RU2754098C1 - Laser space gravity gradiometer - Google Patents

Abstract

FIELD: space industry.

SUBSTANCE: invention relates to a device for measuring the gravitational gradient on board a spacecraft. The device contains two test masses (1, 2) with optical reflective elements of the laser beam fixed on them in the form of a pair of corner reflectors (12-15) and a laser interferometer (5) optically connected to them, located on one coordinate axis of the spacecraft, as well as calculator (7). Additionally, the device includes arresters (3) rigidly connected to the spacecraft body for fixing and ensuring the free flight of test masses (1, 2) inside the spacecraft, gyroscopic stabilizers (10, 11) of the position in space, calibration mass (4), mounted on a movable carriage rigidly connected to the spacecraft body. The device also contains two additional laser space gravity gradiometers in the same composition, located on two other coordinate axes of the spacecraft, meters (21) of the Doppler shift of laser radiation as part of laser interferometers (5), a source of highly stable counting pulses in the form of a highly stable frequency standard (6). Moreover, the output of a highly stable frequency standard (6) is connected to laser interferometers (5) of all three gradiometers, and the outputs of laser interferometers (5) of all gradiometers are connected to a computer (7).

EFFECT: ensuring simultaneous measurements of three components of the gravitational gradient on board the spacecraft, increasing the measurement accuracy by increasing the accuracy of measuring the signal parameters at the output of the photodetector, by increasing the degree of stabilization of the laser beam reflectors and increasing the path length of the working laser beam, as well as the flight calibration of the device by introducing in the composition of the device of the calibration mass; facilitating the placement of the instrument on board a spacecraft of complex design by avoiding obstacles for the measuring laser beam near the center of mass of the spacecraft.

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Description

The invention relates to measuring equipment, is intended to measure the gravitational gradient on board spacecraft and can be used, in particular, in geology for the global search and determination of mineral reserves, in geodesy to clarify the global and local models of the Earth's gravitational field (GPF) and others planets, for monitoring temporal variations of the gravitational field, as well as in the navigation through the GPZ for the preparation of global navigation gravity maps.

Known laser ballistic gravimeter (RU 2475786 C2), which can be used on board a spacecraft to measure the gravitational gradient. It is based on the use of one test body freely falling in the Earth's gravitational field. The free fall acceleration is determined from the results of measuring the distance traveled by a freely falling test body for a known period of time, counted by a time interval meter. The distance traveled is determined using a laser interferometer by counting the number of interference fringes that have passed in front of the interferometer's photodetector. In this case, each strip corresponds to the movement of the test body by half the wavelength of the laser radiation. The pulses from the photodetector corresponding to the passage of each strip, as well as the results of measurements of the corresponding time intervals from the time interval meter, are fed to the computer system, which determines the value of the gravitational acceleration.

An analog device for measuring the gravitational gradient in space on board the spacecraft has low accuracy, since in zero gravity the free fall acceleration of the test mass is about 10 ⁶ times less than on Earth, and the spacecraft, simultaneously with the gravitational field, is additionally affected by a poorly predicted drag force residual atmosphere. In particular, at a spacecraft orbit altitude of 500 km, the residual gravitational acceleration caused by the horizontal gradient of the Earth's gravitational field W _xx = 1210E at a distance of 1 m from the spacecraft's center of mass is 1.2⋅10 ^-6 m / s ² . The average value of the horizontal component of the atmospheric drag acceleration caused by the influence of the residual atmosphere on the spacecraft has a comparable value for a spacecraft of medium size - 10 ^-5 -10 ^-6 m / s ² , and in different parts of the orbit, depending on the influence of the Sun, this value changes by 20-30%. This limits the accuracy of determining the true value of the gradient, as well as its anomalies along the orbit. When the instrument axis is placed along other coordinate axes of the spacecraft, it is difficult to control the effect of solar pressure, the Earth's albedo, etc., which also reduces the accuracy of determining the gradient.

Known gravitational gradiometer (patent US 3693451), which can be used on board a spacecraft (SC) to measure the gradient of the Earth's gravitational field (GPF). The prototype diagram includes the following elements (Fig. 1):

1 - the first trial weight;

2 - second trial weight;

3 - laser;

4 - beam splitter;

5 - corner reflector (retroreflector) with lower and upper light-transmitting edges;

6 - corner reflector (retroreflector) with a lower light-transmitting edge;

7, 8 - light-transmitting channels passing through the centers of test masses 1 and 2;

9 - laser beam;

10 - photodetector;

11 - meter;

12 - calculator;

CM KA - the center of mass of the spacecraft;

OX _KA , OY _KA , OZ _KA - axes of the spacecraft onboard coordinate system;

OXe, OYe, OZe - axes of the geocentric rectangular coordinate system.

The device is a gravity gradiometer (prototype) based on the use of two test bodies 1 and 2, placed at a distance L from each other, connected by a laser interferometer, which includes: laser 3, beam splitter 4, corner reflectors 5 and 6 at the center of mass of test bodies 1 and 2 light-transmitting channels 7 and 8 built into test masses 1 and 2; laser beam 9 connecting the corner reflectors 5 and 6, as well as the photodetector 10. The measuring axis of the prototype coincides with the direction of the laser beam 9. A meter 11 is connected to the photodetector 10, which is designed to measure the number of interference fringes transmitted to the input of the photodetector 10, as well as for measuring time intervals corresponding to the passage of each interference fringe. Calculator 12 is connected to the output of the meter AND.

