Spend trajectory measurements.

Trajectory measurement is carried out after the SPACECRAFT in geosynchronous orbit. This operation is typical for all SAS.

5. Define (build) the locus of the change of the eccentricity vector under the action of light pressure.

Schematic diagram of the locus shown in Fig.7. Introduced the following notation:

1 - vector e;

2 is a vector of minimum eccentricity e_minaimed at the Sun;

3 is a vector of maximum eccentricity e_maxaimed at the Sun;

4 - the pointer movement direction counterclockwise vector e_mouth;

5 - a large circle described by the ends of the vectors e and e_mouth;

6 - current vector e_mouth.

A large circle hodograph is divided into equal parts, representing time intervals (day, week). Knowing the current date and the value of e, you can always tell when we will have those or other real values of the eccentricity and the angle θ of deviation of the Laplace vector (direction of the perigee) from healthy lifestyles is to the Sun.

The ratio of e_min/e_maxhodograph guarantees the amplitude A_θ= 48° oscillation angle θ (Fig.7) (fluctuations within ±24° relative to the zero - initial direction of the Sun), which corresponds to the same fluctuations in the line of apses relative to the line of nodes, ascending node, which is fixed in space, according to the prototype, first in the region of 270°, and from mid-CAC - around 90°, due to the choice of initial parameters excretion (operation 1). These oscillations is comparable with the access to care line of apses of the line of nodes of the orbit of the SPACECRAFT, which is in the state of collocation with other SPACECRAFT from the moment of bringing to the point of standing. In this regard, check the value of Δe_zfor dismissing the argument of latitude of perigee at 24°. In Fig.4, Fig.5 shows the worst ways of calculating the inter-satellite distances: Fig.4 - i₁=30"; i₂=30" (value indicative of no importance); Ω₁=Ω₂=0; ω₁=336°; ω₂=24°; e₁=0,00068; f₂=0,00030; Fig.5 - Ω₁=Ω₂=0; ω₁=336°; ω₂=90°; e₁=0,00068; f₂=0,00030, in which, however, the inter-satellite distance Sz is greater than 10 km. are Finally going to have Δε_z= 0,00038 (which is optimal for operation at diametrically spaced perigee orbits: e₁=e₂=0,00019 and (Ω+ω)₁=(Ω+ω)₂±180°), e_min=0,00068, e_max≈0,00158 (depending on the particular meant is I e _mouth), or, to be more precise (see page 7,$$\Delta e_{z_0}$$=0,00024), Δε_z=0,00032, e_min=0,00061, e_max≈0,00151. The angle θ (Fig.7) varies in the same range: ±24° relative to zero.

6. Define the term of "0" during which implemented the initial inclination will decrease to zero.

This is a great period, calculated in years. Although we are actually interested in the period during which the inclination will decrease to a certain value of i_beforeaverage of several angular minutes, there is no need to define it at the initial stage of operation of the AC, because it still has to be clarified.

7. Determine the optimal value of the vector of initial eccentricity e₀at the initial epoch.

The hodograph at the inception of KA for the intended purpose defined two values: e_mine_maxdiverging 180° and satisfying the condition of alignment of the line of apses with the radius vector of the Sun.

From these two vectors eccentricity choose one - e₀whose evolution at maturity "0" guarantees the minimum difference between the current vector e and e_minand will require carrying out correction of the current vector eccentricity up to par for collocation in C is this area of standing values (e _Mr.) with the lowest energy consumption.

Paragraphs 5-7 may require restrictions on launch date. Launches of satellites will probably be held in the "open" winter and summer solstices. However, placing restrictions on the starting date, for whatever reasons, is a common practice. So, the value of e₀remove from seismic data.

8. At the stage of bringing the SPACECRAFT into the specified area of standing simultaneous correction of the orbital period and eccentricity bring the actual current value to the calculated eccentricity e₀thus combining the line of apses with the line of nodes.

9. At the stage of retention spend clarification transfer time AC mode operation in geostationary orbit.

The refinement is carried out towards the end of the period of "0".

10. Determine the limit value of the inclination i_beforeat which the output of latitude for the limit value for geostationary satellites is on the border of the nominal area of standing in longitude.

