RU2816322C1 - Method of forming dust flow for mechanical interaction with orbital space objects - Google Patents

Abstract

FIELD: cosmonautics.

SUBSTANCE: invention relates to control of space objects using finely dispersed substance, for example, lunar dust — regolith. Dust (particles sized 10–100 mcm) is removed from the region of the orbit of the Moon into a parabolic or hyperbolic transfer orbit and scattered along a certain trajectory in the vicinity of this orbit. Under the action of gravity and solar pressure, a dust flow (plume) is formed, which is oriented tangentially at perigee and transmits its pulse to a certain space object on a near-earth orbit passing through perigee. In order to increase the length of the plume, dust can be scattered in series by several initiating devices.

EFFECT: reduced undesirable scattering of fine substance plume with possibility of controlling its size and structure in perigee.

3 cl, 11 dwg

Description

Field of technology

The invention relates to methods and means for carrying out inter-orbital maneuvers of space objects (SO) using external resources of the space environment and, specifically, fine matter, for example, lunar regolith (“lunar dust”), the reserves of which on the surface of the Moon are quite large.

The expected industrial and technological applications of regolith are diverse, and among them we can highlight the possibility of its direct use as a working fluid for movement in space (see, for example, [1] WO 2020155460 A1; 08/06/2020, where the use of small regolith to create a reactive thrust during flights between points on the lunar surface).

The energy resources of “moon dust” can manifest themselves to a much greater extent in relation to spacecraft maneuvers in the Earth-Moon system. This is evident from the fact that the gravitational potential -mμ/R _M of mass m of matter in the orbit of the Moon, outside its sphere of influence, is greater than the gravitational potential -mμ/R _o of the same mass on the Earth's surface (R _o ≈ 6400 km) or in low-Earth orbit (R _o > 6400 km) by the amount

, (1)

where R_o <<R_M(≈ 384000 km); μ - gravitational constant of the Earth, R_M - the average radius of the Moon's orbit. Here and below, the motion of the spacecraft and lunar matter is considered within the framework of a limited two-body problem.

Thus, the difference in gravitational potentials (1) is practically equal to the energy of the mass m in a parabolic orbit (with the “second cosmic” speed ν _e at perigee), and therefore, when transferring this energy of lunar matter to some SO, the mass of which is commensurate with m, one can obtain significant change in the orbit of the spacecraft.

Obviously, for such a transfer of energy, matter (regolith) must be removed from the surface of the Moon and leave the sphere of influence of the Moon, moving onto a parabolic (or weakly hyperbolic) trajectory intersecting the orbit of the spacecraft or touching it. To do this, the substance must be given a speed of the order of the “second cosmic” for the Moon, which is only 2.38 km/s and is relatively easily achieved, for example, with the help of electromagnetic accelerators (EMA). The energy consumption in this case will, as is easy to see, be an order of magnitude less (1).

The schemes for transferring the energy of lunar matter to a spacecraft (with a purely mechanical interaction, it is more accurate to talk about the amount of motion) are varied, but the general requirement for them should be to limit the loads acting on the spacecraft during its interaction with the flow of matter, which is why the flux density should be quite low and its dimensions (in the direction of motion relative to the KO) are correspondingly large - so that a mass of matter reacts with the KO, sufficient for a significant change in the speed of the KO.

To perceive the flow incident on the KO, you can use a conventional screen (including a heat-resistant one) or a more complex system that converts the flow.

Prior Art

In addition to [1], other proposals were made, and quite a long time ago, to use crushed extraterrestrial matter to change the motion (orbits) of various EOs, including lunar regolith according to the scheme described above - see [2] A.V. Andreev. Some issues of transportation of lunar matter. Proceedings of X1X Readings by K.E. Tsiolkovsky. Section "Problems of rocket and space technology". M., Institute of Electronic Engineering of the USSR Academy of Sciences, 1986. P.87-96 (with bibliography).

In [2], it was proposed to form on a hyperbolic trajectory of motion from the region of the Moon’s orbit, through the pressure of solar radiation, an extended dust “tail” (by analogy with a comet), interacting with the CO at perigee, and the fundamental possibility of tangential orientation at perigee of the “tails” was shown. two types: (I) with the leading of small dust particles of the regolith (<1 μm), carried farthest by the solar wind from the initial point of formation of the “tail”, and (II) with the leading of large dust particles (>100 μm), not far from the beginning formation of a “tail”; the first type provides a “soft mode” of interaction between the spacecraft and the “tail”, and the second type provides a “hard mode” (can be used to eliminate space debris, destroy unwanted objects, etc.).

The advantage of the solution [2] is that the part of the dust flow that did not interact with the spacecraft leaves the sphere of gravitational influence of the Earth, and therefore does not serve as a source of space debris. The particles remaining after the interaction either burn up in the atmosphere or are gradually “swept out” by solar radiation.