The principle of operation of the prototype gravitational gradiometer on board the spacecraft is as follows. Two test masses 1 and 2 are lined up by light-transmitting channels 7 and 8 along the measuring axis, and then they are brought into a state of free movement. Due to the difference in vertical gravitational accelerations g ₁ , g ₂ , corresponding to the centers of test masses, as well as due to centrifugal acceleration, they begin to move away from each other. In this case, the distance by which two masses scatter over a known period of time is proportional to the gravitational gradient. The task is to measure the increment in the distance between freely falling test masses over a known period of time. For this, a laser interferometer is designed, which works as follows. From the laser 3, the light beam is directed to the beam splitter 4, reflected from which it hits the semi-transparent corner reflector (retroreflector) 5. Part of the beam (usually about 50%) from the retroreflector 5 is reflected back to the beam splitter 4, the other part of the beam 9 (about 50%) - passes to the corner reflector 6, is reflected from it and through the retroreflector 5 is directed back to the beam splitter 4. Passing through the beam splitter 4, both returned beams interfere on the plane of the photodetector 10, forming a traveling interference pattern in the form of a sequence of light and dark interference fringes. Each stripe corresponds to a half-wave path difference between the two interfering beams. At the output of the photodetector, a sequence of electrical pulses is formed, corresponding to the beginning and end of each half-wave band, and the number of pulses determines the desired increment in the distance at the end of the free motion of the masses.

Let us estimate the error of the prototype when using the traditional method of counting the number of interference fringes in the interval of motion of the test masses. To do this, we determine the increment in the distance between the masses caused by the action of the desired gradient. On this day, we will agree (Fig. 1) that the OX axis of the _{spacecraft of the spacecraft} onboard coordinate system is directed tangentially to the spacecraft orbit along the vector of its orbital velocity, the OY _KA axis - along the normal to the orbital plane. In this case, the vertical axis OZ _KA with respect to the Earth of the spacecraft onboard coordinate system is constantly directed vertically away from the Earth. For this reason, the spacecraft and its coordinate system rotate in orbit around the OY _KA axis with the orbital angular velocity Ω _y . We will place the measuring axis 9 of the prototype laser interferometer (Fig. 1) so that it coincides with the axis OZ _KA , and the center of mass of the spacecraft is located on the measuring axis of the device between the test masses.

The difference of gravitational and centrifugal accelerations between the points of placement of corner reflectors 5 and 6, respectively g ₁ , g ₂ , at a distance L is represented as:

- вертикальный гравитационный градиент ГПЗ.where

- vertical gravity gradient of the GPZ.

The increment in the distance ΔL between the test masses with their accelerated free "runaway" in the time interval Δt will be (we neglect the initial speed of "runaway"):

The interferometer, through the use of forward and backward beams, measures twice the increment of this distance, which can be represented in two forms:

where n ^meas - the measured number of half-wave interference fringes in the interferometer; n _G , n _Ω - the number of stripes corresponding to the influence of the gradient and rotation;

- distance increment caused by the influence of the gravitational gradient;

- distance increment caused by the influence of centrifugal forces during the rotation of the coordinate system.

. Поэтому из (5) находим:It is known that for a circular orbit the angular velocity of the coordinate system is determined with high accuracy by the geocentric gravitational constant μ _e and the current spacecraft radius vector ρ _KA in the form of the formula:

... Therefore, from (5) we find:

This value is calculated using the current parameters of the spacecraft orbit with a relative error of 10 ^-7 -10 ^-8 .

Further, from (3) using (4) - (6) we find:

whence the desired result follows:

From here, by differentiation, we find the error in determining the gradient:

where δn _meas is the error in counting the number of strips.

The estimation of the number of interference fringes corresponding to the influence of the gradient G _zz in accordance with formula (7) and the determination of the error in determining the gradient will be carried out with the following initial data:

1) Δt = 5 s. This choice is explained by the fact that when measuring the gradient using a prototype on the Earth's surface, the fall time with a difference in the heights of the fall of the test masses of about 1 m is t ₂₁ ≈0.45 s. During this time, the change in the position of the corner reflectors in free flight on Earth does not go beyond the permissible limits. When using the prototype in a state of zero gravity, this time must be increased, but no more than 10 times, otherwise the unstable position of the reflectors will introduce uncontrollable errors;

2) λ = 0.63 μm (helium-neon laser); L = 1 m (as in the prototype);

3) G _zz ≈ 2660 Е = 2.66⋅10 ^-6 s ^-2 , 1Е = 1Eotvos = 10 ^-9 s ^-2 , which corresponds to an altitude of the spacecraft's circular orbit of 300 km.

As a result, we have n _G = 211, and at δn = 1 the error is 12.6 Eotvos.

Such measurement accuracy when solving the problem of refining the parameters of the GPZ from space is unacceptable.

In general, the disadvantages of the prototype when placed in space are as follows:

- low accuracy of measurements, which, in particular, is explained by the lack of means for calibrating the device during space flight, as well as the lack of stabilization of test masses, which limits the time of their free flight and, as a consequence, the accuracy of measurements;

- impossibility of placing the device near the center of mass of the spacecraft if other devices are located there, for example, fuel tanks, propulsion systems, etc .;

- impossibility of simultaneous measurement of other components of the GPZ gradient tensor.

