RU2575556C2 - Control over spacecraft at orbiting of artificial satellite orbit - Google Patents

Abstract

FIELD: aircraft engineering.

SUBSTANCE: invention relates to the control over the spacecraft, mainly, at the orbiting path atmospheric section. Claimed process comprises the online by onboard means of the altitude of the path pericentre immediately after the spacecraft re-entry. Then, the reactive correction of said path nearby the entry corridor lower boundary is performed. At skipping, the optimum control programs are operated for control over aerodynamic forces before spacecraft exit from atmosphere. Note here that the spacecraft flight nearby said entry corridor lower boundary can be performed in more rarefied atmosphere layers to ensure the higher speed at the transition orbit apocentre. At said apocentre the spacecraft receives the extra acceleration pulse to generate the preset orbit of the planet artificial satellite.

EFFECT: higher efficiency of control, decreased consumption of fuel.

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Description

The invention relates to astronautics, in particular to the field of launching a spacecraft (SC) into orbit of an artificial planetary satellite (ISP) using preliminary aerodynamic drag in the atmosphere.

A number of methods are known for launching spacecraft into ICP orbits. So, in the work of Eismont N.A. “Optimal control of a spacecraft transferred from a hyperbolic trajectory to the orbit of a planetary satellite by braking in the atmosphere”, Space Research, 1972, v. 10, no. 2, pp. 290-292 - [1] describes the rocket-dynamic method of forming satellite orbits, where the spacecraft is transferred from a hyperbolic approach path to the planet into ICP orbit by damping the kinetic energy of the spacecraft by controlling high-thrust propulsion systems. The main disadvantage of this method is the extremely high fuel consumption.

The method of controlling the spacecraft during its launch into ICP orbit using preliminary aerodynamic drag in the atmosphere followed by an acceleration pulse in the apocenter of the transitional orbit is described in the work - Ivanov N.M., Martynov A.I. "Control of the motion of a spacecraft in the atmosphere of Mars." M .: "Science", 1977, pp. 357-360 - [2]. The indicated method consists in controlling the spacecraft in the atmospheric section by switching the effective aerodynamic quality K _eff = K _b cosγ from one boundary value to another (γ is the angle of heel, K _b is the balancing aerodynamic quality set at a given constant angle of attack). The switching moments of effective aerodynamic quality are determined from the condition of ensuring the maximum speed of the spacecraft in the apocenter of the transitional orbit. This method allows to reduce the fuel costs required for the formation of a given orbit.

The disadvantage of this method is the low efficiency of preliminary aerodynamic drag in the atmosphere of the planet in connection with the control of the spacecraft only by changing the angle of heel γ. At the same time, the introduction of an additional control parameter - the angle of attack α, allows to reduce the required fuel consumption for the formation of the specified ICP orbits.

In the work of Ivanov V.M., Sokolova N.L. et al., "Optimal control of spacecraft during the ascent of Mars artificial satellite." 63nd International Astronautical Congress, Naples, Italy, 2012, No. IAC-12, A3,3A, 18.p1, x13148 - [3] describes a method for launching a spacecraft into orbit of an ICP, where the device is controlled in the area of aerodynamic braking by changing angle of heel and attacks. It is shown that there is a gain in the mass of fuel compared to the method that provides for one-parameter control of the spacecraft by the roll angle. At the same time, a general pattern was revealed that is characteristic of a wide range of changes in the initial data and boundary flight conditions. It consists in the fact that when the spacecraft enters the atmosphere near the lower boundary of the corridor, the fuel consumption several times exceeds the consumption corresponding to the spacecraft's entry into the atmosphere by 65-75% of the entrance corridor, measured from its upper boundary. This feature allows us to conclude that there is a significant drawback of the considered method, which consists in a significant overspending of the mass of fuel in cases of spacecraft entering the atmosphere near the lower boundary of the corridor and the existence of reserves to reduce the required energy consumption.

