RU2562908C2 - Method of control over active space object to be docked to passive space object - Google Patents

Abstract

FIELD: transport.

SUBSTANCE: invention relates to space engineering and can be used during approaching and subsequent docking of two space objects. The method includes determination of departure impulse amount and place of application before active spacecraft (ASO) transfer to trajectory of flight to other celestial body based on condition of ASO crossing the orbit of passive spacecraft (PSO). Then the ASO is transferred to the orbit of other celestial body by means of simultaneous application to it a braking impulse (to provide specified orbit height parameters) and lateral impulse (to align planes of docking objects orbits). Against large braking impulse, insignificant lateral impulse will not virtually cause increased fuel consumption by ASO, but will significantly reduce time of ASO flight till docking to PSO.

EFFECT: reduced period of approaching to PSO and lower fuel consumption.

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Description

The proposed control method can be used in space technology during the approach and subsequent docking of two space objects located in the orbits of various celestial bodies, for example, a spacecraft (SC) located in orbit around the Earth as an active space object (AO) and an orbital station (OS) ) located in orbit around any celestial body, such as the Moon (VOC) as a passive space object (FFP).

A known control method, selected as an analogue, in which to ensure convergence and subsequent docking of two space objects, the AKO is displayed in the plane of the orbit of the FFP. After deducing, the AKO is transferred to the so-called phasing orbit located between the initial orbit of the AKO and the orbit of the FFP to eliminate the initial angular mismatch between the two objects, because being in different orbits, the AKO and FFP have different angular velocities of rotation around the celestial body. After several turns (the number is determined by the selected ballistic approach circuit), the AKO, using a two-pulse maneuver, is transferred to the vicinity of the FFP, where the approach is completed by automatic docking. This method of controlling an active ship is used when approaching and docking the spacecraft with the OS [1. R.F. Appazov, O.G. Sytin, "Methods of designing the trajectories of carriers and satellites of the Earth", Nauka, Moscow, 1987]. The main disadvantage of this control method is that for the transition of the ACS from the orbit to the orbit of the FFP and the convergence, it is necessary to spend additional fuel on the transition from the phasing orbit to the orbit of the FFP and the time for phasing.

A known control method, selected as a prototype, includes a sequential application to an AQS located in the orbit of one celestial body of the take-off impulse V _exl and the brake impulse V _brakes to go into the orbit of another celestial body with specified parameters in height and position of the orbit plane. This method of controlling an active ship was used during lunar missions under the Apollo program [2. IN AND. Levantovsky "The mechanics of space flight in an elementary exposition", Nauka, Moscow, 1970].

The first take-off impulse V _excursion transfers the AKO from the orbit of an artificial Earth satellite (AES) to a transitional orbit along the flight path to the Moon, providing at the end of the flight a predetermined position of the orbit plane, determined by the inclination i and the longitude of the ascending node Ω of the _VU , as well as the required height of resettlement. The second braking impulse V _brake , performed in perisection against the velocity vector, ensures the AKO transition to the target orbit of the artificial moon satellite (ISL) with the specified altitude parameters.

The disadvantage of this method is the low likelihood of AKO getting directly into the vicinity of the FFP, which will require additional time and fuel for subsequent phasing for the final approach of objects.

The technical result of the invention is to reduce the duration of the approach to the FFP located in the orbit of another celestial body and reduce the cost of fuel for the approach.

The technical result is achieved due to the fact that in the method of controlling the motion of the ACS that is interfaced with the ACS, which includes the sequential application to the ACS located in the orbit of one celestial body of the take-off impulse V _exc and the braking impulse V _brakes to go into the orbit of another celestial body with specified height parameters and the position of the orbital plane, in contrast to the known one, before transferring the AKO to the flight path to another celestial body, the magnitude and place of application of the take-off impulse V _exc is determined on the basis of the crossover condition cheniya ACH FFP orbit while finding objects in the vicinity of the orbits of the intersection point, whereupon ACH translate the orbit of another celestial body by the simultaneous application thereto braking pulse V _Brk for given parameters of orbit altitude and lateral momentum ΔV _used for combining orbital planes abutting objects calculated by the formula

where V ₀ is the orbital velocity of rotation of the FFP around another celestial body;

ΔΩ _WU - the difference in the longitudes of the ascending nodes of the orbits of the joined objects;

i - the inclination of the orbit of the FFP;

u is the argument of the latitude of the FFP at the intersection point of the orbits of the joined objects.