The inclination of i_beforeyou need to know and achieve the indicative values of i_beforemove on hold (possibly collocation) in the conditions of active existence of geostationary satellites, because, if not in the specified area of standing in latitude and longitude, in related fields are (can be) geostationary satellites, and there is a norm (DHL is a COP) of the width of the field standing in a geostationary orbit. For arbitrary areas of standing in relation to the Central point

$$i_{pped}=2e_{\min }\cdot \frac{\Delta {\phi }_{n\mathrm{about}m}}{\Delta {\lambda }_{n\mathrm{about}m}}+arctg\left(\frac{1-\cos \Delta {\phi }_{n\mathrm{about}m}}{2\sqrt{\cos \Delta {\phi }_{n\mathrm{about}m}}}\right),\left(18\right)$$

where ±Δφ_Mr.and ±Δλ_Mr.respectively the nominal area of standing KA in latitude and longitude. The first element directly follows from the geometry of the total area of standing, the second takes into account variations in longitude due to the orbital inclination. For the region of ±(0,1-0,05)° i_before=4,5 coal.min (see Fig.8).

Correction Greenwich longitude of the ascending node (the same correction period KA) plan so that a graph of the vector eccentricity according to the hodograph strictly observed.

11. When reducing the current inclination to limit values Provo is Yat correction of the eccentricity vector.

The current vector eccentricity transferred to the nominal vector e_Mr..

12. Are actively collocation KA (unlike passive colocasia, when the combination of the line of nodes and the line of apses within ±24° occurred automatically without interaction with the control centers of adjacent SATELLITES.

Typically, the active collocation KA spend on approved schemes. All schemes equivalents are reduced to ravnoudalenie aiming points of the vectors e_n[e_n,(Ω+ω)_n] (n=1,2,...) and i_n[i_n,Ω_n] (n=1,2,...) in the corresponding phase planes KA and maintenance of all vectors e_nand i_nwithin their respective areas of selected radii, the centers of which are appropriate aiming point. The ideal option is for the two SPACECRAFT separation longitude of the ascending node (Ω_nand direct ascents perigee (Ω+ω)_naiming points 180°, and the arguments of latitude of perigee KA should be close to zero. For three KA figure 180 replace 120.

Operation 12 is an essential and distinctive feature of the invention. Its essence boils down to the following:

a) for the purpose of active collocation does not need to do the correction vectors inclination nor geostationary satellites, neither of geosynchronous SPACECRAFT, it is sufficient to maintain the line of apsides of the orbit only geosynchronous SPACECRAFT in C the data within the line of nodes of its orbit carrying out correction of the eccentricity vector, i.e.

$$\omega =\pm \frac{1}{2}{A}_{\theta },\left(19\right)$$

or

$$\omega =\pi \pm \frac{1}{2}{A}_{\theta },\left(20\right)$$

and, because the value of Δe_z≥e_SSand more e_Mr.then the best option is active collocation will be the diversity of perigee orbits of the two SPACECRAFT at 180° (Fig.3, page 7), when

$$\omega =\pi \pm \frac{1}{2}{A}_{\theta },\left(21\right)$$

(of Fig.9: i₁=i₂=1', Ω₁=90°, Ω₂=0°, ω₁=45°, ω₂=315°, e₁=0,00019, e₂=0,00019),

despite the fact that active collocation current within not more than two months;

b) there is no need for interaction with the control centers of adjacent KA, relatively simple because adaco explode eccentricity vectors (or vectors Laplace) can be solved by monitoring data on tactics and strategies to retain adjacent KA (for example, using the international system of tracking NORAD) and the adaptation control geosynchronous SPACECRAFT to the data that may be more effective than trying to establish close contact with the control centers of adjacent SATELLITES.

13. As soon as the inclination becomes larger i_beforeincrease the eccentricity to a value of e_minwith the installation of the Laplace vector in the direction from the Sun and in the remaining CAC time correction of the eccentricity vector is not performed.

14. In the absence of collocation at the stage of bringing the conduct simultaneous correction of the orbital period and eccentricity, so that the current eccentricity equal sustainable.

15. With decreasing inclination to the value of i_beforecarry out correction of the eccentricity so that the current eccentricity was no more valid when you hold the SPACECRAFT in longitude.

16. With increasing inclination to the value of i_beforerestore the eccentricity to a steady value with the installation of the Laplace vector in the direction of the Sun and in the remaining CAC time correction of the eccentricity vector is not performed.