The closest in the totality of existing signs and the achieved result (prototype) to the claimed invention is a method of transferring a spacecraft into ICP orbit, which provides for the impulse of the characteristic velocity in the plane of flight of the spacecraft at an angle of about 90 °, counted from the velocity vector of the spacecraft counterclockwise in direction from the planet, when the spacecraft enters the atmosphere near the lower boundary of the corridor, as well as the control of aerodynamic forces in the area of movement at the sphere, followed by the acceleration of the spacecraft at the peak of the transitional orbit. The specified known method is described in the book - Ivanov N.M., Martynov A.I. "The movement of spacecraft in the atmospheres of planets." M .: "Science", 1985, p. 347-364 - [4]. Due to the motion of the spacecraft in the more rarefied layers of the atmosphere, carried out after the correction of the flight path, the speed of the spacecraft is damped weaker and the fuel consumption for the formation of final orbits is reduced. In the framework of this method, it is assumed that the main sign of spacecraft motion near the lower boundary of the entrance corridor is the high intensity of the increase in apparent velocity after the spacecraft enters the atmosphere. In this case, the impulse of the characteristic speed is applied in the plane of flight of the spacecraft at an angle of about 90 °, measured from the velocity vector of the spacecraft counterclockwise in the direction from the planet, 20-40 seconds after the spacecraft enters the atmosphere. It is shown that theoretically such a control method during optimal corrections of the trajectories of the spacecraft motion when it enters the atmosphere near the lower boundary of the inlet corridor allows to reduce fuel mass by 1.5-2 times in comparison with the method that does not provide for the supply of a correction pulse in the atmosphere.

. Это обстоятельство дает основание предполагать, что значительным резервом снижения суммарных затрат топлива на формирование спутниковых орбит является выбор и отработка рациональных значений корректирующих импульсов характеристической скорости, зависящих от высот условного перицентра траекторий входа. При этом в ряде случаев представляется энергетически эффективным последовательно подавать в атмосфере несколько корректирующих импульсов характеристической скорости различной величины.At the same time, the analysis of spacecraft control operations during the implementation of this method reveals a number of disadvantages. First, a high rate of increase in apparent velocity can be not only a sign of spacecraft movement near the lower boundary of the entrance corridor, but also arise in connection with a possible spread of planetary atmosphere density towards the densest atmospheric models. So, for example, the atmospheric densities of Jupiter for the “cold” and “warm” models differ by 2-3 orders of magnitude [4, p. 23]. Errors in diagnosing the reasons for the intense increase in apparent speed can lead to an incorrect decision about the need for spacecraft motion corrections in the atmosphere: the impulse of the characteristic speed in most of the entrance corridor (65-75% of the total width of the corridor) can lead to additional fuel overruns, and when the spacecraft moves near the upper boundary of the corridor - to the impossibility of launching the spacecraft into a given orbit and to the disruption of the flight program. Secondly, in the prototype method, it is assumed that the motion paths are corrected 20-40 seconds after the spacecraft enters the atmosphere, for example, when Jupiter enters the atmosphere after 21 seconds. Despite the fact that during this time the speed of the spacecraft changes little, the flight altitude decreases by about half. As a result, the spacecraft is subjected to excessive aerodynamic drag and, as a result, to a decrease in the speed of flight of the vehicle from the atmosphere. At the same time, for the indicated time (20-40 seconds after the spacecraft’s entry into the atmosphere), the problem of autonomous determination of the spacecraft’s position inside the atmosphere’s entry corridor can be successfully solved by using on-board algorithms for predicting the vehicle’s motion parameters in the remaining areas and the need (or absence) spacecraft motion correction. Thirdly, in the prototype method, a pulse of characteristic speed is provided, the value of which does not depend on the height of the conditional pericenter of the input path. At the same time, the nature of the dependence of the required energy consumption ΔV on the height of the conditional re-center of the entry path shows an extremely intense increase in ΔV as h _π approaches the lower boundary of the corridor

. This circumstance suggests that a significant reserve for reducing the total fuel consumption for the formation of satellite orbits is the selection and development of rational values of the correcting impulses of the characteristic speed, which depend on the heights of the conditional pericenter of the input paths. Moreover, in a number of cases, it seems energetically efficient to consistently deliver several corrective impulses of characteristic velocity of various sizes in the atmosphere.