The principle of changing the speed of the spacecraft, including when it is launched into orbit, based on the utilization of the energy of lunar matter, was developed in [3] by A.O. Mayboroda. Satpush system: use of extraterrestrial potential and kinetic energy reserves for space launches. Aerospace sphere / Aerospace Sphere Journal, No. 2(95), 2018.

According to [3], many spacecraft with drop generators/collectors (DGC) and reserves of lunar water and regolith, from which a suspension is prepared, are launched onto a transition trajectory connecting low lunar and near-Earth orbits. When approaching the Earth, the spacecraft are lined up in a motorcade through which the KO (an aircraft launched into orbit) flies, sequentially crossing the suspension jets (“hydropushers”) formed by the CGS and receiving from the interaction with the jets, through the heat shield, an increase in speed along the launch trajectory.

Previously, the same author proposed “active” versions of the scheme [3], where instead of a screen a ramjet engine (PRE) was used, and the jets were formed in the form of linear elements: tapes, threads, fibers, etc. structures based on gels and solid materials or a combination of solids with liquid or gaseous substances, forming one or more flexible cords (length from 100 m to 300 km), including fuel-carrying ones. These cords (one at a time or in a bundle) must pass through the PRD channel and, increasing their enthalpy (due to kinetic heating or combustion), are ejected from the PRD nozzle with greater speed, creating thrust. These cords can be made, in particular, on the Moon from local raw materials - see [4] RU 2385275 C1; 03/27/2010.

A common disadvantage of the known solutions [1] - [4] is the insufficient consideration or insufficient use of those physical conditions and phenomena that affect the movement of dust particles in outer space and, consequently, the formation of their flows interacting with CO.

The main factors of the space environment in the Earth-Moon system are:

- gravity,

- electromagnetic radiation from the Sun (with solar constant ≈ 1400 W/ ^m2 ),

- solar wind (mainly proton-electron plasma with a temperature of ≈10 ⁵ K, an average concentration of 7 * 10 ⁶ m ^-3 and a particle flux density of ≈10 ¹² m ^-2 s ^-1 ),

- near-Earth plasma (ionospheric and magnetospheric).

A true picture of the formation and evolution of the dust flow can be obtained only by considering the combined action of these factors, which are significantly different in different regions of the Earth-Moon system (taking into account, among other things, the presence of shadow sections of orbits) and time variables (due to fluctuations in the level of solar activity, daily variations in electron concentration in the ionosphere, etc.).

One can also note particular disadvantages of the known solutions, such as the low energy efficiency of using regolith as a reactive working fluid in [1] (where regolith particles are ejected from the CO using a rotating impeller); the complexity of the technical implementation of the interaction of CO with matter flows in [3] and [4].

In [3], this complexity is essentially due to the fact that the interaction of the CO with the jet flow is relatively unproductive, because The spacecraft moves across the flow, and not along it - which requires a large number of spacecraft with “hydropushers” (according to example [3], about 80).

In [4], a difficult problem is the precise entry of an extended cord (bundle of cords) into the intake device of the PRD, if we also take into account that the orientation of the cord along the orbit is gravitationally unstable (the cord will tend to go into a vertical or wave-like configuration); with a cord length of ~1000 m or more, a very non-trivial system for its stabilization may be required.

The disadvantage of the technical solution [2], which is accepted as the closest analogue, is the lack of methods and means that reduce the unwanted dispersion of the generated dust flow under the influence of these factors in the space environment.

The ensemble of dust particles forming the flow will be called a plume.

The essence of the invention

The objective of the present invention is to eliminate the above-mentioned disadvantage of the prototype [2] by developing a method for the orderly formation of a plume of finely dispersed substances, reducing its unwanted scattering.

The technical result is the reduction of unwanted dispersion of a plume of finely dispersed substances, with the ability to control its size and structure (distribution of particles according to their sizes along the plume).

The solution to the problem, obtaining the specified technical result, is achieved in the proposed method of forming a dust flow, which includes the removal of finely dispersed matter, for example, lunar regolith from the region of the Moon's orbit into a transition parabolic or weakly hyperbolic geocentric orbit in the ecliptic plane, in contact at perigee with the initial near-Earth orbit of the SO, initiate the process of forming an extended plume of the specified substance by the combined effect of light pressure and gravity on dust particles, ensuring the tangential orientation of the plume as it passes perigee, where the plume interacts with the SO, and the difference of the method is that to form a single plume, dust particles of the same type are selected on average effective diameter (d) and at the same time:

- specify a coordinate system OXY with center O moving along the specified transfer orbit, and with axes invariably directed in inertial space, with the OX axis parallel to the tangential direction at perigee, and the OY axis parallel to the perigee radius vector;

- select the position of the specified transition orbit of the center O relative to the Sun so that the solar luminous flux makes specified angles with the specified coordinate axes, close to 45°;