The technical result in the proposed control method is achieved in that the take-off impulse V _exc is determined on the basis of the condition that the AKO and FFP, having a mismatch between the orbit planes, simultaneously arrive in the vicinity of the intersection point of the orbits at the time of the execution of the braking impulse V _brake . After the simultaneous application of the braking impulse V _brake and the lateral impulse ΔV _b , the angle between the orbit planes of the ACS and the ACS is eliminated. As a result, the AKO is in the vicinity of the FFP without additional fuel costs and time for phasing and subsequent rapprochement. The invention is illustrated in figure 1 ÷ 4 and table 1 ÷ 2,

where figure 1 shows the approximation scheme of the spacecraft, as AKO with the OS, as the FFP;

figure 2 shows a diagram of the launch of spacecraft "Apollo-11" from near-Earth orbit to the target near-moon orbit;

figure 3 shows the mutual geometry of the orbits of the spacecraft and the VOCs located in polar orbits (i = 90 °) with a difference in longitude of the ascending node of the orbit ΔΩ _WU ,

figure 4 shows the mutual geometry of the intersecting orbits of the spacecraft and the VOCs with different inclination and position of the ascending nodes of the orbit;

Table 1 for a hypothetical case presents the results of numerical integration of a plane flight into the polar orbit of the ISL with an inclination of i = 90 °, including the time of launch from the Earth and the time of the take-off impulse V _departing to the Moon in UTC (Universal Time Coordinated), the flight time ΔT, the longitude of the ascending node of the orbit Ω _WU , the magnitude of the take-off impulse V _exc and the braking impulse V _brake ;

Table 2 shows the characteristics of flights with different times of arrival of ISL into orbit relative to the nominal flight to the polar orbit of ISL with the longitude of the ascending node Ω _WU = 154 °, presented in Table 1, where Δt is the relative change in the time of arrival into the orbit of ISL, u - the argument of the latitude of the arrival point, Ω _WU - the longitude of the ascending node of the orbit, the magnitude of the take-off pulse VOTJ1 and the braking pulse V _brakes , Δt _st and Δt _exc - the change in the start time and the output time of the take-off impulse V _exc compared to the nominal flight, ΔT - flight time to the moon.

Figure 1 shows a well-known approximation scheme QC with the OS. The spacecraft is put into orbit (position 1), which coincides with the OS orbit plane (position 2) with the initial phase angle F. After the first two-pulse maneuver (V ₁ and V ₂ ), the spacecraft passes into the phasing orbit (position 3), for elimination of angular mismatch, after which, by conducting a two-pulse maneuver (V ₃ and V ₄ ), the spacecraft is transferred to the vicinity of the OS (pos. 4).

Figure 2 shows the well-known flight scheme of the spacecraft "Apollo-11" to the orbit of the ISL. First, the spacecraft is launched (pos. 1) into the satellite orbit (pos. 2). The first take-off impulse V _{exclusion of the} spacecraft is transferred to the transitional orbit (pos. 3) for the flight to the moon. The magnitude of this pulse is ~ 3150 m / s. Flight duration ~ 3.5 days. When the orbit around the moon is _{overpopulated by the} second braking impulse V _brake (~ 900 m / s), which is directed against the speed of movement, the spacecraft is transferred to the ISL orbit (item 4).

Figure 3 presents a spherical image of the intersecting polar orbits of the spacecraft (pos. 1) and VOC (pos. 2), differing in the longitude of the ascending node of the orbit by the angle ΔΩ of the _VU . At the time of application to the brake pulse V CC _Brk and the transition to the target orbit (point O ') (item 3) VOC is at O (position 4) with the same angular distance U to Equator (item 5). The point of intersection of the orbits, in which it is necessary to apply an impulse to combine the planes of the orbits of the spacecraft and the VOC, is at the pole (point C) (pos. 6).

с длиной U, а орбите КК (поз.2) дуга

(наклонение i₁≠90°). За счет отличия в наклонении орбиты КК и варьирования времени прилета КК в точку перехода на целевую орбиту ИСЛ, можно обеспечить одновременный приход ЛОС и КК в окрестность точки О (поз.3).Figure 4 presents a spherical image of two intersecting orbits. The polar orbit of the VOC (pos. 1) with an inclination of i = 90 ° belongs to the arc

with a length U, and the orbit of the spacecraft (pos. 2) is an arc

(inclination i ₁ ≠ 90 °). Due to the difference in inclination of the orbit of the spacecraft and the variation in the time of arrival of the spacecraft to the transition point to the target orbit of the ISL, it is possible to ensure the simultaneous arrival of VOCs and spacecraft in the vicinity of point O (position 3).

