INTRODUCTION

The beginning of direct measurements of the profile of the main parameters of the atmosphere of Mars goes back to the Soviet devices Mars-3, -5, and -6. But, unfortunately, profiles were not received in these missions. On all other missions, before the Viking flights, pressure and temperature measurements were carried out by remote methods. For the first time, direct profile measurements were carried out with the Viking-1 and -2 devices (Seiff and Kirk, 1977). The vertical structure of the Martian atmosphere was obtained. It formed the basis of the model of the atmosphere of Mars.

To date, out of 40 missions directed to Mars, only seven have successfully measured vertical profiles (density, pressure, and temperature) using accelerometers during deceleration of the spacecraft in the atmosphere. This technique is used for all landers in order to cancel the speed of entry of the device into the atmosphere of the planet (Loch, 1966). It should be taken into account that the hardware (descent and landing scheme) and the characteristics of the acceleration sensors determine the profile parameters, the height of the beginning and end of the acceleration measurement. After braking on an aerodynamic shield in dense layers of the atmosphere, as a rule, a parachute with a shock-absorbing device and a propulsion system are used for a soft landing. And this means that acceleration measurements stop at a certain height above the surface after the parachute opens. It is from this moment, as a rule, it becomes possible to use pressure and temperature sensors for direct measurements. But in some cases, as for the Mars Pathfinder mission, inflatable balloons were used to soften the landing load, which did not allow direct measurements in the atmosphere. Therefore, in the lowest atmosphere, the ability to measure temperature and pressure using sensors is not always available. It should be noted that when the jet propulsion system is turned on from altitudes from 2 to 4 km, the measurements of the temperature and pressure of the atmosphere will also be incorrect due to the influence of the jet stream. Therefore, the profiles obtained in previous missions and presented in Fig. 1 (Ferri et al., 2019) start and end at different heights from the surface. The profiles are tied in longitude and latitude to the landing site.

Fig. 1.
figure 1

Calculated pressure profiles from accelerometer data for all missions to Mars.

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Below are brief explanations for Fig. 1:

− Mars-6 denotes the first measurements of the structure of the atmosphere of Mars with the help of the Soviet vehicle (Kerzhanovich, 1977).

− VK1 and VK2 are measurements made by the lander of the Viking-1 and -2 spacecraft in the daytime (Seiff and Kirk, 1977).

− MPF are measurements made by the Mars Pathfinder spacecraft at night (Schofield et al., 1997; Magalhães et al., 1999).

− MER1 and MER2 are measurements (with a much lower accuracy) carried out by the PAs with the Spirit and Opportunity Mars rovers (Withers and Smith, 2006).

− PHX are measurements made with the Phoenix lander spacecraft. The first profile was obtained from the polar regions of Mars (Holstein-Rathlou et al., 2016).

− MSL are measurements made by PA with the Curiosity rover. The shortest profile was obtained, but it extends almost to the surface (Holstein-Rathlou et al., 2016).

The meteorological complex prepared for the ExoMars-2022 mission includes instruments that allow obtaining a vertical profile of the main parameters of the Martian atmosphere (density, pressure, temperature). The acceleration is measured along the entire descent trajectory from the moment of entry into the atmosphere from a height of about 160 km (determined by the sensitivity of the accelerometer) at an entry velocity of the vehicle of V0 > 6 km/s until the moment of parachute deployment. From the moment the parachute opens and the aerodynamic shield is ejected, atmospheric parameters are measured by pressure and temperature sensors, which become unreliable after the landing engines are turned on. These measurements are important for studying the dynamics and structure of the Martian atmosphere. Measurements after landing continue to refine the gravitational acceleration and the process of soil erosion under the influence of wind, as well as to look for effects caused by vibrational external loading. Based on the data obtained from the accelerometers during landing, the atmospheric density profile is calculated in accordance with the equation:

$$\rho \left( z \right) = 2({m \mathord{\left/ {\vphantom {m {{{C}_{x}}}}} \right. \kern-0em} {{{C}_{x}}}}(a){{S}_{{\text{m}}}})({a \mathord{\left/ {\vphantom {a {{{V}^{2}}}}} \right. \kern-0em} {{{V}^{2}}}}),$$
(1)

where Сх(α)is the coefficient of aerodynamic drag of the aerodynamic shield of the vehicle (determined by modeling and testing in a wind tunnel; α is the angle of attack; Sm is the section of the midsection of the vehicle; ρ is the atmospheric density (according to the model); V is the velocity of the vehicle in the atmosphere; m is the mass of the vehicle; and a is the acceleration that occurs during braking in the atmosphere.