The technical result obtained from the implementation of the invention is to provide simultaneous measurements of three components of the gravitational gradient on board the spacecraft, increase the measurement accuracy by increasing the accuracy of measuring the signal parameters at the output of the photodetector, by increasing the degree of stabilization of the laser beam reflectors and increasing the path length of the working laser beam, as well as flight calibration of the device by introducing a special calibration mass into the device. In addition, it is possible to bypass obstacles for the measuring laser beam near the center of mass of the spacecraft, which facilitates the placement of the device on board a spacecraft of complex design.

The essence of the invention is illustrated in FIG. 2, where it is indicated:

(1x, 2x); (1y, 2y); (1z, 2z) - test (sensitive) masses of gradiometers located on the axes of the orbital coordinate system of the spacecraft;

3x, 3u, 3z - devices for recording and arresting test masses;

4х, 4у, 4z - calibration masses located on the axes of the orbital coordinate system of the spacecraft;

5x, 5y, 5z - laser interferometers;

6 - onboard source of highly stable counting pulses;

7 - calculator.

In comparison with the prototype, the proposed device additionally includes two more gradient meters oriented along the OX and 0Y axes of the spacecraft orbital coordinate system, devices for launching into free flight and locking test masses 3, calibration masses 4, as well as an onboard source of highly stable counting pulses 6 to increase measurement accuracy.

To clarify the essence of the invention, let us agree that the OX axis of the _{spacecraft of the} onboard orbital coordinate system of the spacecraft OXYZ is directed tangentially to the spacecraft orbit along the vector of its orbital velocity, the axis OY _KA is directed along the normal to the orbital plane. In this case, the vertical axis OZ _KA with respect to the Earth of the spacecraft onboard coordinate system is constantly directed vertically away from the Earth. For this reason, the spacecraft and its orbital coordinate system rotate in orbit around the OY _KA axis with the orbital angular velocity Ω _y .

Along each axis of the orbital coordinate system, there are gravitational gradient meters (they are marked with appropriate indices), each of which includes test masses 1 _xyz and 2 _xyz , located at the initial distance L _xyz , mass cages 3 _xyz , calibration masses 4 _xyz , and laser interferometers 5 _xyz . The test masses are brought into a state of free motion along the corresponding axes and return after a given time interval to their initial state with the help of cages 3. The test (sensitive) masses, brought by cages 3 to a state of free motion, due to the action of gravitational gradients of the GPZ, begin to approach (or move away) along the corresponding axis relative to the initial state. As is known, the sensitive masses located on the OZ axis move away from the spacecraft's center of mass with an acceleration proportional to the distance from the center of mass. Sensitive masses, placed on the other two axes - approach with acceleration, also proportional to the distance from the center.

The distance increment proportional to the gravitational gradient (positive or negative) is measured using laser interferometers 5, to the input of which counting pulses are fed from a source of highly stable counting pulses 6. The results of measurements of the gradients G _xx , G _yy , G _zz along all three axes are fed to the calculator 7, where the compliance of the results of the three current measurements with the Laplace relation is carried out: G _xx + G _yy = 0.

The use of calibration masses 4 consists in creating an additional calibration gravitational gradient, which, for a certain period of time, moves the test masses of the device relative to each other by a calibrated distance. In particular, a 10x10x10 cm calibrated tungsten-rhenium alloy mass has a mass of 19.3 kg. The center of the calibration mass is 5 cm away from the edges. It is easy to calculate that when approaching a test mass of the same design at a distance of 10-11 cm between their centers, a gravitational field is created with an acceleration of about 1.3⋅10 ^-7 m / s ² . The created gradient on the base of about 1 m will be 130 Eötvös, which is commensurate with the gradient of the anomalous GPZ.

As a highly stable source of counting pulses, either quartz small-sized frequency standards with a relative instability of ^{at least 10 -11} can be used, or small-sized rubidium frequency standards of the "KSCh CPN" type, created in recent years, based on the effect of the so-called coherent population trapping - KSCh CPT [1] ... Its relative instability does not exceed 10 ^-11 -10 ^-12 , volume 60 cm ³ (5x4x3 cm), power consumption 300 mW. According to some indicators, it surpasses foreign counterparts.

The essence of each of the three identical meters of the gravitational gradient along the corresponding coordinate axes is shown in Fig. 3, where it is indicated:

1, 2 - test (sensitive) masses;

3 ₁ , 3 ₂ - test masses cages;

4 - calibrated mass M _Z ;

5 _Z - laser interferometer;

6 - source of measuring pulses (Fig. 2);

7 - calculator (Fig. 2);

8, 9 - light guide channels;

10, 11 - gyroscopic position stabilizers;

12, 13 - reflectors on a test mass 1;

14, 15 - reflectors on test weight 2;

16 - laser;

17, 18 - beam splitters;

19 - a beam of parallel laser beams;

20 - photodetector;

21 - Doppler frequency and gradient meter.

In relation to the prototype, the proposed device, located on the OZ axis on board the spacecraft, additionally introduced gyroscopic stabilizers 10 and 11 test masses, test masses arresters 3, calibration mass 4, as well as additional corner reflectors of the laser beam on each test mass. Additional reflectors double the working path of the laser beams, thereby increasing the sensitivity of the device by 2 times.

