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Mars global dynamics analysis (MAGDA) project
Acta Astronautica Vol. 21, No. 3, pp. 197-200, 1990 Printed in Great Britain.All rights reserved
0094-5765/90 $3.00+ 0.00 Copyright © 1990PergamonPress pie
MARS GLOBAL DYNAMICS ANALYSIS (MAGDA) PROJECTt PH. HARTL and W. SCH.~.FER Institute of Navigation, Stuttgart University, Keplerstrasse 11, 7000 Stuttgart 1, F.R.G. and J. B. ZIELIlqSKI Space Research Centre, Polish Academy of Sciences, Bartycka 18, 00-716 Warsaw, Poland (Received 26 January 1989; revised version received 6 October 1989)
Abstract--In view of the forthcoming interplanetary missions to Mars, especiallythe impressiveprogram of investigations of Mars announced by the Academy of Sciences of the U.S.S.R., we propose to undertake the complex study of the gravity field and the kinematics of Mars. By means of range and range rate ratio measurements and with the help of dedicated vehicles (Mars orbiter, subsatellite, Mars ground stations) the following scientific objectives can be achieved: (1) Improvement of the Mars gravity field up to 3° x 3° resolution (spherical harmonics development 60,60). (2) Determination of the Martian geoid with accuracy of + 1-2 m. (3) Establishment of the reference system on the surface of Mars with an accuracy of approx. 10 cm. (4) Determination of the rotation parameters of Mars. (5) Provision of high accuracy orbitography data for the Mars Orbiter. The envisioned measuring system will be the modified version of PRARE (precise range and range rate equipment), the extremely precise two-way microwave tracking system. The pseudo-noise coded signal in S-band emitted from the master station and retransmitted by the remote transmitter will allow one to measure the distance with a precision of 1 cm and the range rate with a precision of 0.003 cm/s. In the paper the scenario of the proposed mission is described and an accuracy analysis of measurements and solution is presented.
I. INTRODUCTION A detailed model of the Mars gravity field is essential for the study of the internal structure of the planet and the verification of any hypothesis concerning its evolution. For the topography mapping of Mars the reference system is necessary, consisting of normal figure parameters, geoid (areoid) and some ground fixed bench marks. Since the Viking mission, some Martian gravity models have been published[I-4], however, their accuracy and resolution is not satisfactory[5]. The Mars rotation model has also been improved thanks to Viking data[6] but there is still much room for further improvement of the rotation parameters. Geodesy gathered many experiences in investigating the Earth gravity field. One of the methods developed recently is that of satellite-to-satellite tracking. The Polish Project DIDEX was elaborated some years ago[7] and a number of theoretical and numerical analyses were made. In Germany and France a number of works have been done in connection with the proposed SLALOM Project[8]. Experimental results in this domain have been
obtained in the U.S.A.[9]. All the abovementioned results and analysis confirm the validity of the satellite-to-satellite tracking method for gravity field investigations. Point positioning via satellite ratio signals has been analysed and realised in Germany in connection with the POPSAT Project[10]. The microwave positioning system PRARE, a follow-on project of the MITREX experiment[11] has been developed in the Institute of Navigation, University of Stuttgart and is scheduled for the 1990 ERS-1 Mission. In the proposed M A G D A Project we are going to exploit all of the abovementioned methods and analyses. 2. GENERAL OUTLINE OF THE MAGDA PROJECT
The M A G D A measuring system will consist of the following elements:
tPaper IAF-88-401 presented at the 39th Congress o f the International Astronautical Federation, Bangalore, India, 8-15 October 1988. 197
(1) Orbiter station (OS). A transmitter and receiver located on-board the Mars Orbiter. Assumed orbit: polar, circular, altitude of about 500-550 km. (2) Subsatellite transponder (ST). Located on the small compact subsatellite with an orbit coplanar to the main Orbiter and an altitude of about 200-250 km.
198
PH. HARTLeta/. /4
Earth
/ / /
/
/
\\ \
/
\
/
\
/
\
/ / /
" sT
\ \
/ / L
For satisfying coverage a 3-month observation campaign is necessary at least, and with more observations we can obtain more accurate results. The OS-MG link will function in parallel. The most favourable position for the MG would be in the polar region. Then many orbital passes of the Orbiter could be controlled by this station. Two stations in two opposite polar regions would bring optimal results. However, the location of the MG can be accommodated to the mission constraints. The a S - T O link will work as long as Mars-Earth communication is assured. We plan to use this data as an enhancement of measurements made on Mars. It is expected that this data will be used by other experimentors also in the areas of celestial mechanics, relativity physics, space physics, etc. 3. SYSTEM DESCRIPTION
A MG
Fig. 1. Scheme of the MAGDA Project.
