Main features of Moon’s radio beacon and orbiter Ka-band receiver, included into “Luna-Resource-1” project

A. Kosov1, J. Ping2, A. Gusev3, V. Gromov1, V. Dehant4, S. Le Maistre4, M. Vasilev5

1Space Research Institute, Russian Academy of Sciences, (IKI RAS), Moscow, Russia

2National Astronomical Observatories of CAS, Beijing (NAOC), China

3Kazan University, Kazan, Russia

4Royal Observatory of Belgium, (ROB), Brussels, Belgium

5Institute of Applied Astronomy (IAA RAS), St-Petersburg, Russia

Abstract

Russian Luna space exploration program up to 2025 includes: Luna-Resource orbiter and Luna-Resource lander shown on the figure 1;




A) Luna-Resource-1 Orbiter




B) Luna-Resource-1 Lander

Figure 1 A) – Orbiter and B) – Lander

Currently two different radio science (RS) instruments have included into the projects: radio beacon, deployed at the lander and Ka band receiver, deployed at the orbiter. By means of radio beacon and Ka band receiver it will be possible to conduct a lot of valuable investigations and celestial mechanics experiments. Moreover the instruments will be very useful for service tasks such navigation and low rate telemetry transfer to Earth.

Key words: coherent transponder, microwaves, Moon, lander, orbiter, transmitter, receiver, antenna

1 Radio Beacon deployed on Lander

Lander’s radio beacon have one X band receiver and two transmitters: X band and Ka band. The radio beacon has three main modes of operation: autonomic mode of operation, mode of coherent transponder and mode of scientific data transmitter. In autonomic mode the frequency stability of irradiated signal will be determined by the stability of internal reference source. In coherent transponder’s mode the transmitter’s signals will be locked by reference signal sending from Earth. In scientific data transmitter mode the radio beacon can transmit data to Earth’s antenna with speed up to 0.1 Mbps depending of performance of Earth ground station. This feature is very useful when the lander will powered from nuclear power source and main radio link will be not operational. The chart of the radio beacon is depicted on figure 2.

The instrument consists of X band receiver chain, synchronization chain, X band and Ka band transmitters chains. The instrument is powered by two types of sources: the first one is spacecraft power source net on 28 V voltage; the second one is nuclear power source net on 4 V voltage. The digital part performs information exchange between radio beacon and spacecraft.

Figure 2 The chard of the coherent radio beacon

During autonomic mode of operation the receiver chain is turned off. The instrument is clocked from free running quartz oscillator MV341-C2D-10,0М-ULN-1.2E-13, working at 10 MHz frequency. To improve phase noise performance of the transponder and to perform the requirements of CCSDS 401.0-b, CCSDS 414.0-g2 and CCSDS 414.1-b2 the RF PPLs and clocked at 100 MHz frequency. The reference 100 MHz frequency signal is generated from 10 MHz reference signal using narrow bandwidth frequency translation circuit based on HMC1031 low noise PLL circuit and low noise oscillator VX-805 from Vectron, USA. Autonomic operational mode will be used in RS experiment with orbiter Ka band receiver, in which the acceleration of orbiter with respect to lander will be measured. During the experiments the only Ka band transmitter will be turned on. The short term frequency stability (1 sec, Allan variance) of Ka band signal equal to stability of reference clock, 1.2×10-13. As a result of the orbiter acceleration measurement error with respect to lander will be about 3 mGal (1 Gal = 1 cm/sec2).

The picture of the engineering model of the radio beacon is shown on figure 3.

Figure 3. Lander’s Radio Beacon, engineering model.

The Radio Beacon instrument is a single box with mass about 2 kg and volume about 2 liters. There are three antennas: patch receiver antenna at frequency 7.2 GHz (X band up-link), patch transmitter antenna at frequency 8.4 GHz (X band down-link) and waveguide transmitter antenna at frequency 32 GHz (Ka band). Main beams of X band antennas are directed to the Earth, main beam of Ka band antenna is directed to zenith. The received reference signal at 7.2 GHz is converted to transmitted signals at 8.4 GHz and 32 GHz without loss of coherency. Such type of conversion is possible by means of fore PLL circuits with 749/880 and 749/3344 ratios for X band and Ka band frequency translation respectively. As a result frequency fluctuations of internal reference source will not affect to the frequency of transmitted signals. The instrument is capable to irradiate up to 0.1 W in each channel. The antennas gain is 5-7 dB. The polarization of all antennas radiation is circular right.

The specification of Lunar Radio Beacon is in table 1.