The gravitational gradient meter contains two test (sensitive) bodies 1 and 2, cages 3, calibration mass 4, interferometer 5, to which the output of the source of counting pulses 6 is connected (see Fig. 2), and the output is connected to the calculator 7 (Fig. 2 ). The centers of test bodies 1 and 2 are located along the spacecraft coordinate axis at a distance L from each other and can freely move relative to each other under the action of the Earth's gravitational field gradient. The test masses are cylindrical bodies, on the test mass 1 there are light-guiding channels 8 and 9, the axes of which are parallel to the symmetry axes of the test bodies. Test bodies 1 and 2 are mechanically connected with cages 3 ₁ and 3 ₂ , designed to launch them into a free flight state and subsequent cage in their initial state, while they are rigidly connected to the spacecraft body. To stabilize the longitudinal axes of symmetry of the test masses 1 and 2 in space during free flight, they are equipped with small-sized gyroscopic stabilizers 10 and 11, the power supply of which is made through locks 3 at rest. The calibration mass 4 in the calibration mode may approach the trial mass 2.

Light-guiding channels 8 and 9, corner reflectors (reflectors) 12-13, placed on the test mass 1, as well as corner reflectors (retroreflectors) 14-15, placed on the test mass 2, form a single measuring axis of the laser interferometer 5 _z . It includes: a laser 16, beamsplitters 17 and 18, corner reflectors 12-15, connected by a beam of parallel laser beams 19, as well as a photodetector 20. The direction of the beam of laser beams 19 coincides with the measuring axis of the device OZ. A meter 21 is connected to the photodetector 20, which is designed to measure the number of interference fringes that have passed to the input of the photodetector 20, as well as to measure the Doppler frequency shift of the signal taken from the photodetector and the corresponding Doppler time intervals corresponding to the passage of each interference band. The output of the source of measuring pulses 6 (Fig. 2) is connected to the meter 21, and the output of the meter 21 is connected to the calculator 7 (Fig. 2).

The principle of operation of the proposed gravitational gradient meter, located along one of the axes of the spacecraft onboard system, is as follows. Two test masses 1 and 2 are _{aligned with the longitudinal axes of symmetry along the measuring axis with the help of cages 3 1} and 3 ₂ , and then they are brought into a state of free movement. In the process of free movement, test masses 1 and 2 are stabilized in space with the help of gyroscopic stabilizers 10 and 11 attached to them, respectively. Due to the difference in gravitational accelerations g ₁ , g _{2 of the} centers of test masses, as well as due to centrifugal acceleration, they begin to move away from each other. In this case, the distance by which two masses scatter over a known period of time is proportional to the gravitational gradient. The task is to measure the increment in the distance between freely falling test masses over a known period of time. For this purpose, a laser interferometer 5 is intended, which operates as follows. From the laser 16, the light beam is directed to the beam splitter 17, passing through which, through channel 8, it enters the semi-transparent corner reflector (retroreflector) 12. Part of the beam (usually about 50%) from the retroreflector 12 is reflected back to the beam splitter 17, the other part of the beam (about 50 %) - passes to the corner reflector 14, is reflected from it, hits the reflector 13, is reflected from it, then falls on the retroreflector 15, reflected from which towards the test mass 1 through channel 9 is then directed to the beam splitter 18. Having passed through the beam splitter 18, both returned beams interfere on the plane of the photodetector 20, forming a traveling interference pattern in the form of a sequence of light and dark interference fringes. Each stripe corresponds to a half-wave path difference between the two interfering beams. At the output of the photodetector, a sequence of electrical pulses is formed, corresponding to the beginning and end of each half-wave band, and the number of pulses determines the desired increment in the distance at the end of the free motion of the masses.

Calibration mass 4 with a known mass M _z in the inoperative state is at a certain distance from the test masses. In the operating mode, it approaches the test mass as much as possible at a distance d, creating an additional calibrated gravitational acceleration, which is recorded by a laser interferometer.

Due to the double pass of the laser beam between the test masses, the measured effect is doubled, providing an increase in the sensitivity of the device, in comparison with a single pass in the prototype, by about 2 times.

As an alternative version of a high-precision gradiometer, a device with special wedge-shaped reflecting mirrors is proposed, which ensures multiple passes of the laser beam between the test masses. The device contains (Fig. 4):

1, 2 - test (sensitive) masses;

3, 6 - wedge-shaped fully reflecting mirrors;

4, 5 - channels for input and output of the laser beam;

7, 8 - cages of test masses;

9.10 - gyroscopic stabilizers;

11 - laser;

12, 13 - beam splitters;

14 - photodetector;

15 - meter.

A feature of this version of the gradiometer is the use of wedge-shaped mirrors 3 and 6, mounted on test masses 1 and 2. The wedge-shaped mirrors 3 and 6 provide multiple reflection of the working laser beam in the space between them, thereby increasing the measured effect and increasing the accuracy of the gradient measurements. The test masses are equipped with cages 7 and 8, which ensure the free flight of the test masses. A stable position in space of test masses 1 and 2 and mirrors 3 and 6 is provided by gyrostabilizers 9 and 10. Measurement of the characteristics of interference fringes is performed by a laser interferometer, which includes a laser 11, beam splitters 12 and 13, and a photodetector 14.