The error in the aerodynamic coefficients for the angle of attack is taken into account according to the data obtained from the device that measures the angular velocity.

The pressure is determined by integrating the hydrostatic equation:

$${{\partial P} \mathord{\left/ {\vphantom {{\partial P} {\partial Z}}} \right. \kern-0em} {\partial Z}} = -rg,$$
(2)

where P is the pressure; ρ is the density of the atmosphere (obtained from Eq. (1)); Z is the height above the surface; and g is the acceleration due to gravity on Mars.

Temperature is calculated from pressure and density in the ideal gas approximation:

$$T = {{\mu P} \mathord{\left/ {\vphantom {{\mu P} {\rho R}}} \right. \kern-0em} {\rho R}}.$$

The uncertainty in the values of the parameters of the upper atmosphere of Mars (density and molecular weight) leads to a noticeable discrepancy between the possible profiles at altitudes greater than 120–125 km for the Martian atmosphere. Below, the atmosphere is well mixed and has an average molecular weight of 43.49.

The rate of descent is determined by integrating the acceleration over time with reference to the height:

$${\mathbf{V}} = {{{\mathbf{V}}}_{{0~}}}-\int {adt} ,$$

where V0 is the speed of entry of the vehicle into the atmosphere, V is the speed of descent, and a is the acceleration.

When separated from the spacecraft, the lander spins around the velocity vector with an angular velocity of 16.5–18.5 degrees per 1 s. This is necessary to stabilize the flight and enter the atmosphere at a given angle. The accelerometers are not located at the center of mass of the descent vehicle due to design limitations. Therefore, a weak centrifugal acceleration occurs, which introduces a second-order error. In this regard, a three-axis angular velocity meter is included in the instrumentation. The measurement of the angular velocity makes it possible to calculate the resulting error from the angular velocity and the distance to the lander’s center of mass.

SCIENTIFIC TASKS

The study of the atmosphere of Mars is a basic task in understanding the nature of the processes occurring in our Solar System. To study these processes, it is necessary to know the distributions of temperature, density, and pressure over height. As mentioned above, the main parameters of the vertical profile of the atmosphere are determined by the classical method using accelerometers mounted on landers.

The profiles of the main parameters of the atmosphere make it possible to understand how the Martian atmosphere is stratified in height. Stratification makes it possible to determine the stability of the atmosphere at all altitudes, as well as where the change in the nature of stratification occurs. This makes it possible to estimate the zones of possible turbulence in the atmosphere and their contribution to the global circulation dynamics. Of course, one profile shows the current state of the atmosphere at the time of the spacecraft’s descent into the atmosphere; nevertheless, for Mars, each such profile provides additional information about stratification variations. These variations are often associated not only with dynamics, but also with gaseous (H2O, CO2, and O3) or aerosol components in the atmosphere, which are heat absorbers and carriers. This complements the understanding of the processes occurring in the atmosphere and dynamics.

The first measurements of the vertical profile of the atmosphere using meteorological instruments mounted on the Viking landers (Chamberlain et al., 1976) were made in the daytime. And with the help of the ASI/MET Mars Pathfinder mission (Schofield et al., 1997), a third profile was obtained, moreover, at night, which provided information on daily variations in the vertical structure of the atmosphere, especially its upper part, which is inaccessible to available remote methods. In addition, an area with ice clouds was detected, although both profiles received from Viking had not recorded this before.