The essence of the invention lies in the preliminary determination of the height of the conditional pericenter of the trajectory of the spacecraft entering the atmosphere inside a given physically feasible corridor. This is achieved by determining immediately after the spacecraft enters the atmosphere at the i-th (i = 1, 2, 3 ...) time instants of the velocity of the spacecraft V _i , the angle of inclination of the velocity vector to the local horizon θ _i , and the radius vector r _i , atmospheric density ρ _i and predicting on their basis the values of velocities V _k and the angles of inclination of the velocity vector to the local horizon θ _k at the time of the spacecraft’s departure from the atmosphere, as well as its velocities in the apocenter of the transitional orbit V _α when moving in the aerodynamic drag section from n the angle of heel and the angle of attack α ^* corresponding to the maximum value of aerodynamic quality.

Also, the essence of the claimed method of controlling a spacecraft when it is put into orbit of an artificial satellite of the planet lies in the approach of the spacecraft to the planet in a given corridor of entry into the atmosphere, in the definition in i, where i = 1, 2, ..., N, time points of parameters the motion of the spacecraft, namely its speed - V _i , the angle of inclination of the spacecraft's velocity vector to the local horizon θ _i , the radius vector r _i and the atmospheric density ρ _i , in ensuring the spacecraft enters the atmosphere with a roll angle γ about 0 rad and the value of the angle of attack of the spacecraft about α ^* , corresponding to the maximum value of aerodynamic quality, in the impulse of the characteristic velocity in the plane of flight of the spacecraft at an angle of about 90 °, counted from the velocity vector of the spacecraft counterclockwise in the direction from the planet, at its entry into the atmosphere near the lower boundary of the entry corridor, in controlling the spacecraft at the angles of heel γ and attack α before departure from the atmosphere, and at the ith, where i = 1, 2, ..., N, time instants for of a given positive increment of the angle of inclination of the velocity vector to the local horizon δθ≤0.1 ° determine the values of the impulse of the characteristic velocity in the flight plane of the spacecraft at an angle of about 90 °, counted from the velocity vector of the spacecraft counterclockwise in the direction from the planet, the application of which provides an increase angle θ _i by δθ; for each of the two positions of the spacecraft characterized by known values of its motion parameters S _1i = {V _i , θ _i , r _i , ρ _i } and S _2i = {V _i , θ _i + δθ, r _i , ρ _i } predict the values of the velocities V _k (S _1i ) and V _k (S _2i ), the angles of inclination of the velocity vector to the local horizon θ _k (S _1i ) and θ _k (S _2i ) at the time of the spacecraft’s departure from the atmosphere and the speeds of the spacecraft in the transition apocenter the orbits V _α (S _1i ) and V _α (S _2i ) when moving on the remaining flight sections in the atmosphere with a zero roll angle and an angle of attack equal to α ^* in accordance with mathematical their dependencies:

V_k(S_1i) = exp [-z_k(S_1i)],  V_k(S_2i) = exp [-z_k(S_2i)],

where - m is the mass of the spacecraft;

V _i - the current value of the speed of the spacecraft at time t _i

θ _i is the current value of the angle of inclination of the velocity vector to the local horizon at moments t _i ;

r _i is the current value of the radius vector at time t _i ;

ρ _i - the current value of the density of the atmosphere at time t _i

i = 0, 1, 2 ... N;

g is the acceleration of gravity;

R is the radius of the planet;

µ is the gravitational parameter of the planet;

β is the logarithmic coefficient of change in the density of the atmosphere from height;

C _x - aerodynamic drag coefficient of the spacecraft;

With _γ - aerodynamic coefficient of lift of the spacecraft;

S is the area of the mid-section of the spacecraft;

α is the angle of attack of the spacecraft;

ρ _p is the value of the density of the atmosphere at the time of the rebound of the spacecraft;

z _p is the value of the variable z at the time of the rebound of the spacecraft;

S _1i is the position of the spacecraft at time t _i ,

characterized by the flight speed V _i , the angle of inclination of the velocity vector to the local horizon θ _i , the radius vector r _i , the density of the atmosphere ρ _i ;

S _2i is the position of the spacecraft at time t _i ,

characterized by the flight speed V _i , the angle of inclination of the velocity vector to the local horizon θ _i + δθ, the radius vector r _i , the density of the atmosphere ρ _i ;

δθ is the increment of the angle of inclination of the velocity vector to the local horizon, which is formed when a corrective impulse of the characteristic velocity is applied;