(3) Martian ground stations (MG). Minimum one, but if more could be deployed this would improve the measurement capabilities. (4) Terrestrial observing stations (TO). The crucial element of the experiment will be the satellite-to-satellite tracking from the a S to ST. The tracking will consist of range and range rate measurements along the line of sight between two satellites. Similar measurements will also be performed between MG and aS. Eventually a S will be tracked by TO on the Earth (Fig. 1 illustrates the scheme.). We assume that the link a S - T O (Orbiter-Earth) will be independent from the routine orbit control system, so some redundancy in the orbiter orbit determination is expected. The measurement precisions assumed are given in Table 1. The following experiment scenario is proposed: After insertion of ST into the low orbit, the range rate measurements in a S - S T link began. Because of the difference in heights and velocities the period of common visibility between two satellites is comparable to the period of revolution of the lower satellite (approx. 100 min). Then the time of nonvisibility is about six times longer. So, during one Martian day, two measurement periods occur.
Table 1. Assumed measurement precisions
OS-ST OS-MG OS-TO
Range (em)
Range rate (cm/s)
I 1 4
0.003 0.003 0.05
The instrument's primary operation mode is satellite-to-satellite tracking between a S and ST. Both range and range rate measurements are performed. The main part of the equipment will be contained in the aS, where the instrumentation in the ST shall be limited to those which are necessary. This automatically leads to a maste~slave concept, the master located in a S and the slave being a suitable transponder on the ST, both performing in a two-way tracking mode. All transmissions are initiated on the aS, then relayed by the ST. After signal conditioning in the a S the received signals are compared in time and phase against the original transmission. All measurement data are taken in the aS, stored in the instrument's own memory, and are finally handed over to the aS-telemetry system on request, whereas the ST consists of a relatively simple "dumb transponder". This two-way tracking system eliminates all firstorder errors induced by frequency uncertainties of the local clock. During visibility between satellites, the equipment operates continuously and data points (both range and range rate) are taken once per second. The a S part of the instrument consists of a relatively self-contained unit. It is housed in one box to which the antenna is connected via one coaxial cable. The antenna itself uses a crossed dipole system of approx. 4cm in height above a slightly grooved metallic ground plane. The field of view of the instrument's antenna will not be obstructed by other parts of the satellite in order to reduce the possibility of multipath effects. Besides these mechanical interfaces, only a few electrical interfaces exist: primary power, 3 command and 4 status lines and I serial link for data exchange. For precise orbit observation of the a S from Earth, there is an additional output providing a pn-modulated r.f.-signal phase-locked to the internal reference. This signal is injected into the lowpower section of the a S transmitter chain within its bandwidth, amplified in the satellite's high power
199
MAGDA Project amplifier and makes use of the main Earth-pointing high-gain antenna of the Orbiter. Multipath effects on this link are not likely to occur because of the small bandwidth of the antenna. On Earth an antenna of approx. 25 m in dia is used for reception. The carrier phase and the time of arrival of the modulation are compared to an atomic clock generating doppler and pseudo range information. The instrument's drift is < 1 cm of pseudo-range per day and is much smaller than external influences along the propagation path such as plasma and the Earth's ionosphere and troposphere. A network of Earth stations normally used for deep space operations (e.g. Wettzell, ESA stations and some Soviet stations) in receive only mode will allow for continuous observations and monitoring of the on-board rubidium clock.
Table 2. Physicalcharacteristics OS ST Mass
Power 11W stby/19Woper Data rate 2 kB/s r.f. Power 1W r.f. Frequency 2.0 GHz Antennagain 5dB
(2)
(3) Main modules of the S T and MG units The ST transponder regenerates the r.f.-carrier and transmits the received signal after noise reduction and frequency translation back to OS. For telemetry purposes (temperature, internal signals, etc.) up to 2 kBit/s are modulated on the same signal. In addition to the range unit a battery with associated charger and a small housekeeping module are mounted in a sphere of 30 cm dia which is covered by the solar array and the conformational antenna array. The ST itself is gravity gradient stabilized by an appropriate boom. Some other methods of stabilization are also being considered. The batteries are charged continuously during sunlight, whereas the transmitter section providing 1 W of r.f.-power is operating during satellite-tosatellite visibility periods only. The duty-cycle allows for the relatively high r.f.-power compared with the solar array capabilities. The M G unit consists essentially of the same transponder section as it is used in ST, but rough electrical power is assumed to be available from the carrier (i.e. Mars Lander), for different codes for signal discrimination in the OS. Simultaneous observation of two of these transponders is possible. All carriers and modulation signals are generated coherently to the master oscillator. A combination of pseudo-noise codes and discrete tones is used for coarse (ambiguity) and fine resolution at the same time. In addition there is a data transmission capability on all RF-links which handles 2 kBit/s for instrument control and telemetry exchange between OS and ST, OS and MG and vice versa. The physical characteristics are given in Table 2. 4. SCIENTIFICOBJECTIVES The objectives of M A G D A are stated as follows: (1) Improvement of the Mars gravity field model up to 3° x 3° spatial resolution equivalent to the spherical harmonics development 60, 60. AA 2 L/3----D