For the Earth, vertical profile measurements are made in the thousands per day. This highlights the importance of each such profile of the Martian atmosphere. Of course, it would be good to constantly obtain atmospheric profiles during a yearly period. It is practically impossible to carry out such measurements by hardware for Mars. But in the future, it may be possible to apply remote measurements of atmospheric parameters from the surface, which, together with long-term measurements near the surface, will reveal the long-term dynamics of the vertical structure of the atmosphere and the processes that generate it, and better understand the synoptic and global circulation of Mars.

Researched processes on Mars are:

— Static stability of the atmosphere.

— Dynamics of the vertical structure.

— Study of soil erosion under wind load.

— Study of vibrational (seismic) loads of various nature.

DESCRIPTION OF THE DEVICE

Measurements of accelerations during deceleration on landers cover the range from 10 µm/s2 to 200 m/s2. The lower limit is determined by the sensitivity threshold of the sensor (corresponds to the upper atmosphere at an altitude of about 160 km). The upper limit of the sensor range is determined by the maximum acceleration of the lander during deceleration in dense layers of the atmosphere. The entire measurement range is divided into two subranges with overlap: the first is from 10 µm/s2 to 1 m/s2 (from 10–6 g to 0.1 g), and the second is from 0.1 m/s2 to 200 m/s2 (from 10 mg to 20 g). Two triaxial accelerometers have been developed for each measurement subrange. The limiting sensitivity is determined by its own thermal equilibrium noise:

$${{a}_{{{\text{min}}}}} \approx {{\omega }_{0}}\sqrt {\frac{{\kappa T}}{m}} ,$$

where κ is Boltzmann’s constant, T is the absolute temperature, m is the value of the test mass of the accelerometer, and ω0 is the natural frequency of the elastic sensitive system of the accelerometer.

The natural frequency f of the oscillations is defined as:

$$f = 2\pi {{({m \mathord{\left/ {\vphantom {m k}} \right. \kern-0em} k})}^{ - }}^{2},$$

where k is the coefficient of elasticity of the spring, m is the value of the test mass of the accelerometer.

The limiting sensitivity of the accelerometer determines the lower limit for the test mass and the upper limit for the coefficient of elasticity of the spring.

Both accelerometers can be used as tiltmeters. The angular resolution of the low acceleration accelerometer is 2 × 10–4 deg. After landing at this point, the vertical and the gravitational component are determined. In the future, the effects of wind on the apparatus and soil erosion under it are monitored by changing the position of the apparatus to the vertical.

To measure small accelerations in the upper atmosphere, an accelerometer was designed and built according to the classical scheme. A test mass is suspended on the elastic element. Each axis has its own elastic element. The appearance of such an accelerometer is shown in Fig. 2.

Fig. 2.
figure 2

Sensory element of the accelerometer: 1, spring; 3, mass load of the spring; 2 and 4, electrodes; h is the width of the spring; Lm is the length of the membrane; Wo is the deflection in the center of the spring; and δ the membrane thickness.

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As can be seen from the figure, there is an elastic element (spring) in the center of which is the calibration mass. A differential capacitance is formed between the calibration mass and the electrodes. Under the influence of acceleration acting perpendicular to the plane of the spring, the gap between the spring and the electrodes changes, which leads to a change in the differential capacitance. The design of the sensor is made symmetrical in order to reduce temperature influence errors. For this purpose, the superinvar NKD32 with a low thermal expansion coefficient was used as a sensor material. To improve the stability of characteristics, the sensor was subjected to heat treatment and aging. The measuring surfaces of the differential capacitance were polished to optical class 1 to reduce the nonlinearity that occurs due to surface roughness. Quartz glass was used as the insulating material of the gasket. Quartz glass has sufficient mechanical strength and extremely high performance stability. To eliminate sensitivity from the effects of lateral loads, the elastic element was assembled from two rigidly connected springs located at an angle of 90° to each other (see Fig. 1) with a transverse ratio of the spring thickness to its width δ/h of at least 0.04.