As an example, the problem of convergence of spacecraft with VOC located in the polar orbit of the ISL with an inclination of i = 90 ° is presented. The spacecraft begins flight to the moon from a circular satellite orbit of a satellite with a height of N _cr = 200 km and an inclination of 51.6 ° along a flat path. To determine the momenta of the flight, a limited circular three-body problem is used [3. "Fundamentals of the theory of spacecraft flight", ed. G.S. Narimanova and M.K. Tikhonravova, Moscow, "Engineering", 1972] with the motion of the spacecraft in the gravitational field of the Earth and the Moon, solved by numerical integration. The diagram of an energetically optimal plane flight includes two transverse impulses. The first take-off impulse V _{exclusion of the} spacecraft is transferred to the transitional orbit for the flight to the moon. Since the radius of the Moon’s orbit is about 384,000 km, for the Hohman transition to a highly elliptical orbit reaching the apogee of the Moon, it is necessary to apply a take-off impulse [1]

,

,

и

- большая полуось орбиты перелета к Луне [1]. Через время перелета ΔT~5 суток, равное половине периода орбиты перелета, КК достигает окрестность Луны.where µ is the gravitational constant of the Earth, r _n is the radius of the initial orbit, r _k is the radius of the final orbit, which is approximately equal to the radius of the lunar orbit. Moreover, the maximum possible flight time is half the period T of the flight orbit, where

and

- the semimajor axis of the orbit of the flight to the moon [1]. After the flight time ΔT ~ 5 days, equal to half the period of the orbit of the flight, the spacecraft reaches the vicinity of the moon.

According to the Lambert problem [1], a flight can be completed in less time due to a small increase in the take-off impulse V _ex . For example, an excess of the take-off pulse by 50 m / s, compared with the minimum necessary for the Goman transition, leads to the achievement of spacecraft near the moon in 2.5 days [3].

. При подлете к Луне основное влияние на движение КК начинает оказывать гравитационное поле Луны. Относительно Луны скорость КК V_α будет превышать местную параболическую скорость, т.е. 2-ую космическую скорость для Луны. Поэтому вторым тормозным импульсом V_торм КК переводится на орбиту ИСЛ. Величина этого импульса около 900 м/с и рассчитывается как V_торм=V_α-V₀, где V₀~1730 м/с - орбитальная скорость ИСЛ [3]. Плоский двухимпульсный перелет в любую дату обеспечивает переход на окололунную орбиту с заданным наклонением i и высотой, но при этом плоскость орбиты, определяемая долготой восходящего узла Ω_ВУ, может отличаться от плоскости целевой орбиты ЛОС. Каждый день, за счет естественного вращения Луны вокруг своей оси, достижимая долгота восходящего узла Ω_ВУ при перелете КК с Земли будет изменять свое значение на ~13.2° [3]. Таким образом, в течение лунного месяца (период 28.5 дня) появляется возможность решить задачу с плоским перелетом от Земли к Луне на орбиту ИСЛ с заданным наклонением i и временем перелета ΔT с точностью по долготе Ω_ВУ в 13-14°. Варьируя длительностью перелета ΔT в пределах ±1 день, за счет незначительного изменения величины отлетного импульса V_отл можно решить точную задачу выхода на окололунную орбиту с заданной долготой восходящего узла Ω_ВУ.The velocity of spacecraft at the peak of the transitional highly elliptical orbit will be