Table 1. The specification of the Radio Beacon

The specification of Lunar Radio Beacon

Parameter Value Remarks
Transmitters frequencies 8,4 GHz and 32 GHz Coherent, transponder ratios 749/880 and 749/3344
Frequency stability 1·10-15 coherent transponder mode
Radiating power, W 0.1 For each channel
Receiver frequency 7.2 GHz Specified channel
Receiver noise TN 200 K  
Antennas gain and beam width 7 dB 120 deg. (G=0 dB) For each channel
Polarization Circular right For each channel
Power consumption, W 7 For each channel
Power sources Solar and nuclear  
Dimensions, mm 190 x 150 x 125  
Mass 2.0 kg  

Autonomic mode frequency stability (Allan variance)

3-30 sec 1.5·10-13 MV341-D1D-10,0М-ULN-1.5E-13
1-300 sec 5·10-13 -“-
0.1-1000 sec 1·10-12 -“-
24 hours 5·10-12 -“-
1 year 2·10-9 -“-

Scientific data transmitter mode

Modulation type QPSK CCSDS standard
Speed of data transfer Up to 0.1 Mbps BER£10-4 Earth antenna 1000 m2
Forward Error Correction (FEC) Viterbi ½ or Turbo ½ CCSDS standard

2 Ka band receiver, deployed on Orbiter

Ka band receiver has been included into scientific payload of the Luna-Resource-1 orbiter. The Ka-band receiver is intended for receiving the signal from Luna’s radio beacon or from Earth’s transmitter and precise measurements of Doppler shift and relative acceleration and velocity. The chart of the Ka band receiver and the picture of the instrument are depicted on figures 5 and 6 respectively.

Figure 5 The chart of the Ka band receiver

Figure 6 The picture of the engineering model of the Ka band receiver

The instruments consists of two parts: electronic box with receiver and internal antenna and remote antenna, connected to electronic box via flexible coaxial cable. The antenna in the electronic box should be directed to nadir, the remote antenna should be directed to zenith.

The electronics box antenna is intended to work with signal source on Moon surface: radio beacon from Lunar-Resource-1, lander or with Chinese lander.

In the case then no radio beacons are on Moon’s surface the remote antenna cuold be used to receive reference signal from transmitter on the Earth.

The active receiver antenna is chosen during planning of scientific experiment and will be turn ON by command from the Earth.

The second mode of operation has advantage for Moon surface coverage – all visible part of Moon surface. The nadir antenna mode could investigate only Moon’s regions which are in the vicinity of Radio beacons.

Table 2 snows specification of the orbiter Ka band receiver

Table 2 Specification of the Ka band receiver

Parameter Value Note
Noise figure, dB ≤ 1.6  
Stability of LO frequency 3-30 sec,          8·10-14; 1-300 sec, 1·10-13; 0,1-10000 sec, 1·10-12; 24 h, 5·10-12; year, 2·10-9; -30О…+60О С, 1·10-10 Reference oscillator MV341-D1D-10,0М-ULN-1.5E-13
Accuracy of acceleration measurement, mGal 3 Averaging time 3-30 sec, 1 Gal = 1 cm/sec2
S/N 40 dB PTX = 0.5 W, 0.1 Hz, 500 km

The chart for Doppler shift measurement in the case of the signal is from the radio beacon deployed on the Moon is shown on figure 7

The reference signal at 32 GHz is radiated by Radio beacon via waveguide antenna to the zenith. By measuring the signal frequency by orbiter receiver it is possible to measure the acceleration of the receiver with respect to radio beacon. As a result it will be possible to retrieve the parameters of local gravitation field and to create the gravitation field map in vicinity of the Radio beacon.

Figure 7 The chart for Doppler shift measurement.

3 Operation of the Radio beacon

There are several types of possible operational actions with Lunar’s radio beacon, depicted on figure 6. It will be possible to conduct a lot of valuable RS experiments with Lander’s radio beacon and Orbiter’s receiver and support service tasks.

Figure 6. Chart of celestial mechanics experiments with Luna’s radio beacons

Due to unprecedented accuracy of velocity and shifts measurements where is a possibility to make the next measurements:

  1. The first one is the measurements of Doppler shift and relative velocity with accuracy 0.01 mm/sec,
  2. The second one is by receiving the X-band signal by Earth’s VLBI network it is possible to measure the Lander’s position with accuracy about 10 cm.
  3. Orbiter’s Ka-band receiver can measure acceleration with high accuracy. The acceleration variations could be related to variation of Luna’s gravitation field. The accuracy of measurement would be competitive with GRAIL data.
  4. If two or more Radio Beacons will be deployed on Moon the SBI (Same Beam Interferometer) experiments will be possible. For SBI experiments several radio beacons on Moon surface should work simultaneously and be synchronized from a single Earth’s reference source. SBI experiments allow to measure 3D displacements with accuracy about 0.1 mm. (Gregnanin, 2012).
  5. The Radio beacon working in coherent transponder mode could be used for precise ranging and could compete with Lunar Laser Ranging (LLR) (Gromov 2016). The ranging technology is based on Pseudo-Noise (PN) phase modulation of reference signal transmitted from Earth’s Ground Station. The recommendation for high accuracy spacecraft position determination using Pseudo-Noise (PN) ranging systems are provided by standard of the Consultative Committee for Space Data Systems CCSDS 414.1-B-2. The Committee is held at NASA Headquarters, and includes main space agencies as members and a number of organizations as observers such as IKI RAS. CCSDS recommends to use the Tausworthe PN-codes T2B and T4B for phase modulation of the uplink carrier as a ranging signal. An alternative PN-code was recommended by ESA standard ECSSE-ST-50-02C. Fundamentals of PN ranging are described in CCSDS 414.0- G-2 informational report, which define a PN-sequence as a binary ±1 sequence of period L whose autocorrelation function has peak value +L and all (L–1) off-peak values equal to –1. It is a definition of one more PN-code, a well known pseudo-noise M-sequence. The examples of all four codes are given on the diagrams below, figure 7, where C1 is the corresponding range-clock waveform.

Figure 7 The examples of four Tausworthe PN-codes

The autocorrelation function of the codes T2A and T2B oscillates in a range ±L/2, and that of ESA code in in a range about ±L/10. The two important quality parameters of the ranging measurement are: ΔR – its random-noise variation, and U – its ambiguity resolution. A first parameter depends on thermal noise of a receiver, on instrument phase fluctuations, and on delay fluctuations in the troposphere, ionosphere and in interplanetary media. The one-way ambiguity for the PN ranging sequence is:

                                                             (1)

For L~106 km, and range-clock frequency fRC = 106 Hz (in the CCSDS book) U ~ 75·103 km.

A requirement for an ambiguity interval depends on a priori knowledge of an object position. For regularly investigated planets and satellites with stable orbits, a predicted position accuracy is very high. In this case a maximum ranging accuracy could be realized without PN-coding with a carrier frequency as a range clock. It permits to reveal fine details of solar system body movement, reflecting its internal structure and its specific interaction with external fields.

ΔR~0.05 mm of the Luna’s radio beacon corresponds to such measurements with integration time 60 s. The main sources of errors are tropospheric fluctuations (46%), receiver noises (24%), phase fluctuations and calibration errors (15% both). Other effects are negligible.

A random-noise accuracy of PN-ranging depends on a number of transitions between +1 and -1 in a PN-code. A ratio of the number of transitions in the PN-code to that of in the range-clock is 0.95, 0.72 and 0.7 for T2A,T2B and ESA codes, correspondingly. This value for M-sequence is order of magnitude less, as seen on the diagrams. A reduction of the ratio is equivalent to an attenuation of a range-clock signal with corresponding reduction of a signal-to-noise ratio, determining an accuracy.

The RS lunar ranging provide 1-2 order of magnitude better accuracy than laser ranging. A future progress in laser ranging is possible after a development of active laser transponders with low power consumption, and after finding long-living sources of energy for them, in order to replace passive retroreflectors.

4 Scientific outcome of RS Experiments with lander’s radio beacons

Below there is list of possible scientific objectives for Luna investigation by RS methods (Dehant, 2012):

  • improvement of the reference frames for the Earth:

The existing tie of the reference frame attached to the Moon to the quasar frame is presently at the 1 milliarcsec (mas) based on VLBI observations of orbiting spacecraft and a good connection between the lunar orbit and the Earth’s orbit from LLR. With the two or more Radio beacons we expect to reach one order of magnitude better. Such accuracy will be useful for determining precise orbit parameters of the Moon. However, it must be mentioned that the time variations of the Moon’s orbital elements can be long and would require years (ideally 18.6 year) of tracking. Today the accuracy of post-fit residuals is at the centimeter level and of a few to 10 mm/s in the time domain in ranging and range rate respectively. An improvement of a factor 10 of this accuracy in the time domain, would provide accuracy in the frequency domain at the level of 0.05 mm and 0.5 mm/s. This translates into an orbital position of the Moon at the millimeter level.

  • better understanding of the Moon’s interior, and in particular, through the determination of the moments of inertia of the whole Moon and of its core (inner core and outer core), the core oblateness, the free and forced librations, and the tides and their dissipation, obtain a better determination of the core radius and of the possible presence of an inner core, of the mantle mineralogies, and of the core composition, and there with better constrain the Moon’s evolution:

For the physical librations the Radio beacons will provide millimeter level at the surface of the Moon from range measurements and the accuracy in the frequency domain will be one order of magnitude more accurate than the range rate accuracy in the time domain. This is important for the determination of Moon’s tides and librations. Pushing the measurements into the regime of millimetric or sub-millimetric range precision will be of highest interest for these parameter determinations (at least an order-of-magnitude improvement).