P _x - reduced load on the frontal surface of the spacecraft;

K is the aerodynamic quality of the spacecraft;

V _k - the speed of the spacecraft at the time of departure from the atmosphere;

r _k is the radius vector of the spacecraft at the time of departure from the atmosphere;

θ _k is the angle of inclination of the velocity vector to the local horizon at the time of the departure of the spacecraft from the atmosphere;

V _α - the speed of the spacecraft in the apocenter of the transitional orbit,

calculate the difference between the change in the speed of the spacecraft in the apocenter of the transitional orbit and the magnitude of the impulse of the characteristic velocity, providing an increase in the angle of inclination of the velocity vector to the local horizon by δθ in accordance with the formula

δV _i = V _α (S _2i ) -V _α (S _1i ) -ΔV _i ,

and when the condition δV _i > 0 is fulfilled, an impulse of the characteristic speed of ΔV _{i is} applied; starting from the point in time when δV _i is less than zero, the spacecraft is controlled without rocket dynamic corrections of the motion paths until the spacecraft takes off from the atmosphere only by changing the angle of heel and attack.

: в этих случаях проводить коррекцию движения космического аппарата не требуется. В случаях значительного увеличения скорости V_α(S_2i) по сравнению с V_α(S_1i) (или снижения потребных энергетических затрат ΔV) при положительной вариации угла δθ (или δh_π) следует вывод о входе космического аппарата в атмосферу вблизи нижней границы коридора и энергетической целесообразности проведения ракетодинамической коррекции траектории движения для обеспечения полета космического аппарата в более разреженных слоях атмосферы.Given the nature of the dependences of the required energy costs ΔV on the height of the conditional pericenter of the input path h _π (see Fig. 10.2 on page 289 and Fig. 10.12 on page 314 in [4]) and giving small increments to the angle of inclination of the velocity vector to the local horizon δθ≤0.1 ° (which according to the solution of the Kepler equations uniquely corresponds to the increment of the height of the conditional pericenter δh _π ,), we can determine the position of the height h _π inside the corridor of the spacecraft entering the atmosphere. The principal factor is the comparison of the speeds of the vehicle in the apocenter of the transitional orbit V _α at two positions of the spacecraft in the initial portion of the flight in the atmosphere: at the position indicated by S _1i and characterized by well-known motion parameters (speed of the vehicle V _i , angle of inclination of the velocity vector to the local horizon θ _i , by the radius vector r _i and the atmospheric density ρ _i ) and at the position indicated by S _2i different from the position S _{1i by the} value of the angle of inclination of the velocity vector to the local horizon, increased by a small amount δθ≤0, 1 °: θ = θ _i + δθ. A small change in the velocity V _α (S _2i ) relative to V _α (S _1i ) with an increment of δθ (or δh _π ) indicates the apparatus enters the atmosphere with heights h _π far from the lower boundary of the entrance corridor

: in these cases, the correction of the motion of the spacecraft is not required. In cases of a significant increase in the velocity V _α (S _2i ) compared to V _α (S _1i ) (or a decrease in the required energy consumption ΔV) with a positive variation of the angle δθ (or δh _π ), a conclusion should be made about the spacecraft entering the atmosphere near the lower boundary of the corridor and the energy feasibility of conducting rocket dynamic correction of the trajectory of motion to ensure the flight of the spacecraft in more rarefied layers of the atmosphere.

To calculate the values of the velocity V _k and the angle of inclination of the velocity vector to the local horizon θ _k at the time of the spacecraft departure from the atmosphere, corresponding to the positions S _1i and S _2i , as well as the spacecraft velocities in the apocenter of the transitional orbit V _α (S _1i ) and V _α (S _2i ) used mathematical dependencies developed, justified and given in the appendix to this application:

V _k (S _1i ) = exp [-z _k (S _1i )], V _k (S _2i ) = exp [-z _k (S _2i )],

where m is the mass of the spacecraft;

V _i - the current value of the speed of the spacecraft at moments t _i ;

θ _i is the current value of the angle of inclination of the spacecraft velocity vector to the local horizon at moments t _i ;

r _i is the current value of the radius vector at time t _i ;

ρ _i - the current value of the density of the atmosphere, moments t _i , i = 0, 1, 2 ... N;

g is the acceleration of gravity;