. When approaching the moon, the main influence on the motion of spacecraft begins to have a gravitational field of the moon. With respect to the moon, the velocity of the spacecraft V _α will exceed the local parabolic velocity, i.e. 2nd space velocity for the moon. Therefore, the second inhibitory pulse V _brake KK is transferred to the orbit of the ISL. The magnitude of this pulse is about 900 m / s and is calculated as V _brake = V _α -V ₀ , where V ₀ ~ 1730 m / s is the orbital velocity of the ISL [3]. A flat two-pulse flight at any date provides a transition to a near-moon orbit with a given inclination i and altitude, but the orbital plane, determined by the longitude of the ascending node Ω of the _VU , may differ from the plane of the target VOC orbit. Every day, due to the natural rotation of the Moon around its axis, the attainable longitude of the ascending node Ω of the _WU will change its value by ~ 13.2 ° [3] when the spacecraft flies from Earth. Thus, during the lunar month (28.5 day period), it becomes possible to solve the problem of a flat flight from Earth to the Moon to the ISL orbit with a given inclination i and flight time ΔT with an accuracy in longitude Ω of the _WU of 13-14 °. Varying the flight duration ΔT within ± 1 day, due to a slight change in the magnitude of the take-off impulse V _exc, it is possible to solve the exact problem of reaching the near-moon orbit with a given longitude of the ascending node Ω _W.

To demonstrate the above, Table 1 presents the characteristics of the flight to the ISL orbit from the satellite orbit. We considered the problem of launching a spacecraft from the Baikonur cosmodrome to a circular satellite orbit with parameters N _cr = 200 km and an inclination of i = 51.6 °, followed by the issuance of a take-off pulse V _otl to the Moon. Upon reaching perilune at a distance of 200 km from the surface of the moon by QC was applied brake pulse V _Brk transforming QC LIS circular polar orbit with an inclination of i = 90 ° and orbit height h _cr = 200 km. The time of flight to the Moon AT varied from 4.5 days to 2.5 days in order to provide the necessary value of the longitude of the ascending node Ω _WU , corresponding to the plane of the target orbit of the VOC. All calculations were performed using the Satellite Tool Kit 9.0 software package. In the following presentation, we will assume that the VOC orbit is located at the time of the spacecraft arrival in the ISL plane with Ω _WU = 154 °, which corresponds to the flight duration ΔТ = 2.98 days.

After the braking impulse V brake is _performed and the spacecraft transitions to the _FSC orbit, additional phasing is necessary, similar to the approach of the spacecraft to the OS, since it is very unlikely that the AKO will enter the vicinity of the spacecraft. This will require additional time and fuel for the subsequent rapprochement.

Additional phasing of the spacecraft can be avoided by ensuring that the VOC arrives at the latitude argument u at the moment of issuing the braking impulse V _brake for the spacecraft to transition to the target orbit (i.e., O ′ Fig. 3). This result can be achieved by insignificant variation in the time of arrival of QC in perisettlement. Table 2 presents the characteristics of the flight relative to the nominal flight to the orbit of the moon on January 2, 2013 with the longitude of the ascending node Ω _WU = 154 °. Since the duration of the orbit in a circular lunar orbit with an altitude of N _cr = 200 km is 127.5 min, to cover all possible phase angles in the range of ± 180 ° at the time of spacecraft arrival to the target VOC orbit, the table shows data with a discrete shift relative to the nominal spacecraft arrival in perisulation ± 10 minutes.

As can be seen from Table 2, the maximum value of the difference in longitude of the ascending node of the orbit of the spacecraft Ω _VU from the nominal value Ω _VU for VOCs is about 0.5 ° and can be eliminated by a lateral impulse ΔV _b at the intersection points of the orbits of the colliding objects located in the case of a polar orbit VOC, above the poles of the Moon - t.S (see figure 3), which will require additional flight from the point of delivery of the brake pulse V _brakes to the point of intersection near the half-turn. The marginal cost of the characteristic velocity per lateral impulse ΔV _b for eliminating the angular mismatch ΔΩ _WU ~ 0.5 ° is 10-12 m / s.

In order to reduce the fuel consumption of the spacecraft for conducting the side pulse ΔV _b and the flight time before docking, it is proposed to combine the execution of the side pulse ΔV _b simultaneously with the brake pulse V _brake . To do this, two conditions must be provided. Firstly, the point of intersection of the VOC orbit and the transitional orbit of the spacecraft should be on the argument of the latitude of the point of arrival of the spacecraft in the relocations, and secondly, the time of arrival of the spacecraft in the relocation should coincide with the time of the passage of the VOCs of the point of intersection of the orbits (item 4 of Fig. 4).