- move the initiating device along a trajectory passing in the OXY coordinate system from a given starting point (X_O, Y_O) to a given end point (X_To, Y_To), and Y_o>Y_To>0, X_To>X_O; X_O<0 at ϑ_O>90° and X_O >0 at ϑ_O<90°, where ϑ_O - true anomaly of the center O in the transfer orbit at the moment the movement begins;

- continuously or in portions release the dust substance from the initiating device at the points of the specified trajectory at zero speed of dust particles relative to the OXY coordinate system, ensuring the optical transparency of the ensemble of particles, and the coordinates (X, Y) of the release points correspond to the initial conditions of movement, bringing the particles to the OX axis for time from the moment of release until the center O reaches perigee;

- to form a composite loop, several initiating devices are used, for which coordinate systems O ⁱ X ⁱ Y ⁱ are specified, as indicated above (i = 1, 2,…n), whose centers are O ⁱ distributed along the transfer orbit, and the dust substance is released from the initiating device at trajectory points depending on the selected effective particle diameter (d ⁱ ) in the i-th coordinate systems.

Dust matter can be delivered from accumulation and processing sites either on the surface of the Moon, or in lunar orbit or at other points in the Moon's orbit around the Earth, for example, using EMU.

The motion of the initiating device (ID) along the transfer orbit and dust near this orbit are considered within the framework of a limited two-body problem (without taking into account the gravitational fields of the Moon and the Sun).

Moreover, in the proposed method, centers O ⁱ can be distributed along the transfer orbit so that the moments of their sequential arrival at the point of this orbit with the above true anomaly ϑо are separated from each other by a time of at least τ = L/ν _π , where L and ν _π are the length and speed of the previous (i -1)-th single plume at perigee, while the trajectory of release of dust matter in the k-th coordinate system is obtained by stretching or compressing the release trajectory in the i-th coordinate system with a coefficient (d ⁱ / d ^k ) along each of the O ⁱ X axes ⁱ , О ⁱ Y ⁱ , where i, k =1, 2,…n.

It is desirable that the dust flow be formed in the region of cosmic plasma, where the Debye radius (length) of the surrounding plasma is significantly smaller than the transverse dimensions of the plume, in order to reduce the electrostatic scattering of dust particles during their photoemission and other electrification.

List of figures

The essence of the proposed invention is illustrated by the following detailed description of examples of its implementation with the accompanying drawings, which illustrate:

Fig. 1 is a schematic diagram of the formation of a loop, according to the invention.

Fig. 2-4 - approach to assessing the nature of the movement of plume particles.

Fig. 5, 6 - trajectories of the initial conditions for the formation of the plume.

Fig. 7 - estimation of plume parameters at perigee.

Fig. 8, 9 - examples of the design of the control unit for the emission of dust.

Fig. 10 - rate of expansion of the plume during the emission of dusty substances

Fig. 11 - diagrams of the interaction of the plume with the spacecraft at the perigee of the transfer orbit.

Disclosure and examples of implementation of the invention

Let us assume that the SO interacting with the plume (not shown) is in some initial orbit around Earth 1, which is in contact with transfer orbit 2 at perigee. The interaction occurs in the area indicated by position I, where plumes of various structures can be formed: a) - a homogeneous (single) plume of particles of the same effective diameter d (hereinafter referred to as simply diameter); b) - a composite of individual, at intervals, single plumes with the same or different particle diameters; c) - continuous variable structure (for example, type I).

As shown in Fig. 1, in the vicinity of the transfer orbit 2, an initial plume 3 is formed, subject to the gravity of the Earth 1 and the pressure of solar radiation 4. The plume begins to form by releasing dust from the PS 5 (with the same average particle diameter d ⁱ ) at a certain initial point with coordinates (X ⁱ =с, Y ⁱ = b) in one of ix coordinate systems (for example, in the same OXY, which is shown at other points of the transfer orbit).

The coordinates (c, b) of the point of release of each elementary (“instantaneous”) portion of particles correspond to the initial conditions of movement of these particles, bringing them to the OX axis during the time from the moment of release until the center O reaches perigee (region position I in Fig. 1). Since the center O moves along orbit 2 towards perigee, the indicated time (as well as the true anomaly ϑ) decreases, therefore the indicated coordinates of the release points depend on time and set the release trajectory (initial conditions curve): x*= c(t), y* = b(t). IU 5 moves along this trajectory, releasing particles continuously or in finite portions.

The released ensembles of particles must be optically transparent so that the particles do not obscure each other from the light stream 4. Here attention should be paid to ensuring that the effective diameter of the particles in a single plume is the same on average. This diameter is chosen so that particles with mass m = ρπd ³ /6 and midsection σ = πd ² /4 experience the same acceleration S _η from the force f _η of sunlight pressure, which can be estimated as:

where k =1…2 is the coefficient of reflection (scattering) of light (taking into account the spectral dependence of k); q _s ≈ 1400 W/m ² - solar constant; c is the speed of light; ρ is the density of regolith (for example, taken equal to 3100 kg/m ³ ). The parameters indicated in (1) are idealized (they do not reflect the imperfection of the shape, heterogeneity of the particle composition, etc.). The best selection of the required particles would be in the case of an advance process of their separation under the influence of the same pressure of sunlight (for example, in cislunar space) and collection of particles that, after a certain time, have reached the same distance (within a narrow tolerance) from the point of their release by the device , similar to the IS. Such particles should be considered to have the same “effective diameter”.