The device works as follows. Test masses 1 and 2 with mirrors 3 and 6 attached to them are brought into free flight with the help of cages 7 and 8 and are simultaneously stabilized by gyro stabilizers 9 and 10. The laser beam is divided into two beams by the beam splitter 12, one of which is the reference one, is reflected from beam splitter 13 and falls on the plane of the photodetector. Another beam - the working one - is reflected from the beam splitter, through the channel 5 of the mirror 3 falls on the mirror 6, is repeatedly reflected from it and through the channel 4 in the mirror 3, through the beam splitter 13 it enters the plane of the photodetector 14, where, together with the reference beam, it forms a traveling interference pattern. Further, the electrical signal from the photodetector, as in other versions of the device, is fed to the meter 15, from the output of which information about the gradient is taken.

The main feature of the embodiment according to FIG. 4, is an increase in the measured effect and, as a consequence, in the measurement accuracy due to multiple (up to 10 times) re-reflection of the working laser beam between the wedge-shaped mirrors.

Another possible implementation of the gradiometer, the diagram of which is shown in Fig. 4, is based on the use of flat parallel mirrors 3 and 6, mounted on test masses 1 and 2. The peculiarity of such a device is that when the test masses pass into the free mutual motion mode, which is performed using cages 7 and 8, parallel mirrors 3 and 6 form a multi-pass Fabry-Perot interferometer. In this interferometer, with multiple reflections from flat mirrors, a system of interference fringes with a very sharp contrast is created, which, when the mirrors move together, move along the surface of the mirrors in one direction or the other, depending on the direction of the mutual movement of the mirrors. The movement of these stripes along the plane of mirror 3 through channel 4 is fixed by a photodetector 14. To implement a Fabry-Perot interferometer, mirrors with a very high reflectance are required. An important feature of the interference pattern in the Fabry-Perot interferometer is the increased sharpness of the interference fringes, which exceeds the sharpness of the fringes in the Michelson interferometer considered above by at least ten times. This circumstance makes it possible to increase the accuracy of fixing the transition of the brightness of the interference pattern through zero and, accordingly, to increase the accuracy of the formation of pulses corresponding to these moments at the output of the photodetector. These pulses are used in the meter 15 to count the number of interference fringes that have "run through" the field of the photodetector and their duration. The error of the moment of generation of these pulses in the Fabry-Perot interferometer, in comparison with the interference pattern in the Michelson interferometer, is reduced by at least ten times, which makes it possible to increase the accuracy of determining the gravitational gradient at the output of the meter 15.

At the same time, the use of a Fabry-Perot interferometer imposes increased requirements on the accuracy of stabilization of plane mirrors in space using gyro stabilizers 9 and 10.

As another alternative technical solution that provides an increase in the measurement accuracy, it is proposed to use Luneberg optical lenses as test masses 1 and 2 with reflectors. The use of these ball lenses does not require stabilization of the test masses, which can introduce additional errors, and thereby increases the measurement accuracy. An embodiment of these lenses is shown in FIG. 5, where it is indicated:

1 and 2 - test masses in the form of optical Luneberg lenses;

3 ₁ and 3 ₂ - cages;

4 - translucent coating on the hemisphere of the lens 1;

5 - fully reflective coating on the hemisphere of the lens 2;

6 - laser interferometer;

7 - laser;

8 - beam splitter;

9 - laser beam between the test masses, coinciding with the measuring axis of the device;

10 - photodetector;

11 - Doppler frequency and gradient meter.

The main feature of the well-known Luneberg lens is the dependence of the refractive index on the radius "r" of the point under study according to the "1 / r" law. In the center of the lens, the refractive index is maximum. For this reason, any optical beam entering the lens from one hemisphere is bounced back, reflected from the metallized coating covering the second hemisphere (see Fig. 5). If the input beam propagates through the center of the lens, then the reflected output beam will also pass through the center of the lens. Input rays that do not go through the center exit back symmetrically to the input rays on the other side of the center. One hemisphere of the lens 1 (in Fig. 5 - the lower one) is covered with a semitransparent metallized layer 4 so that part of the beam passes to the lens 2, and part of the beam is reflected back into the laser interferometer 6. In lens 2, the upper hemisphere is covered with a reflective layer 5, which ensures the return beam on the lens 1. Arresters 3 are designed to start in the free movement mode and then lock test masses 1 and 2 to their original state after a given period of time.

The proposed version of the device works as follows. With the help of restraints, 3 test masses 1 and 2 are brought into a state of free movement. The requirements for the angle of rotation of both lenses around the center of mass during free hovering are low, since the optical properties of the lenses do not depend on the angle of entry of the laser beam. This property of the lenses improves the measurement accuracy. Under the action of the gravitational gradient, the distance between the test masses changes, and the increment in the distance is measured by a laser interferometer 6. For this, the laser 7 sends a beam of light to the beam splitter 8, the reflected beam hits the semitransparent coating 4 of the lens 1. This beam is partially reflected back and partially passes through the body lens 1 on lens 2 in the form of ray 9. Here, refracting in the body of lens 2, the ray is reflected back to lens 1. Further, passing through the body of lens 1 and semitransparent coating 4, it hits the beam splitter 8, at the output of which, together with the first ray, it forms the interference pattern on the plane of the photodetector 10, to the output of which the Doppler signal parameters meter 11 is connected. According to the measurement results, the desired gradient is found.

The considered alternative construction of the gradient meter on Luneberg lenses provides higher accuracy than the prototype based on the use of unstabilized corner reflectors (Fig. 1). This is explained by the fact that the fed-square spread of the reflection time error (the so-called "target error") for an unstabilized Luneberg lens is about an order of magnitude smaller than for unstabilized corner reflectors [2].