As follows from Table 2, the argument for the latitude of the spacecraft arrival point corresponds to u ~ 300 °, which is characteristic of the “southern” flight paths to the moon [3]. The first condition is proposed to be satisfied due to a slight change in the inclination of the transitional orbit of the spacecraft. In this case, the closest intersection point of the orbits of the spacecraft and the VOC, at which the application of the braking impulse V _brake , is moved from the pole (pos.6 of Fig.3) to pos.3 (Fig.4). The second condition characterizing the phase mismatch can be fulfilled by choosing from Table 2 the corresponding variant of the time shift of the SC arrival in the vicinity of the Moon.

принадлежит орбите КК с наклонением i₁. Дуга

принадлежит орбите ЛОС с наклонением i=90°. По условию задачи длины этих дуг U практически одинаковы (КК и ЛОС находятся на одном аргументе широты u~300°). Дуга

определяется разностью между долготами восходящих узлов ΔΩ_ВУ обеих орбит (в нашем примере ΔΩ_ВУ~0.5°). Угол i_R - угол между плоскостями.Define the required value of the inclination i_one spacecraft transition orbit and marginal cost of the characteristic velocity per lateral impulse ΔV. To do this, we use the variant of the orbit with the arrival of spacecraft in periostations with the maximum deviation in longitude of the ascending node Q_By from the longitude of the ascending VOC node, i.e. with Δt = -67 min and u ~ 300 ° (Table 2). Figure 4 presents the intersection point of two orbits (VOC and CC) at a given argument of latitude (t.O). Consider the spherical triangle ΔАOW. Arc

 belongs to the orbit of the spacecraft with inclination i_one. Arc

 belongs to the orbit of the VOC with an inclination of i = 90 °. By the condition of the problem, the lengths of these arcs U are almost the same (KK and LOS are on the same argument of latitude u ~ 300 °). Arc

 determined by the difference between the longitudes of the ascending nodes ΔΩ_WU both orbits (in our example ΔΩ_WU~ 0.5 °). Angle i_R - the angle between the planes.

From the solution of narrow spherical triangles [4. K.A. Kulikov "Course of Spherical Astronomy" ed. Physics and mathematics of literature, Moscow, 1961]

sini _R sinU = sinΔΩ _WU sini

and, in view of the smallness of i _R and ΔΩ _WU

because u = 360 ° -U, then sinu = -sinU and

Since the variant with Δt = -67 min corresponds to ΔΩ _VU = 0.48 °, the angle between the planes of the orbits of the spacecraft and the VOC will be i _R = 0.55 ° or ~ 0.01 radians.

The inclination of KK i ₁ is determined using the equation of cosines for a spherical triangle ΔАOW.

cosi ₁ = -cosi _R cosi + sini _R sini cosU

or, taking into account the smallness of i _R

i ₁ = arccos (-cosi + i _R sini cos U).

Thus, the required inclination i _{1 of the} spacecraft arrival orbit in the case of VOCs in the polar orbit will be 89.73 °, and the lateral momentum

The formation of the inclination of the lunar orbit and the ascending node of the orbit is ensured by the moment of issue and the magnitude of the take-off impulse V _ex . The transition to the lunar orbit is provided by the braking impulse V _brake . Against the background of a large (~ 900 m / s) brake pulse V _brake [3], the lateral pulse ΔV _b ~ 17 m / s will increase the total pulse by

Thus, the use of the proposed method eliminates phasing in orbit of another celestial body, due to a direct transition to the vicinity of the orbital station and significantly saves the spacecraft fuel for convergence.

Claims (1)

A method for controlling movement of the active space object abutting a passive space object, comprising the sequential application to the active space object in orbit a celestial body into fly-away pulse V _exc and braking pulse V _Brk to move into the orbit of another celestial body with preset parameters height and position orbital plane, characterized in that before the transfer of an active space object to the flight path to another celestial body, the magnitude and place of application are flown away th pulse V _exc is determined from the intersection conditions active space object orbit passive space object while finding objects in the vicinity of the orbits of the intersection point, whereupon the active space object translate the orbit of another celestial body by the simultaneous application thereto braking pulse V _Brk for given parameters along the height of the orbit and the lateral impulse ΔV _b for combining the planes of the orbits of the joined objects, calculated by the formula

where V ₀ - orbital speed of rotation of a passive space object around another celestial body;
ΔΩ _WU - the difference in the longitudes of the ascending nodes of the orbits of the joined objects;
i is the inclination of the orbit of a passive space object;
u is the argument of the latitude of the passive space object at the intersection point of the orbits of the joined objects.

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