Each particle, after release, receives acceleration (1) from light pressure and gravitational acceleration, which relative to the selected coordinate system OXY, due to the relatively short trail (~100 ... 1000 m) and the small distance from the center O (of the same order), can be considered in a linear approximation . In this approximation, a particle of plume 3 with coordinates (x, y) is affected along the radius vector by a gradient-type acceleration g' = [2g(R) + ω ² R] Δ/R, where g(R) is the acceleration due to the gravitational force of the planet at a distance R from its center; ω = ν _n /R - local angular orbital velocity (ν _{n -} transversal component of orbital velocity); Δ = x sin ϑ - y cos ϑ - displacement of the particle along the radius vector R of the center O in transfer orbit 2 (see Fig. 1).

Along the orthogonal direction there is an acceleration w' = [g(R) - ω ² R] ν/R, where the orthogonal displacement of the particle is ν = - x cos ϑ - y sin ϑ. At the focal point of the orbit (ϑ = 90°) w'= 0, therefore, not too far from this point, we will neglect the acceleration w' in order to obtain a qualitative picture of the motion.

From these considerations in projections on the OX and OY axes, it is easy to obtain the following approximate equations of particle motion:

where S _x , S _y are projections of acceleration (1) onto the indicated axes: S _x = S _η cosγ, S _y = S _η sinγ (γ is the angle between the direction of the sun's rays 4 and the OX axis).

This (degenerate) system (2) can be split into the following subsystems:

A simple solution:

satisfies (2’) quite well if we use dimensionless time, according to its known connection with the true anomaly:

(see, for example, [5] Reference Guide to Celestial Mechanics and Astrodynamics. Edited by G. N. Duboshin. M. "Nauka". 1976, p. 336).

The initial values in (3) satisfy the conditions:

- at τ = 0; . (5)

The last condition means that the particle at the final moment τ _k (i.e. at perigee) falls on the OX axis. We denote dimensionless quantities as:

b and c. (6)

Choosing the orientation of the transfer orbit relative to the sun's rays, i.e., angle γ = arctan(S_at/S_x), can be estimated based on the best approximation of the last relation (2’) by solution (3). Corresponding calculations show that γ ≈ 45° (S_x≈ S_at).

In fig. 2-4 show approximations of the function ctg ϑ by a function obtained based on solutions (3):

for different values of the initial true anomaly ϑ ₀ . The ordinate axis shows the time T of the particle moving from the point ϑ ₀ (τ = 0) to the perigee ϑ = 0 (T→ τ _k ). The same curves show dependence (4) for the case of a parabola (e = 1), when integral (4) is taken explicitly; The hyperbolas used in the proposed method differ little from the parabola, since the optimal values of their eccentricities are e ~ 1.01. It is clear from this that solution (3) gives a qualitatively correct picture of the motion of particles in the plume.

The actual motion of the plume particles and the corresponding initial conditions should be clarified on the basis of calculations using more complete and accurate models. These calculations can be carried out on board the spacecraft and/or the control unit carrier, during the exchange of navigation and other information between them. The construction of the OXY coordinate system can be carried out using stellar landmarks when also using gyroscopic means.

In fig. Figure 5 shows a dimensionless curve of initial conditions in a certain system OXY located at points of transfer orbit 2 at different moments τ (at different values of ϑ ₀ ). Each point of this curve is {X=c(τ), Y=b(τ)} or {X=c(ϑ ₀ ), Y=b(ϑ ₀ )}, where all quantities are dimensionless, according to (4) and ( 6).

Since the dimensional coordinates (6) are proportional to S _η ~ d ^-1 , the dimensional curves of the initial conditions (particle emission trajectories) for particles of different diameters (d ⁱ , d ^k ) will differ from each other by the scale factor - compression or stretching with the coefficient (d ⁱ /d ^k ) along the coordinate axes. Such release trajectories are shown in Fig. 6 for particles with sizes of 20, 7 and 2 μm, using a transfer orbit with a focal parameter p = 14000 km (perigee altitude ≈ 616 km). For this orbit, the parameter ω* = (μ/p ³ ) ^1/2 ≈ 0.00038 s ^-1 .

As can be seen from Fig. 6, the emission trajectories for particles with d ≥ 20 μm run from the center O at distances of ~ 10 m, with d ≥ 7 μm at distances of ~ 100 m, with d ≤ 2 μm at distances of ~ 1000 m or more. The characteristic processing times for ejection trajectories lie in the range ΔТ = 0.2 - 0.8 (Fig. 2-4), i.e. in the range Δt = ΔТ/ ω*= 530 - 2100 s. From here we can estimate the order of the speeds (u) of movement of the IU in the OXY system: when the largest particles are ejected, u ~ 1-4 cm/s; average particles u ~ 10 - 40 cm/s; small (~ 1 µm) particles u ~ 1 - 4 m/s.