Another alternative option for constructing a gradient meter, providing a higher accuracy and avoiding an obstacle near the center of mass of the spacecraft, is a meter based on the use of Luneberg lenses and optical fibers. It contains (Fig. 6):

1, 2 - test masses in the form of Luneberg optical lenses;

3 ₁ , 3 ₂ - test masses cages;

4 - translucent reflective coating of the lower part of the surface of the lens 1;

5 - fully reflective coatings of the surfaces of lenses 1 and 2;

6 - laser interferometer;

7-10 - fiber optics with focusing lenses at both ends;

11 - a bundle of optical fibers, bending around an obstacle for direct laser beams;

12 - introductory focusing lens;

13 - output focusing lens;

14 - laser;

15 - beam splitter;

16 - mirror;

17 - photodetector;

18 - gauge of the gradient G _aa along this axis.

19 - an independent unit of the test mass 1 equipment;

20 - independent unit of test mass equipment 2.

The main feature of this version of the meter are optical Luneberg lenses and fiber optic fibers 7-10 with focusing lenses at the ends, which are assembled in a bundle 11. It allows you to bypass an obstacle on board the spacecraft that arises in the path of direct laser beams. These can be rocket engines, fuel tanks, telescopes, etc. Another feature is the use of Luneberg lenses 1 and 2, through which optical beams can propagate at different angles without interfering with each other. A partially reflective coating 4 is applied to the lens 1 in the lower part of the hemisphere, and reflective coatings 5 are applied to both lenses. The end focusing lenses of the optical fibers are located near the surface of test bodies 1 and 2 at a distance of 1-2 mm. The input of light beams into the Luneberg lens 1 from the interferometer 6 is carried out using a focusing lens 12, the output of the beam into and the interferometer is carried out using a lens 13. The laser interferometer 6 contains a laser 14, a beam splitter 15, a mirror 16, an introductory focusing lens 12, an output focusing lens 13 , photodetector 17, the output of which is connected to the meter 18.

The device works as follows. After launching test masses 1 and 2 with the help of cages 3, the laser beam from the laser 14 through the beam splitter 15 hits the mirror 16, then through the lens 12 onto the partially reflecting coating 4 on the Luneberg lens 1. Part of the beam is reflected back and as a reference beam through the mirror 16 and the beam splitter 15 hits the plane of the photodetector 17. The other part through the center of the Luneberg lens 1 enters the light guide 7. From the output of the light guide 7, the beam enters the Luneberg lens 2, is reflected from the coating of its rear hemisphere 5 and enters the light guide 8. Further, the beam through the light guide 8 enters the lens 1, is reflected from its coating 5 and enters the light guide 9. Similarly, passing the light guides 9 and 10, the beam through the center of the lens 1 and the focusing lens 13 through the divider 15 enters the plane of the photodetector 17, where it interferes with the reference beam. The output of the photodetector is connected to the meter 18, which operates in the same way as in the previously considered variants of the gradiometer.

All light guides 7-10 are assembled in a flexible compact bundle 11, with which you can easily bypass obstacles to direct laser beams. The working beam of the interferometer passes the distance between the test bodies twice, increasing the measured effect and increasing the sensitivity of the device.The increment in the distance between the test masses measured with the interferometer is determined by the change in the optical paths between the Luneberg lenses 1 and 2 and the focusing lenses of the optical fibers 7-10. The rest of the optical paths are constant.

The entire device can be divided into 3 independent structural units: 19 - an independent unit of the test mass 1 equipment; 20 - an independent unit of the test mass 2 equipment, as well as an independent unit - a flexible bundle of optical fibers 11. This opens up great possibilities in the design of the device, when the spacecraft dimensions are used to the maximum to increase the sensitivity of the gradiometer.

Justification of the capabilities of the triaxial system of onboard space gradiometers shown in Fig. 2.

Let us justify the adopted technical solution for the simultaneous measurement of several components of the gradient tensor.

Above we agreed (Fig. 2) that the orbital coordinate system OXYZ is associated with the spacecraft's center of mass. The OX axis of the _{spacecraft of} this coordinate system is directed tangentially to the spacecraft orbit along the vector of its orbital velocity, the OY _KA axis is directed along the normal to the orbital plane. In this case, the vertical axis OZ _KA of the spacecraft coordinate system, vertical with respect to the Earth, is constantly directed vertically in the direction from the Earth. For this reason, the spacecraft and its orbital coordinate system rotate in orbit around the OY _KA axis with the orbital angular velocity Ω _y . Along each axis of the orbital coordinate system, there are gravitational gradient meters, each of which includes test masses 1 and 2, located at the initial distance L, as well as laser interferometers 5. The test masses are brought into a state of free motion along the corresponding axes with the help of cages 3 and return after a specified time interval to their original state. The increment in the distance between the trial masses along the selected coordinate axes is caused by their mutual accelerations along these axes.

The acceleration acting on a material point on board the spacecraft is determined by the well-known relation [3]:

where the first term determines the gravitational acceleration of the material relative to the center of mass of the spacecraft; the second is acceleration due to the acceleration of the center of mass of the spacecraft itself (for example, due to the resistance of the residual atmosphere, etc.); third - centrifugal acceleration due to the rotation of the coordinate system; fourth - acceleration due to angular acceleration; the latter is Coriolis acceleration due to the velocity of the mass itself.