Improvements on the LLR alone is already a very nice advance in Moon science. The models that sustain the geophysical interpretation of the data will have to be advanced in parallel as detailed by Kopeikin (2009). These models will be based on the theory of general relativity, will fully incorporate the relevant geophysical processes, lunar librations, tides, and should rely upon the most recent standards and recommendations of the IAU for data analysis.

  • better determination of the parameters of General Relativity, through the values of the PPN parameters and even tests for the violations of general relativity in the context of other metric theories of gravity:

High precision ranging measurements allow as well to test several relativistic parameters. The associated precisely measured lunar motion is a reality that any proposed laws of attraction and motion must satisfy.

RS ranging offers very accurate measurements of the positions of Radio beacons on the Moon (the weighted rms residual currently are at the centimeter level or 5×10-11 in fractional accuracy). The analysis of these very precise data contributes not only to understand the interior and rotation of the Moon (selenophysics) but as well help to determine parameters of some general relativity tests and several key properties of weak-field gravity, including Einstein’s Strong Equivalence Principle.

As stated in Turyshev and Williams (2007) the current LLR data yield the strongest limits to date on variability of the gravitational constant (the way gravity is affected by the expansion of the universe): -5×10-13<dG/dt<13×10-13 year-1 and the best measurement of the geodetic precession rate of the orbital motion of the Moon (of the lunar perigee). General relativity does not predict a changing G, but some other theories do, thus testing for this effect is important.

The set of Lunar’s Radio beacons will push lunar ranging into the regime of millimetric range precision which translates to an order-of magnitude improvement in the determination of fundamental physics parameters. For the Earth and Moon orbiting the Sun, the scale of relativistic effects is set by the ratio (GM/rc2) over v2/c2 of the order of 10-8. Relativistic effects are small compared to Newtonian effects. The 1 mm range accuracy corresponds to 3×10-12 of the Earth–Moon distance. The resulting RS ranging tests of gravitational physics would improve by an order of magnitude: the Equivalence Principle would give uncertainties approaching tests of general relativity effects at <0.1%, and estimates of the relative change in the gravitational constant would be 0.1% of the inverse age of the universe (13.7 billion of years, so 0.1% corresponds to one part in 1013 year-1, or 10-14 if determined over 10 years).

Williams et al. (2004) report a test of the geodetic precession which, expressed as a relative deviation from general relativity, is Kgp = -0.0005±0.0047. The measurements from the point-mass orbit perturbations performed with LLR can also be expressed in terms of the combination of the PPN parameters h=4b-3-g (with g and b being the two Eddington parameters that are both equal to one in general relativity, providing h=0 in that theory) and by examining the value of the displacement of the lunar orbit along the direction to the Sun. As stated in Turyshev and Williams (2006), the accurate RS ranging and LLR data has been able to quickly eliminate several suggested alterations of physical laws.

5 Conclusions

Together with information from RS and the radial laser ranging (the position and velocity of the Moon with respect to the Earth will be determined at a never-reached precision of the millimeter level and a few hundredths of mm/s), the tangential component from VLBI will push the insight into the Moon’s orbital behavior including its libration to as yet unknown frontiers and there with obtain information on the core of the Moon. This conclusion is further strengthened in the context the recent reprocessing of lunar seismic data and the findings related to a liquid core, a partial melting boundary layer, and a solid inner core inside the Moon.

Constraining the detailed structure of the lunar core is necessary to improve our understanding of the present-day thermal structure of the interior and the history of a lunar dynamo, as well as the origin and thermal and compositional evolution of the Moon.

References

Gregnanin, M., at al, (2012). Same beam interferometry as a tool for the investigation of the lunar interior, Planetary and Space Science, 74, 194–201.

Gromov, V. D., Kosov, A. S. (2015) 6M-S3 Symposium Abstract Book, pp. 43-44 (6MS3-MN-20).

Gromov, V. D., Kosov, A. S. (2016) The Ranging Accuracy of the Radioscience Experiment with the Radio-Beacon Transponder in Comparison with Laser Ranging, 7M-S3 Symposium

Dehant, V., at al, (2012). Geodesy instrument package on the Moon for improving our knowledge of the Moon and the realization of reference frames, Planetary and Space Science, 68, 94–104.

Kopeikin, S.M., 2009. Millimeter Laser Ranging to the Moon: a comprehensive theoretical model for advanced data analysis. In: Schilliak, S. (Ed.), Proceedings of 16th International Workshop on Laser Ranging Entitled ‘SLR – the Next Generation’, Held in Poznan Poland. vol. 1, October 12–17, 2008, pp. 254–263.

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Williams, J.G., Turyshev, S.G., Murphy, T.W., 2004. Improving LLR tests of gravitational theory. International Journal of Modern Physics D 13 (3), 567–582. doi:10.1142/S0218271804004682.