It is technically easier to eject relatively large particles in batches, and relatively small ones continuously, using some kind of accelerator.

Figure 7 shows the parametric dependences c (τ) and b (τ), as well as X _k (τ) = X _k [c (τ)] - the coordinates of the corresponding particles on the OX axis at the moment they reach perigee (the same for all particles released in a given OXY system along the emission trajectory). The point τ ≈ 0.667 is marked - the time of movement to perigee from the orbital point with ϑ ₀ = 90°. The difference in values ΔX _k = X _k (τ ₁ ) - X _k (τ ₂ ) characterizes the length of the plume (L) at perigee, formed during the time (τ ₁ - τ ₂ ) of the movement of the control unit along the emission trajectory.

As can be seen from Fig. 7, the length L=ΔX _k of a single plume at perigee is several times less than its original length when formed along the ejection trajectory. This means that the plume becomes denser compared to the initial rarefied (optically transparent) state.

This compaction partially compensates for the scattering of the plume in the plane of the transfer orbit (including due to a decrease in its transparency near perigee). Deviations of particles normal to the orbital plane also decrease significantly at perigee, because the perigee argument (ω) and the longitude of the ascending node (Δω) do not change with these deviations. The values of normal speeds ν _n must be limited by the value | _νn | ~ 1 cm/s (as can be seen, for example, from Newton’s equations [5], p. 335).

By repeating the described process of forming a single plume by a plurality of IUs following each other along orbit 2, it is possible to increase the length of the plume at perigee and obtain its desired structure, as shown in Fig. 1, item 1. To obtain a continuous composite train, the moments of sequential arrival of centers O ⁱ to the point with a true anomaly ϑ _o should follow each other very quickly, obviously with a delay of no more than Δτ = L/ν _π , where L and ν _π are the length and speed of the previous (i - 1)-th single plume at perigee. Since L ≈ 100 - 1000 m, and ν _π ≈ 11 km/s, then Δτ ≈ 0.01 - 0.1 s. Along orbit 2, the centers O ^i-1 and O ⁱ should be separated from each other by a distance of the order of 75 - 750 m, i.e. not far. For longer delays, the loops will be at intervals (type b) in Fig. 1, pos. I).

To form several single loops (i = 1, 2,...), a plurality of IU 5 ⁱ can be used, removed from the lunar orbital region by a carrier 6, launched mainly using an EMU (for which, for example, windings 7 are provided). The carrier has on board the necessary systems for orientation, correction (8), navigation, modeling blocks (including blocks for specifying coordinate systems O ⁱ X ⁱ Y ⁱ ) and calculating the movement of the control unit along ejection trajectories. The control units have minimal hardware: mainly receivers of commands from the carrier and actuators for moving along ejection trajectories: blocks 9 of microjet engines on a retractable rod (which can be hingedly connected to the housing 10 of the control unit) and means for releasing particles integrated with the housing 10. The corresponding commands from the carrier 6 are transmitted, for example, by means of phased array antennas (including folding ones) 11 to the DUT; control and telemetry are transmitted in the opposite direction using antennas 11 installed on the DUT (Fig. 8).

To coordinate with the movement of the spacecraft towards perigee, information exchange is also established between the carrier 6 and/or PS 5 ⁱ - directly or through remote points.

The IUs are separated from the carrier at points of orbit 2 with their required distribution, according to the sequence of ejection of particles of single plumes described above. Fixation of virtual points O ⁱ and axes can be done on the basis of astronomical landmarks (stars, quasars, etc.) observed from the carrier, using, if necessary, also gyroscopic systems. To facilitate navigation of the PS, radio or laser beacons (reflectors) can be placed at points O ⁱ , and some simple beacon traffic control systems can be installed on board the PS. Monitoring data can be transferred to the media along with other data.

In fig. 9 schematically shows possible means of releasing particles from the IU. For emission velocities ν > 1 m/s of the smallest particles, an electrostatic system according to FIG. 9 a), containing a container 14 with a dust substance, a dust fluidization device 15 that transfers dust particles into a “suspended” state in a thin (< 2-5 cm) layer 16 at the bottom of the accelerating dust guide cup 17 with dielectric walls and a control electrically conductive grid 18. One or more corrective grids 13 can be applied. Electric field sensors 19 are installed inside the glass and between grids 13 and 18, connected to blocks 20 for receiving and processing sensor readings, connected to a decision device 21, which generates control commands to the actuator 22, generating voltages supplied to the grids. The potentials of grids 13 and 18 are set, for example, relative to the potential of layer 16 (the bottom of the glass, “grounded” into the surrounding plasma).