Note that according to the prototype of the initial and final values of the longitude of ascending node of the orbit, respectively 270° and 90°, moreover, the transition from Ω₀for Ω_tooccurs abruptly, so the combination of n is all CAC line of nodes and the line of apses of geosynchronous SATELLITES (action on p. 13 corresponds to the given installation) guarantees the successful coexistence of multiple SPACECRAFT in a given area standing.

Note again that the energy consumption for the correction of eccentricity are not independent and the total energy consumption does not increase.

The proposed method of keeping the SPACECRAFT longitude in the geostationary 24-hour orbit provides:

1 - hold the longitude of the ascending node of the orbit without energy correction of eccentricity;

2 - guaranteed collocation KA with other SPACECRAFT in the field of the operating point of standing in longitude;

3 - reduction of the order of the inputs on hold against geostationary satellites due to the complete exclusion of corrections inclination;

4 is a principled alternative to the geostationary orbit.

The way to keep the spacecraft (SC) into geosynchronous 24-hour orbit, including the definition of initial parameters inclination and longitude of ascending node of orbit launch taking into account the age of the launch SPACECRAFT into orbit and the period of its active existence, defining a new value of the initial inclination decreasing the previous value to the value of the maximum error of deducing the inclination, the prediction calculation, the values of the orbital inclination of the SPACECRAFT at the end of the active lifetime with a maximum error of deducing the inclination and the longitude of the ascending node of the orbit determination of the initial values of the inclination and longitude of ascending node, when the maximum real who organized the initial inclination is equal to the maximum target inclination at the end of the active lifetime, wherein the determining the magnitude of the steady eccentricitye_mouthfor AC output, determine a preliminary value of the minimum eccentricitye_minas the sum of the maximum permissible eccentricity while keeping the SPACECRAFT longitude at zero inclination in the geostationary orbit and the relationship of the radius of the exclusion zone between the SPACECRAFT, occupying the same working position in orbit to the radius of the geostationary orbit, determine the locus of the change of the eccentricity vector under the action of radiation pressure in the polar coordinate system [e,θ], where θ is the angle between the directions of the sun in the initial period (the end date of bringing into the area of standing) and perigee orbit, the polar axis is directed from the center of the Earth to the Sun and includes a radius-vectore_minwhere θ is zero, the polar distance equal to the eccentricity vector polar distances during the year, describes a circle of radius e_mouthand, knowing the amplitude of the oscillation angle θ, specify the value of e_minand hodograph in General; after the SPACECRAFT at geosynchronous 24-hour orbit and determine the actual motion parameters define the term, "0", during which the actual initial inclination is reduced to zero; at the specified locus determine the optimal value of the vector began the aqueous eccentricity e₀at the initial epoch at which the line of apses is aligned with the radius vector of the Sun, and annual cyclic evolution of the vectore[e,θ], in the absence of a negative impact on them active forces guarantee at maturity "0", the minimum difference between vectorseande_minat the stage of bringing the SPACECRAFT into the specified area of standing simultaneous correction of the orbital period and eccentricity bring the actual current value of the eccentricity vector to the estimatede_0,on stage, hold, closer to the deadline "0" conduct clarification-time mode of operation in geostationary orbit, when the inclination of the orbit of the SPACECRAFT will reach the maximum allowable inclination of i_beforeat which the output of latitude for the limit value for geostationary satellites is on the border of the nominal area of standing in longitude correction vector eccentricity so that the eccentricity equal to the nominal for collocation KA in the specified area of standing, and the line of apsides of the orbit of geosynchronous SPACECRAFT coincided with the line of nodes of the orbit, during the time until the inclination produces the evolution in the range [0,i_before], are actively collocation KA without interaction with the control centers of adjacent KA, when the inclination is greater than i_beforee_minwith the installation of the Laplace vector in the direction from the Sun and in the remaining time before the end of the active lifetime of the correction vector eccentricity does not hold in the absence of collocation at the stage of bringing the conduct simultaneous correction of the orbital period and eccentricity, so that the current eccentricity equal stable, decreasing inclination to the value of i_beforecarry out correction of the eccentricity of the ordere_techwas not more than the allowable eccentricity while keeping the SPACECRAFT longitude.