Neglecting the influence of angular acceleration (in a circular orbit it is negligible), the influence of Coriolis acceleration (due to the extremely small velocities of test masses relative to the center of mass of the spacecraft), as well as tidal accelerations from the Moon and the Sun (due to the small dimensions of the spacecraft), as well as taking into attention to the fact of rotation of the onboard coordinate system only around the OY axis with an angular velocity Ω _у (i.e. Ω _х = Q _z = 0), we represent the acceleration of the test mass on board the spacecraft in the form:

- радиус-вектор центра масс КА; g₀, g₁ - гравитационное ускорение центра масс КА и i-й пробной массы. Как видно, влияние внешнего ускорения негравитационного происхождения W_KA на разность ускорений пробных масс внутри КА полностью исключается.where

- radius vector of the spacecraft center of mass; g ₀ , g ₁ - gravitational acceleration of the spacecraft center of mass and the i-th test mass. As can be seen, the influence of the external acceleration of non-gravitational origin W _KA on the difference in the acceleration of test masses inside the spacecraft is completely excluded.

а также раскрывая векторные произведения при принятых условиях, получаем выражение для разностного ускорения пары пробных масс 2 и 1 по координатным осям:Expanding in a series the difference of gravitational accelerations near the center of mass of the spacecraft in terms of the small parameter

and also expanding the vector products under the accepted conditions, we obtain an expression for the differential acceleration of a pair of test masses 2 and 1 along the coordinate axes:

where Δx = x ₂ -x ₁ ; Δy = y ₂ -y ₁ ; Δz = z ₂ -z ₁ ;

- компоненты градиентного тензора, три из которых связаны соотношением Лапласа:

- components of the gradient tensor, three of which are related by the Laplace relation:

We place the measuring axes of the gradiometers in accordance with Fig. 2. For a device located along the ОХ axis, in accordance with (12), provided Δx = L _x ; Δy = Δz = 0 we get:

For a device located on the OY axis at Δy = L _y ; Δx = Δz = 0 we get:

Finally, for a device on the OZ axis at Δх = Δу = 0 we have:

It should be noted that for a spacecraft orbit altitude of about 300 km G _zz ≈ + 2660 Е = 2.66⋅10 ^-6 s ^-2 ; G _xx ≈ -1330 E; G _yy ≈ -13305. They satisfy the Laplace relation (13). The signs in front of the gradients indicate the fact that in gradiometers placed along the OX, OY axes, free test masses under the action of cavitation approach, and on the OZ axis, they diverge.

Thus, three laser gradiometers, placed strictly along the axes of the onboard orbital coordinate system OXYZ, allow, in comparison with the prototype, to measure simultaneously three independent components of the gradient tensor G _αβ . In the calculator 7 (Fig. 2), according to the measurement results, a check summation is carried out according to the formula (13). If one of the three gradiometers fails, the value of the missing component of the gradient tensor can be calculated using the same formula.

Thus, the claimed technical result from the introduction of the invention, consisting in ensuring simultaneous measurements of three components of the gravitational gradient on board the spacecraft, has been achieved.

Assessment of the accuracy of the proposed gradiometer options

The estimation of the accuracy of the proposed version of the gradiometer shown in Fig. 3 is carried out for a gradiometer located along the OY axis of the spacecraft onboard coordinate system. The mutual gravitational acceleration of the two test masses in this case is determined by formula (15).

The mutual speed of the test masses is determined by a single integration of this acceleration over the time interval Δt = tt ₀ :

where V ₀ is the initial velocity of mutual motion, imparted to the masses at the moment of their unloading and launch into free flight by device 3. As can be seen from this formula, the mutual velocity of the test masses increases with time due to the gravitational gradient.

Taking into account that in this version of the gradiometer a fourfold passage of the laser beam between the test masses is realized, the mutual Doppler displacement of the laser beams - reference and working, recorded by the photodetector 20, at times t ₁ and t ₂ will be, respectively:

Since the unknown quantity here is the initial speed of launching test masses, commensurate with the speed of approach of masses due to the influence of gravity, then when taking the difference of Doppler frequencies (18), its influence disappears:

The desired gradient is determined from this formula.

The considered Doppler shift is very small: at G _yy = -1330⋅10 ^-6 s ^-2 ; (t ₁ -t ₀ ) = 13 s; λ = 0.63 μm; L _y = 1 m the Doppler shift due to the influence of the gradient is about 100 Hz. Therefore, it is first necessary to measure the original Doppler frequencies (18) using the periodometer method. The oscillation periods corresponding to the Doppler shifts (18) are determined by the relations:

The magnitude of these intervals is of the order of 0.01 s. Therefore, with the help of counting pulses coming from a source of highly stable pulses 6 (Figs. 2 and 3) with a frequency of F _cp = 10 ¹⁰ Hz and a corresponding repetition period δT _cc = 10 ^-10 s, the specified intervals can be measured with a relative error of 10 ^-8 . Since an error of the same order of the formulas (20) and Doppler frequencies determined (18) and the desired difference frequency (19): δT _{MF / T D = δF D / F} D ≈10 -8.

Based on the results of measurements and calculations of the difference Doppler frequency from relation (19), we find the desired gradient:

- измеренное значение разностной частоты (19).where

is the measured value of the difference frequency (19).