This system operates under the condition of initial electrification of dust particles in layer 16 - either only due to the space environment (near-Earth plasma and solar wind), or with additional short-term irradiation with a beam of charged particles. The Debye length in areas characteristic of the formation of the initial plume is ~ 1-10 m, so shielding near layer 16 is small.

For example, we will consider cylindrical charged regions: ensembles with a volumetric concentration of ejected regolith particles (ρ ≈ 3100 kg/m ³ ):

where M is the mass of the ensemble substance, R, h is the radius and height of the cylinder, d is the diameter of the particles. The initial concentration n ₀ is obtained from (8) at R=R ₀ - the radius of the glass in Fig. 9 a, h=h ₀ - layer thickness 16. The transparency condition of the initial ensemble is reduced to the requirement that the mean free path in it l = (σn) ^-1 be of the order of R, where σ is the midsection of a particle with diameter d, from which and from (8) we have:

(9)

For example, for particles with d = 10 μm (10 ^-5 m), with R = h = 5 m, mass M ~ 1.6 kg. The state of transparency of the ensemble is achieved at the degree of its expansion ξ ≈ h/h ₀ =100-200 (neglecting the change in R). If the initial thin layers 16 of accelerated dust 17 are formed with a frequency ν, then the dust flow rate will be ~ (1.6 ν) kg/s, and during the emission time of ~1000 s, an initial plume with a mass of ~ (1.6 ν) t can be formed.

Particle concentrations in this example: n = 2.6 * 10 ⁹ m ^-3 and n _o = (2.6 - 5.2) * 10 ¹¹ m ^-3 .

To estimate the electrostatic field ( _EH ) created by the described ensemble of charged dust particles and causing expansion of the ensemble in the longitudinal direction, we will use the approach to solving the problem of thin charged disks (see [6] A.N. Parshakov. Principles and practice of solving problems on General Physics, Part 2. Electromagnetism, Perm State Technical University, 2010, pp. 54-55), extending this approach to cylindrical charged regions.

An estimate of the field ( _ER ) created by the described ensemble in the transverse direction and causing its radial expansion can be easily obtained from the Gauss theorem [6, p. 26], considering the flow of the field E _R through a cylindrical surface.

As a result, we can obtain the following formulas for the electric field strengths near the ends ( _EH ) and side surface ( _ER ) of the cylinders:

For intermediate values of h, the expressions E _H and E _R are more complex. Here ε _o = 8.9*10 ^-12 F/m - electrical constant; q is the charge of one particle related to its potential ϕ as follows:

(eleven)

The values of q and ϕ should be considered as averages. The tensions E _H and E _R decrease as they are immersed inside the cylinders, so that the longitudinal and radial expansion of the ensemble of particles is regular (the closer to the surface, the faster, and vice versa).

Electrons from near-Earth plasma and solar wind can charge microparticles up to ϕ = -100 V, photoelectron emission (significant only for a rarefied ensemble of ejected particles) increases this value to ϕ = +2...5 V (see [7] A.I. Akishin, L. S. Novikov, Electrification of spacecraft, Ser. Cosmonautics, Astronomy, 3/85. Publishing house "Znanie". M. 1985, pp. 10-22). However, layer 16 at the bottom of the glass is at least partially protected from the action of the environment and is therefore electrified more slowly than on the outside of the glass.

For the example under consideration, the field of layer 16 (at h₀=0.025 m): E_H ≈ 10⁷ϕ, E_R≈ 2*10⁵ϕ (V/m), and the corresponding particle accelerations: a_N = qE_H /m ≈ 1.7*10³ϕ², A_R= qE_R /m ≈ 70 ϕ²(m/s²), from which it can be seen that even at low particle charging potentials | ϕ | ~ 1 V their accelerations will be explosive in nature: in a time t ~ 0.2 s a 200-fold elongation of layer 16 occurs (with a change in R of only ~ 50 cm), and the elongation rate (ν_H) and extensions (ν_R) of the ensemble reach values that change little over time (in this case ν_H≈ 23 m/s and ν_R ≈ 2 m/s).

Therefore, the need is obvious to either greatly limit the natural charging ϕ of dust particles (for example, by irradiation with charges of the opposite sign), or to reduce E _H and E _R by creating counter compensating fields E _H , E _R that reduce the electrification fields in the ratios: E _H - E _H = η ₁ E _H , E _R - E _R = η ₂ E _R .

The E _H field is created by the grid 18, and the E _R field can be created by the central electrode - the rod supporting the grid 13 (Fig. 9 a).

At significant particle potentials, for example, ϕ = 20 V, the fields E _H and E _R almost completely compensate for E _H and E _R : η ₁ = 2*10 ^-5 , η ₂ = 10 ^-6 ; then the indicators η _i increase in proportion to the decrease in ϕ, and only at very low potentials ϕ < 10 μV (at E _H ~ 10 ⁵ V/m, E _R ~ 10 ³ V/m) η _i ≈ 1, i.e. there is no compensation required.