Calculations of the main parameters of the elastic element of the sensor were carried out using the following equations:

$$W = {{F{{l}^{3}}} \mathord{\left/ {\vphantom {{F{{l}^{3}}} {48E{{J}_{x}}}}} \right. \kern-0em} {48E{{J}_{x}}}},$$

where Jx = δ3h/12; Е is Young’s modulus [n/m2]; F is the force acting on the test mass; h is the width of the elastic element [m]; l is the length of the elastic element [m]; and δ is the thickness of the elastic element [m].

The given dependences allow us to calculate the design characteristics of the elastic element for a given sensitivity and operating conditions.

The gap between the electrodes in the transducers was chosen in the range from 0.2 to 0.3 mm, which corresponds to the nominal capacitance from 10 to 16 pF.

In Table 1 we present the main parameters of the accelerometer for the upper atmosphere.

Table 1.   Main characteristics of the gravimeter-accelerometer
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In Fig. 3 we present a three-dimensional design of a membrane-type sensor.

Fig. 3.
figure 3

The sensitive element of a single-axis sensor with an electronic transducer.

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All sensors are installed in a single block (see Fig. 4) on three orthogonal surfaces. After installation, the nonorthogonality of the axes is calibrated. The accelerometer block itself is installed on the panel of the descent vehicle with temperature stabilization. The block diagram of the device is shown in Fig. 5.

Fig. 4.
figure 4

View of the MTK accelerometer unit.

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Fig. 5.
figure 5

Structural diagram of the accelerometer block.

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To measure small capacitance values, an Analog Devices AD7746 24-bit capacitance-to-digital converter is used.

To process signals from the sensor, an ARM Texas Instruments TMS5703137CGWTQEP microcontroller is used. The main program is loaded into the internal program memory from the external flash memory S25FL256LAGNFM010. Memory size is 256 Mbit, maximum clock frequency 133 MHz. The controller uses a supply voltage: 3.3 V is used for the I/O ports, a 1.2 V voltage regulator is used to power the controller itself. By lowering the clock frequency, power consumption can be reduced. The I2C universal serial port built into the processor is used for communication between the control part of the device and the sensor. The frequency of conversion and transmission of a signal from a 24-bit capacitance converter is set by the controller in the range from 1 to 100 Hz. The controller generates the frequency and cyclogram of the sensor poll and processes the information according to the specified program. The program can change on commands from Earth. The information stream transmits data on acceleration, temperature, supply voltage and reference signal. All these parameters are necessary to correct the temperature dependence of the sensor and the measurement circuit.

CALIBRATION OF THE INSTRUMENT

The accelerometer was calibrated on a stand, the block diagram of which is shown in Fig. 6.

Fig. 6.
figure 6

Block diagram of the accelerometer calibration stand.

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Calibration was carried out in two stages. At the first stage, the dependence of the output signal on the tilt angle of the accelerometer in the Earth’s gravity field was taken. The value of the Earth’s gravitational constant was refined for the calibration site and amounted to 9.81477 m/s2. Each of the accelerometer axes was alternately installed in a vertical plane on a tilting plate with an accuracy no worse than a few angular seconds along the vertical. The signal level was set at the signal extremum point. The angle was changed with a given step up to the maximum value. As a result, a calibration dependence and a zero offset along each axis were obtained.

An example of a static calibration dependence is shown in Fig. 7. The obtained values for the range, accuracy and sensitivity of measurements are summarized in Table 2.

Fig. 7.
figure 7

Plot for the dependence of the capacitance of the sensor C on the inclination angle of the axis at a temperature of 20°С.

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Table 2.   Accelerometer range, accuracy and sensitivity
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After that, all three sensors were assembled into one housing. The three walls of the hull were milled with high precision so that the three planes were orthogonal to each other. To eliminate the arising angular errors of nonorthogonality, measurements were carried out on a tilting plate. The main measurement axis was set in the horizontal plane and perpendicular to the rotation axis. Then, by rotating around the main axis, the maximum value for the second axis was found, and the angle of inclination of the second axis to the first was determined from the obtained acceleration value. Thus, the cosine of the deviation of the second axis from orthogonality was determined. To determine the deviation from the orthogonality of the third axis, the maximum value of the third axis was found by rotating around the main axis. The obtained value was used to determine the cosine of the deviation in the plane of the main and third axes. And the cosine of the deviation of this plane from orthogonality was defined as the deviation of the difference in the angle of rotation from 90°. Thus, the product of two cosines gave the true value of the third component in the orthogonal coordinate system. Based on the data obtained, the matrix A of the nonorthogonality of the instrument axes was calculated:

$${\mathbf{a}} = A{\mathbf{a}}{\kern 1pt} '\,\, + \Delta {\mathbf{a}},$$

where \({\mathbf{a}}{\kern 1pt} '\) is the vector of measured values from the sensor х', y', z'; \(\Delta {\mathbf{a}}{\kern 1pt} '\) is the zero offset vector along each х', y', z'; and а is the vector of true values of acceleration after offset and nonorthogonality corrections;

$$A = \left\{ {\begin{array}{*{20}{c}} {{{{\mathbf{a}}}_{{11}}}}&{{{{\mathbf{a}}}_{{12}}}}&{{{{\mathbf{a}}}_{{13}}}} \\ {{{{\mathbf{a}}}_{{21}}}}&{{{{\mathbf{a}}}_{{22}}}}&{{{{\mathbf{a}}}_{{23}}}} \\ {{{{\mathbf{a}}}_{{31}}}}&{{{{\mathbf{a}}}_{{32}}}}&{{{{\mathbf{a}}}_{{33}}}} \end{array}} \right\}$$

is the nonorthogonality matrix.

At the second stage, the accelerometer was mounted on a vibration stand to obtain the frequency dependence of the calibration parameters. Measurements of acceleration were carried out for various frequencies and amplitudes of oscillations. Statistical data processing was used to eliminate vibration noise errors, but the absolute accuracy in this case did not exceed 1%.

The accelerometer and angular velocity meter (AVM) for the lower atmosphere are assembled in one package based on sensors from Analog Devices ADIS. The sensor includes a triaxial accelerometer and a triaxial angular velocity sensor.

The sensor view is shown in Fig. 8.

Fig. 8.
figure 8

View of the sensor from Analog Devices.

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The accelerometer calibration for the lower atmosphere was carried out similarly to the calibration of the accelerometer for the upper atmosphere. The obtained values of accuracy and sensitivity are given in Table 3.

Table 3.   Accelerometer calibration values by range, accuracy, and sensitivity
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The sensor modes were controlled by an ARM Texas Instruments TMS5703137CGWTQEP microcontroller, which was used for the upper atmosphere accelerometer. This made it possible to save consumption and weight of the accelerometer complex.

In Table 4 we present the main parameters of the accelerometer for the lower atmosphere.

Table 4.   Main characteristics of the accelerometer for the lower atmosphere
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The angular velocity meter, as mentioned above, is assembled on the basis of sensors from Analog Devices. Calibration of the AVM was carried out on a centrifuge and by the pendulum method. Vibration noise was eliminated by statistical processing. The resulting calibration was compared with the manufacturer’s standard calibration. In Fig. 9 we plot the deviation of the resulting calibration from the manufacturer’s calibration.

Fig. 9.
figure 9

Plot of the deviation of the obtained calibration from the manufacturer’s calibration in the entire frequency range at a temperature of 20°C.

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In Table 5 we listed the main parameters of the AVM.

Table 5.   Basic parameters of the angular velocity meter
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CONCLUSIONS

The accelerometer block developed for the landing platform for the ExoMars (-2018, -2020, and -2022) projects by the European Space Agency (ESA) and Roscosmos has been manufactured and passed all the necessary tests in accordance with the project program. Calibrations carried out confirmed its high performance. Field tests have shown the correctness of laboratory calibrations and measurement methods. Upon completion of the joint ESA-Roscosmos program, accelerometers can be used in other projects to explore Mars and other planets of the solar system. In addition, accelerometers are currently part of the meteorological complex of the Venera-D mission. Accelerometers have a reserve for improving the characteristics of accuracy and sensitivity, which is expected to be implemented in subsequent projects.