By differentiation, we find the relative and absolute errors in measuring the gradient, determined by the error in measuring the Doppler frequency:

The root-mean-square relative errors of all quantities included in this formula do not exceed 10 ^-6 . Therefore, the maximum absolute error in determining the gradient along the OY axis is: σG _yy = G _yy ⋅10 ^-6 ≈1.3⋅10 ^-3 Eotvos, which is significantly less than in the prototype (12.6 Eotvos).

Если производить измерения каждого периода доплеровского колебания (а их 10 тысяч), а разность брать между двумя разнесенными по времени измерениями, то таких разностей на интервале 25 секунд будет: N_Δ≈5000. Поэтому в результате статистической обработки погрешность измерения градиента в одном запуске пробных масс уменьшается в

раз. В этой связи, достижимая точность в заявленном устройстве характеризуется погрешностью измерения около

In addition, it is possible to improve accuracy due to statistical processing of measurement results in one run of test masses. With a duration of a flight of masses of 25 seconds, during which the spacecraft flies 200 km (as in the CRACE project), the number of interference fringes passing through the plane of the photodetector, in accordance with formula (4), will be:

If we measure each period of the Doppler oscillation (and there are 10 thousand of them), and the difference is taken between two measurements spaced apart in time, then such differences in the interval of 25 seconds will be: N _Δ ≈ 5000. Therefore, as a result of statistical processing, the error in measuring the gradient in one run of test masses decreases by

once. In this regard, the achievable accuracy in the claimed device is characterized by a measurement error of about

The accuracy of the alternate gradiometers shown in FIGS. 4 and 5, it is settled in the same way and also amounts to about 10 ^-4 Eotvos.

Thus, the claimed technical result from the introduction of the invention, consisting in increasing the accuracy of measuring the gravitational gradient on board the spacecraft, has been achieved.

The claimed technical result - ensuring the possibility of avoiding obstacles for the measuring laser beam near the center of mass of the spacecraft is also achieved in an alternative version of the gradiometer using Luneberg lenses and optical fibers (Fig. 6).

In general, all the stated technical results have been achieved:

- provided simultaneous measurement of three components of the gradient tensor (in the prototype - one component);

- the measurement accuracy is increased, in comparison with the prototype, by at least 3-4 orders of magnitude in all the proposed variants of the gradiometer;

- the possibility of avoiding obstacles for the measuring laser beam near the center of mass of the spacecraft is provided (in the prototype this is not possible).

The proposed space laser gradiometer can be used in the following areas:

- in geology for the global search and determination of mineral reserves;

- in geodesy to clarify the global and local models of the gravitational field of the Earth (GPZ) and other planets;

- for forecasting earthquakes based on global monitoring of temporal variations of the gravitational field;

- to predict climate change by monitoring changes in gas fields during the melting of glaciers and permafrost;

- in the navigation through the gas processing plant for the preparation of global navigation gravity maps.

Sources of information

1. Zotov E.A., Parekhin D.A. Investigation of the metrological characteristics of a subminiature quantum frequency standard. Almanac of modern metrology, No. 3, pp. 128-137, 2020

2. Vasiliev V.P., Sadovnikov M.A., Sokolov A.L., Shargorodsky V.D., Akentiev A.S. Precision spacecraft "BLITZ-M" // Materials of the VII International Symposium. Metrology of time and space. 2014.

3. Landau L. D., Lifshits E. M. Mechanics. Ed. "Science", M. 1973, p. 161.

Claims (6)

1. Laser space gravity gradiometer, including two test masses with optical reflective elements of the laser beam fixed on them in the form of a pair of corner reflectors and a laser interferometer optically connected to them, located on one coordinate axis of the spacecraft, as well as a computer, characterized in that in its composition additionally includes arresters rigidly connected to the spacecraft body for fixing and ensuring the free flight of test masses inside the spacecraft, gyroscopic stabilizers of position in space installed on the test masses, a calibration mass mounted on a movable carriage rigidly connected to the spacecraft body, as well as two additional laser space-based gravitational gradiometers in the same composition, located on two other coordinate axes of the spacecraft, laser radiation Doppler displacement meters from the composition of laser interferometers, a high stable counting pulses in the form of a highly stable frequency standard, and the output of the highly stable frequency standard is connected to the laser interferometers of all three gradiometers, and the outputs of the laser interferometers of all gradiometers are connected to the computer. 2. The laser space gravity gradiometer according to claim 1, characterized in that the Doppler displacement meters of the laser radiation in the interferometers are made in the form of periodometers. 3. Laser space gravity gradiometer according to claim 1, characterized in that the optical reflecting elements of the laser beam, fixed on the test masses, are made in the form of two parallel wedge-shaped mirrors. 4. Laser space gravity gradiometer according to claim 1, characterized in that the optical reflecting elements of the laser beam, fixed on the test masses, are made in the form of flat parallel mirrors forming a Fabry-Perot interferometer. 5. The laser space gravitational gradiometer according to claim 1, characterized in that the test masses are made in the form of optical Luneberg lenses, with a fully reflecting coating applied to the outer hemisphere of one of them, and a translucent reflective coating applied to the hemisphere of the other lens. 6. Laser space gravity gradiometer according to claim 1, characterized in that the test masses are made in the form of optical Luneberg lenses, a flexible multichannel fiber bundle made of a plurality of optical fibers with end focusing lenses is introduced into the gradiometer, and the fiber bundle has no mechanical contact with Luneberg lenses and in relation to them is located so that the working laser beam of the laser interferometer sequentially passes through all optical fibers of the fiber bundle and both Luneberg lenses.

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