For example, ϕ = 20 V, in Fig. Figure 10 shows the increase in the velocities of free longitudinal (ν _H ) and radial (ν _R ) expansions of the initial dust layer 16 until the degree of its elongation ξ = 10 is reached. At the initial moment t = 0 time (abscissa axis) there is a feature: a _H , a _R → ∞. The same expansion pattern will be for other potentials ϕ - with corresponding compensating fields. So, for ϕ = 2 V there will be η ₁ = 2*10 ^-3 , η ₂ = 10 ^-4 , etc.

Speed ν_Hand ν_R quite quickly (at least upon reaching ξ ~100) they come to almost constant values, of which ν_R lies within acceptable limits (< 1 cm), and ν_H = ν = - ν is determined by the speed ν movement of the control unit along the ejection trajectory. To correct this speed, a grid 13 is provided after the grid 18 (Fig. 8, 9).

Since the distribution of particles and fields inside the glass (Fig. 9a) generally changes during the formation of layers 16 and the acceleration of particles, the voltage on the grids 18 and 13 is accordingly adjusted according to the data from the sensors 19.

In fig. 9 b) schematically shows another version of the means for releasing particles from the IU. For emission velocities ν < 1 m/s of larger particles, you can use a mechanical system installed on the i-th control unit and containing a set of cassettes 10 ⁱ _k periodically loaded from a container (not shown) with a dust substance. The cassette (cup type) is connected to a dust fluidization device 24 (vibrator), similar to device 15 in Fig. 9a), to which the movement speed is reported - ν relative to the IU, moving along the emission path at a speed ν. For this, a high-precision manipulator 23 with an appropriate control system and “decoupling” from the vibrator 24 can be used.

By asymmetrical vibrations and reverse feeding of the cassette 10 ⁱ _k the required picture of the scattered ensemble 25 is obtained. Empty cassettes after their (one-time or repeated) use can be collected and loaded, together with the IU 5 ⁱ , onto the carrier 6, which is delivered along the ascending branch of the transfer orbit 2 k Moon.

To return to the lunar orbit for reuse, the carrier 6 is equipped with low-thrust ion or SPT engines 12 (Fig. 8), the consumption of the working fluid and energy of which is relatively small.

At the perigee of any spacecraft, for example, a space tug with a payload, mechanically interacts with a plume, which is elongated mainly tangentially and has the required character of change in the density and/or size of particles along the plume.

The KO interacts with the loop through any screen surface, schematically shown as 26 in Fig. 11. Dust particles fly onto this surface with an instantaneous speed ν(t) and are reflected from it with one or another loss of speed, or stick to the surface - this is determined by the ratio of the elastic (U) and adhesive (A) energies of the microparticles. It is characteristic that for particles with d = 5-10 μm U >>A at speeds up to ν ≈ 1000 m/s; for d = 20 µm U >>A at speeds of 500-600 m/s and U ≈ A at ν ≈ 1200 m/s; for d = 40-80 µm U >A to ν ≈ 1200-1400 m/s (but the difference U - A is small), see [8] S.V. Klinkov, V.F. Kosarev. Modeling of adhesive interaction of particles with a barrier during gas-dynamic spraying. ITAM SB RAS. Physical mesomechanics,5, 3 (2002), pp.31-32.

In the example under consideration, the SO velocity in a circular orbit with an altitude of 616 km ν ₀ = 7.54 km/s, and the speed of the plume at perigee (with the same height) ν _P = 10.67 km/s, therefore the relative speed at the beginning of the interaction is ν(0) = 3130 m/s, so U<A, and the collision of particles with screen 26 is inelastic: the rebound velocity ν'(0) = 0.

Due to the imperfection of the screen surface and the imperfect shape and structure of dust particles, the reflection from the screen will be, to one degree or another, diffuse, with diagram 27 (Fig. 11). We will consider this diagram to be symmetrical relative to the axis 28 of the loop with a strictly transverse position of the screen to this axis. Thus, the speed ν'(t), obtained by averaging over a set of reflected particles, will be determined by both inelastic losses and diffuse scattering, which will be taken into account by the general coefficient σ < 1: ν'(t) = σ ν(t).

When the screen is tilted 26 to the flow (when the normaln to the reflecting surface makes an angle α with the flow axis), the diagram can be deformed, so that the average reflection speed ν'(t) will be directed, in general, to the normaln at an angle β ≠ α.

If naturally (at U ≈ A) or intentionally, part (χ ≤ 1) of the colliding dust particles remains on the screen, then the difference in momentum fluxes to the screen 26 and from the screen will be:

along the normal n

tangent, (12)

Where = γSν - mass of dust colliding with screen 26 per unit time (γ, S - plume density and midsection area of screen 26 in the direction of axis 28).

In order for the action of the dust flow to be strictly normal, the angles must satisfy the condition =0, i.e.