R is the radius of the planet;

µ is the gravitational parameter of the planet;

β is the logarithmic coefficient of change in the density of the atmosphere from height;

C _x - aerodynamic drag coefficient of the spacecraft;

With _γ - aerodynamic coefficient of lift of the spacecraft;

S is the area of the mid-section of the spacecraft;

α is the angle of attack of the spacecraft;

ρ _p is the value of the density of the atmosphere at the time of the rebound of the spacecraft;

z _p is the value of the variable z at the time of the rebound of the spacecraft;

S _1i is the position of the spacecraft at time t _i , characterized by the flight speed V _i , the angle of inclination of the velocity vector to the local horizon θ _i , the radius vector r _i , the atmospheric density ρ _i ;

S _2i is the position of the spacecraft at time t _i , characterized by the flight speed V _t , the angle of inclination of the velocity vector to the local horizon θ _i + δθ, the radius vector r _i , the atmospheric density ρ _i ;

δθ is the increment of the angle of inclination of the spacecraft velocity vector to the local horizon, which is formed when a corrective impulse of the characteristic speed is applied;

P _x - reduced load on the frontal surface of the spacecraft;

K - aerodynamic quality of the spacecraft;

V _k - spacecraft flight speed at the moment of departure from the atmosphere;

r _k is the radius vector of the spacecraft at the time of departure from the atmosphere;

θ _k is the angle of inclination of the spacecraft velocity vector to the local horizon at the time of the departure of the spacecraft from the atmosphere;

V _α is the speed of the spacecraft in the apocenter of the transitional orbit.

Prediction of these values can be carried out on the on-board computer using analytical dependencies, which does not require much time and can be performed much earlier than the time range specified in the prototype method for determining the height of the conditional pericenter of the entry path (20-40 seconds after the spacecraft entered the atmosphere ) Provided that the feasibility of performing rocket dynamic correction of the trajectory of the spacecraft in the atmosphere is determined, the value of the impulse of the characteristic velocity is determined. For this, in the ith (i = 1, 2, 3 ...) time moments, a possible increase in the spacecraft velocity in the apocenter of the transitional orbit when performing rocket-dynamic correction of the motion path ΔV _α = V _α (S _2i ) -V _α (S _1i ) s is _compared size

. В случаях превышения разницы между скоростями движения КА в апоцентре переходной орбиты при условиях проведения и непроведения коррекции над величиной импульса характеристической скорости ΔV_i, т.е. при δV_i=V_α(S_2i)-V_α(S_1i)-ΔV_i>0 осуществляется подача корректирующего импульса ΔV_i в плоскости полета космического аппарата под углом около 90°, отсчитываемым от вектора скорости космического аппарата против часовой стрелки в направлении от планеты. Такие операции осуществляются с самого начала входа космического аппарата в атмосферу до тех пор, пока величина импульса характеристической скорости ΔV_i не будет превышать прогнозируемый выигрыш в потребных энергозатратах на подачу разгонного импульса характеристической скорости в апоцентре переходной орбиты, т.е. до тех пор, пока значение δV_i не будет меньше нуля. С этого момента осуществляется управление только аэродинамическими силами, по аналогии с известными способами управления [3, 4]. Полученные численные результаты показали, что при осуществлении заявляемого способа в зависимости от высоты условного перицентра траектории входа может быть проведено до трех ракетодинамических коррекций траекторий движения КА. При этом общее время проведения коррекций может достигать 8-12 секунд. Такие результаты соответствуют входу космического аппарата в атмосферу по нижней границе коридора. В целом при реализации заявляемого способа при формировании орбит искусственного спутника Марса потребная масса топлива может быть снижена в 2-3 раза по сравнению со способом - прототипом. Аналогичный уровень снижения расхода топлива может быть достигнут при выведении КА на орбиты искусственного спутника Венеры и Юпитера.the applied correction pulse, depending on the current speed of the spacecraft V _i and the increment of the angle of inclination of the velocity vector to the local horizon δθ:

. In cases where the difference between the speeds of the spacecraft in the apocenter of the transitional orbit is exceeded under the conditions of correction and non-correction over the impulse of the characteristic velocity ΔV _i , i.e. at δV _i = V _α (S _2i ) -V _α (S _1i ) -ΔV _i > 0, a correcting pulse ΔV _i is supplied in the plane of the spacecraft at an angle of about 90 °, counted counterclockwise from the spacecraft’s velocity vector from the planet. Such operations are carried out from the very beginning of the spacecraft’s entry into the atmosphere until the characteristic velocity impulse ΔV _i exceeds the predicted gain in the required energy consumption for delivering the accelerating impulse of the characteristic velocity in the apocenter of the transitional orbit, i.e. until the value of δV _i is less than zero. From this moment, only aerodynamic forces are controlled, by analogy with known control methods [3, 4]. The numerical results showed that when implementing the proposed method, depending on the height of the conditional pericenter of the entry path, up to three rocket dynamic corrections of the spacecraft motion paths can be made. In this case, the total time for corrections can reach 8-12 seconds. Such results correspond to the spacecraft entering the atmosphere along the lower boundary of the corridor. In general, when implementing the proposed method when forming the orbits of the artificial satellite of Mars, the required mass of fuel can be reduced by 2–3 times in comparison with the prototype method. A similar level of reduction in fuel consumption can be achieved when the spacecraft is launched into the orbits of the artificial satellite of Venus and Jupiter.

The technical result of the invention is to increase the control efficiency of the spacecraft in the preliminary aerodynamic drag section not only by changing the angle of heel γ and attack α, but also in connection with conducting rocket dynamic corrections of the spacecraft motion paths. This will make it possible, when the spacecraft enters the atmosphere near the lower boundary of the entry corridor, to fly in more rarefied atmospheric layers and reach the specified altitudes of the transitional orbit apocenter at a higher speed, which reduces the total fuel consumption for the formation of ICP orbits with the required parameters.

The indicated technical result is achieved due to the autonomous operational determination of the relative pericenter altitude immediately by the spacecraft’s onboard means immediately after the spacecraft’s entry into the atmosphere and the rocket-dynamic correction of the trajectory when the spacecraft enters the atmosphere near the lower boundary of the entrance corridor. In this case, rational programs for controlling aerodynamic forces before the spacecraft take off from the atmosphere are worked out and the vehicle is accelerated in the transition center orbit apocenter in order to form the ICP orbit with the given parameters.

Also, the technical result is achieved due to the fact that in the known prototype control method of the spacecraft, when it is put into orbit of an artificial satellite of the planet, consisting in the approach of the spacecraft to the planet in a given corridor of entry into the atmosphere, in the definition in i, where i = 1, 2, ..., N, time instants of the motion parameters of the spacecraft, namely its speed - V _i , the angle of inclination of the spacecraft's velocity vector to the local horizon θ _i , the radius vector r _i and the atmospheric density ρ _i , in providing input to spacecraft into the atmosphere with a roll angle γ of about 0 rad and a spacecraft angle of attack of about α ^* , corresponding to the maximum value of aerodynamic quality, in delivering a characteristic velocity impulse in the plane’s flight plane at an angle of about 90 °, counted from the spacecraft’s velocity vector counterclockwise in the direction from the planet, when it enters the atmosphere near the lower boundary of the entrance corridor, in controlling the spacecraft at the angles of heel γ and attack α before departure from atmospheres, in addition to the ith, where i = 1, 2, ..., N, time instants for a given positive increment of the angle of inclination of the velocity vector to the local horizon δθ≤0.1 ° determine the impulse of the characteristic velocity in the plane of flight of the spacecraft at an angle about 90 °, measured from the velocity vector of the spacecraft counterclockwise in the direction from the planet, the application of which provides an increase in the angle θ _i by δθ; for each of the two positions of the spacecraft characterized by known values of its motion parameters S _1i = [V _i , θ _i , r _i , ρ _i } and S _2i = {V _i , θ _i + δθ, r _i , ρ _i } predict the values of the velocities V _k (S _1i ) and V _k (S _2i ), the angles of inclination of the velocity vector to the local horizon θ _k (S _1i ) and θ _k (S _2i ) at the time of the spacecraft’s departure from the atmosphere and the speeds of the spacecraft in the transition apocenter the orbits V _α (S _1i ) and V _α (S _2i ) when moving on the remaining flight sections in the atmosphere with a zero roll angle and an angle of attack equal to α ^* in accordance with mathematical their dependencies:

V _k (S _1i ) = exp [-z _k (S _1i )], V _k (S _2i ) = exp [-z _k (S _2i )],

where - m is the mass of the spacecraft;

V _i - the current value of the speed of the spacecraft at time t _i

θ _i is the current value of the angle of inclination of the velocity vector to the local horizon at moments t _i ;

r _i is the current value of the radius vector at time t _i;

ρ _i - the current value of the density of the atmosphere at time t _i;

i = 0, 1, 2 ... N;

g is the acceleration of gravity;

R is the radius of the planet;

µ is the gravitational parameter of the planet;

β is the logarithmic coefficient of change in the density of the atmosphere from height;

C _x - aerodynamic drag coefficient of the spacecraft;

C _γ — aerodynamic lift coefficient of the spacecraft;

S is the area of the mid-section of the spacecraft;

α is the angle of attack of the spacecraft;

ρ _p is the value of the density of the atmosphere at the time of the rebound of the spacecraft;

z _p is the value of the variable z at the time of the rebound of the spacecraft;

S _1i is the position of the spacecraft at time t _i , characterized by the flight speed V _i , the angle of inclination of the velocity vector to the local horizon θ _i , the radius vector r _i , the atmospheric density ρ _i ;

S _2i is the position of the spacecraft at time t _i , characterized by the flight speed V _i , the angle of inclination of the velocity vector to the local horizon θ _i + δθ, the radius vector r _i , the atmospheric density ρ _i ;

δθ is the increment of the angle of inclination of the velocity vector to the local horizon, which is formed when a corrective impulse of the characteristic velocity is applied;

P _x - reduced load on the frontal surface of the spacecraft;

K is the aerodynamic quality of the spacecraft;

V _k - the speed of the spacecraft at the time of departure from the atmosphere;

r _k is the radius vector of the spacecraft at the time of departure from the atmosphere;

θ _k is the angle of inclination of the velocity vector to the local horizon at the time of the departure of the spacecraft from the atmosphere;

V _α - the speed of the spacecraft in the apocenter of the transitional orbit, calculate the difference between the change in the speed of the spacecraft in the apocenter of the transitional orbit and the magnitude of the impulse of the characteristic velocity, which provides an increase in the angle of inclination of the velocity vector to the local horizon by δθ in accordance with the formula:

δV _i = V _α (S _2i ) -V _α (S _1i ) -ΔV _i ,

and when the condition δV _i > 0 is fulfilled, a characteristic velocity impulse of ΔV _{i is} supplied, starting from the moment when δV _i is less than zero, the spacecraft is controlled without rocket dynamic corrections of the motion paths until the spacecraft departs from the atmosphere only by changing the angle of heel and attacks.

The claimed method of controlling a spacecraft when it is put into orbit of an artificial satellite of the planet is illustrated by the following figures.

In FIG. Figure 1 shows the main stages of launching a spacecraft into orbit of an artificial satellite of the planet using preliminary aerodynamic braking, both with and without missile-dynamic correction of the trajectory of the spacecraft in the atmosphere.

до нижней границе

.In FIG. 2, for the claimed method, graphs are presented of the dependences of the total energy consumption ΔV _Σ on the height of the conditional pericenter of the input path h _π when the spacecraft is put into a circular orbit of the artificial satellite Mars, 500 km high. H _π values ranged from the upper boundary of the entry corridor

to the lower border

.

In FIG. 1 and FIG. 2 adopted the following notation:

1 - approach hyperbolic trajectory of the spacecraft to the planet’s atmosphere,

2 - spacecraft entry into the atmosphere,

3 - the impulse of the characteristic velocity ΔV for correcting the trajectory of the spacecraft,

4 - spacecraft velocity vector after correction of the trajectory of movement,

5 - spacecraft flight path without rocket dynamic correction;

6 - the trajectory of the spacecraft after conducting rocket dynamic correction,

7 - the SC departure from the atmosphere along the trajectory without conducting rocket dynamic correction with a speed V _α (S ₂ ),

8 - the SC departure from the atmosphere along the trajectory after conducting the rocket dynamic correction with a speed V _α (S ₁ ),

9 - transitional orbit of the spacecraft in the absence of correction of motion in the atmosphere;