(13)

Since β(α, ν) is basically a characteristic of surface 26, then (13) is the equation for determining the screen orientation angle α to the flow. The coefficient σ generally depends on α, ν(t) and other factors: σ = σ (α, ν , … ).

With mirror reflection: χ = 0, σ = 1 (which can be done electrostatically), we have α = β; for an inelastic impact: χ = 1, and obviously α = 0.

The movement of a TO with mass m in the direction - n , due to the short duration of interaction with the plume, can be described by the equation:

Moving on to the derivatives with respect to the coordinate (x) along the plume axis: we get

where m’= γS. Solution (15) will be as follows:

where L is the length of the train, and the mass of the KO varies according to the law:

The difference Δν = ν _o - ν is the speed transmitted by the KO. As can be seen, always Δν < ν _o (unless additional energy is imparted to the reflected dust).

In important special cases: a) - with specular reflection of dust particles from the surface of the screen r (α, 1, 0) = 2cos α:

and b) - with complete binding of particles by a transversely located screen r (0, σ, 1) = 1:

which simply expresses the law of conservation of momentum. Here M is the reacted mass of the plume. The most effective mode is a) specular reflection of particles - for example, with M = m ₀ and α ≈ 0 it gives ν = 0.14ν _o (Δν = 0.86ν _o ), while in case b) ν = Δν = 0 ,5ν _o .

The formation of the plume and the interaction of the dust flow with the CO occur in the magnetospheric and ionospheric plasma environment, where the Debye length is estimated in the range of ~ 1-0.01 m, which is quite small compared to the diameter of the plume ~ 10 m, and therefore the shielding of charges is significant, which reduces electrostatic dispersion of dust particles to an acceptable level.

Industrial applicability

The implementation of the proposed invention does not require the development of technologies in the field of space technology based on any new physical principles; here methods and technical means of the traditional type can be used, taking into account the rapid growth of their performance characteristics, in particular, the accuracy and speed of operations, the sharp increase in the flow of information collected, transmitted and processed using compact micro- and nanocircuits, the improvement of executive bodies, in particular , microjet (matrix) engines, etc.

Claims (8)

1. A method for forming a dust stream, including the removal of finely dispersed matter, for example, lunar regolith, from the region of the Moon’s orbit into a transition parabolic or weakly hyperbolic geocentric orbit in the ecliptic plane, in contact at perigee with the initial near-Earth orbit of the spacecraft, which initiates the process of forming an extended plume of the specified substance by joint action on dust particles by light pressure and gravity, ensuring a tangential orientation of the plume as it passes perigee, where the plume interacts with the OC, characterized in that to form a single plume, dust particles of the same average effective diameter ( d ) are selected, while: - specify a coordinate system OXY with center O moving along the specified transfer orbit, and with axes invariably directed in inertial space, with the OX axis parallel to the tangential direction at perigee, and the OY axis parallel to the perigee radius vector; - select the position of the specified transition orbit of the center O relative to the Sun so that the solar luminous flux makes specified angles with the specified coordinate axes, close to 45°; - move the initiating device along a trajectory passing in the OXY coordinate system from a given starting point (X_O,Y_O) to a given end point (X_To,Y_To), and Y_o>Y_To>0, X_To>X_O; X_O < 0 atϑ _O >90⁰and X_O >0 atϑ _O<90⁰, Whereϑ _O – true anomaly of the center O in the transfer orbit at the moment of the beginning of the movement; - continuously or in portions release the dust substance from the initiating device at the points of the specified trajectory at zero speed of dust particles relative to the OXY coordinate system, ensuring the optical transparency of the ensemble of particles, and the coordinates (X, Y) of the release points correspond to the initial conditions of movement, bringing the particles to the OX axis for time from the moment of release until the center O reaches perigee; - to form a composite loop, several initiating devices are used, for which coordinate systems O ⁱ X ⁱ Y ⁱ are specified, as indicated above ( i = 1, 2,… n ), the centers of which О ⁱ are distributed along the transfer orbit, and the dust substance from the initiating device is released at trajectory points depending on the selected effective particle diameter ( d ⁱ ) in the i -th coordinate systems. 2. The method according to claim 1, characterized in that the centers O ⁱ are distributed along the transfer orbit so that the moments of their sequential arrival at the point of this orbit with the specified true anomaly ϑ _o are separated from each other by a time of at least τ = L/V _π , where L and V _π are the length and speed of the previous ( i -1)th single plume at perigee, while the trajectory of the release of dust matter in the k -th coordinate system is obtained by stretching or compressing the release trajectory in the i -th coordinate system with the coefficient ( d ⁱ / d ^k ) along each of the axes O ⁱ X ⁱ , O ⁱ Y ⁱ , where i , k = 1, 2,… n . 3. The method according to claim 1, characterized in that the dust flow is formed in the region of space plasma, where the Debye radius (length) is significantly smaller than the transverse dimensions of the plume.