10 - transitional orbit of the spacecraft after the correction of motion in the atmosphere,

11 - apocenter of the transitional orbit of the spacecraft,

12 - the impulse of the characteristic velocity to form a given orbit of the spacecraft,

13 - the surface of the planet,

14 - conditional boundary of the atmosphere,

15 - dependence of the total energy consumption ΔV _Σ on the height of the conditional pericenter of the entry path h _π in the absence of rocket dynamic correction of the spacecraft in the atmosphere,

16 - dependence of the total energy consumption ΔV _Σ on the height of the conditional pericenter of the input path h _π when a characteristic velocity of 25 m / s is applied to the pulse in the atmosphere,

17 - dependence of the total energy consumption ΔV _Σ on the height of the conditional pericenter of the input trajectory h _π when a characteristic velocity of 50 m / s is applied to the pulse in the atmosphere.

From the dependencies shown in FIG. 2, it follows that for the version with the correction of the spacecraft’s motion in the atmosphere, the flight path passes at high altitudes, which leads to less intensive aerodynamic drag of the spacecraft and a higher value of the spacecraft’s departure velocity from the atmosphere: V _α (S ₂ ) is the spacecraft’s velocity upon departure from atmosphere when using the scheme with the correction of the flight path, V _α (S ₁ ) - the speed of the spacecraft upon departure from the atmosphere without rocket dynamic correction. It was found that V _α (S ₂ ) -V _α (S ₁ ) -ΔV> 0, i.e. there is a gain in the required energy costs when correcting the motion of the spacecraft in the atmosphere.

Claims (1)

The method of controlling a spacecraft when it is put into orbit of an artificial satellite of the planet, which consists in approaching the spacecraft to the planet in a given corridor of entry into the atmosphere, in the definition in i, where i = 1, 2, ..., N, are the moments of time of the parameters of space motion the spacecraft, namely its speed V _i , the angle of inclination of the spacecraft's velocity vector to the local horizon θ _i , the radius vector r _i and the density of the atmosphere ρ _i , in ensuring the spacecraft enters the atmosphere with a roll angle γ of about 0 and an angle at spacecraft about α ^* , corresponding to the maximum value of aerodynamic quality, in delivering a characteristic speed pulse in the plane’s flight plane at an angle of about 90 °, counted from the spacecraft’s velocity vector counterclockwise in the direction from the planet, when it enters the atmosphere near the lower boundary of the entry corridor, in controlling the spacecraft at the angles of heel γ and attack α before departure from the atmosphere, characterized in that in the ith, where i = 1, 2, ..., N, the times for a given n a negative increment of the angle of inclination of the velocity vector to the local horizon δθ ≤ 0.1 ° determines the values of the impulse of the characteristic velocity in the flight plane of the spacecraft at an angle of about 90 °, measured from the velocity vector of the spacecraft counterclockwise in the direction from the planet, the application of which provides an increase angle θ _i by δθ, for each of the two positions of the spacecraft, characterized by the known values of its motion parameters S _1i = {V _i , θ _i , r _i , ρ _i } and S _2i = {V _i , θ _i + δθ, r _i , ρ _i }, predict the values of the velocities V _k (S _1i ) and V _k (S _2i ), the angles of inclination of the velocity vector to the local horizon θ _k (S _1i ) and θ _k (S _2i ) at the time of the spacecraft’s departure from the atmosphere and the speeds of the spacecraft in the apocenter of the transitional orbit V _α (S _1i ) and V _α (S _2i ) when moving in the remaining parts of the flight in the atmosphere with a zero roll angle and the angle of attack equal to α ^* , the difference between the change in the speed of the spacecraft in the apocenter of the transitional orbit and the value impulse of characteristic speed, providing an increase in the angle of incidence is the velocity vector to the local horizon by an amount δθ according to the formula:
δV _i = V _α (S _2i ) -V _α (S _1i ) -ΔV _i ,
and when the condition δV _i > 0 is fulfilled, a characteristic velocity impulse of ΔV _{i is} supplied, starting from the moment when δV _i is less than zero, the spacecraft is controlled without rocket dynamic corrections of the motion paths until the spacecraft departs from the atmosphere only by changing the angle of heel and attacks.

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