6 kg
(4)
(5)
MG
3 kg
2 kg
0.3 W/4W -1W 2.2 GHz 5 dB
0.3 W/4W -1W 2.3 GHz 5dB
The best known model developed by Balmino et al.[l] is 18, 18. We propose to improve this resolution by a factor of 3. Determination of the Martian geoid (areoid) with accuracy of + 1-2 m. Currently the level surface of Mars is known to within an accuracy of several or tens of metres. For any morphological analysis of remote sensing data of the surface this radical improvement is necessary. Establishment of the reference system on the surface of Mars with an accuracy of approx + 10 cm. This is important for the operation of future missions and for the guidance of landing or travelling vehicles as well as for topographical mappings. Determination of the Mars rotation parameters. The long period parameters are known relatively well, but we know practically nothing about the rotation changes, polar motion or short period nutation of Mars. The project will enable one to start these investigations. Provision of high accuracy orbitography data for the Mars Orbiter. With M A G D A data the orbit determination of the Mars Orbiter can be improved by at least a factor of 100 in the areocentric as well as in heliocentric and geocentric coordinate systems. This last feature is especially interesting for studies in relativity. 5. ACCURACYESTIMATIONS
Now we will calculate the sensitivity of the system described above with respect to the gravity field signal. Suppose we are able to determine the motion of the subsatellite with an accuracy of +0.01 cm/s for the velocity vector and of + 3 cm in the position vector every 10 s. This is a rather conservative supposition compared to the technical assumption of the measurement precision of the system. Nevertheless, it permits us to determine the acceleration along the orbit with an accuracy of +0.001 cm/s 2 = + 1 mgal. Now, 10 s of motion along the orbit 200 km above the surface of Mars is equivalent to the track of about 33 km or 0.5 ° of the central angle. Along an orbital arc of 3° (proposed resolution) we will have 6 measurement points. This can occur twice a day, thus during the 3-month duration of the experiment we will have about 1000 measurements in one 3 ° x 3° compartment. The results must be projected on the sphere (or other normal figure) with the mean radius
200
PH. HARTLet al.
of Mars by a downward continuation of the potential field, but fortunately on Mars the attenuation of gravity anomalies with height is twice as small, than on the Earth. Preliminary calculations lead to the conclusion that the expected accuracy of the anomaly in one compartment will be within + 0 . 2 - 0 . 3 m g a l which corresponds to + 1-2 m in areoid undulation. As well as a precision of measurement, equally important is the accuracy of modelling. Most of the forces acting on the system can be modelled with sufficient accuracy, but the atmospheric drag can present a problem. Requirements must be made so that the error induced by the atmosphere will be smaller than the measurement noises (+0.003 cm/s for the velocity). The atmospheric pressure on Mars is only 0.8% of that on the Earth and the density at 200 km altitude on Mars is comparable to 500 km on the Earth. Unfortunately the model of the Martian atmosphere is rather poor and the dispersion in density approaches two orders of magnitude. In this situation the 200 km orbit must be considered as a lower bound for the gravity field determination if a drag-free system will not be applied. Now, let us estimate the volume of observing data. Every 10 s the following measurements will be made: ~ i s t a n c e and velocity between OS and ST, --distance and velocity between M G and OS, - - v e l o c i t y from TO to OS. During one revolution ( ~ 6 5 0 0 s) there will be about 650 observation points which makes 650 x 5 = 3250 observations. In 1 day we should have two revolutions with inter-satellite visibility which makes 6500 observations a day. Thus with the 90-day duration of the experiment we will have approx. 600,000 data set. The number of unknowns will be on the order of 3600 as it is the number of coefficients of spherical harmonics up to a degree and order 60, 60. Acknowledgements--This project has been prepared during the stay of the third author at the Institute of Geodesy, Stuttgart University. The financial support of the Alexander von Humboldt Foundation is gratefully acknowledged. Valuable discussions with Professor E. Grafarend and
Professor B. Schaffrin from the Stuttgart Univeristy, Professor Ch. Reigber from the German Geodetic Research Institute and Professor V. M. Linkin and Dr N. A. Eismont from the Space Research Institute of the Academy of Sciences of the U.S.S.R. contributed essentially to the formulation of the project.
REFERENCES
1. G. Balmino, B. Moynot and N. Vales, Gravity field model of Mars in spherical harmonics up to a degree and order eighteen. J. geophys. Res. 87, 9735 (1982). 2. E. J. Christensen and G. Balmino, Development and analysis of a twelfth degree and order gravity model for Mars. J. geophys. Res. 84, 7943 (1979). 3. E. J. Christensen and B. G. Williams, Mars gravity field derived from Viking 1 and Viking 2. The navigation results. J. GuM. Control 2, 179 (1979). 4. J. P. Gapcynski, R. H. Tolson and W. H. Michael, Mars gravity field combined Viking and Mariner 9 results. J. geophys. Res. 82, 4325 (1977). 5. K. Lambeck, Comments on the gravity and topography of Mars. J. geophys. Res. 84, 6241 (19793. 6. R. D. Reasenberg and R. W. King, The rotation of Mars. J. geophys. Res. 84, 623l (1979). 7. J. B. Zielinski and J. Kazmierski, DIDEX-Project for determination of the earth gravity field anomalies. CSTG Bull. No. 3 (1981). 8. G. Balmino, G. Barthel, L. Castel, T. Haldorson, H. Hufnagel, G. Leibold, D. Meissner, Ch. Reigber, R. Rummet and Ch. Schmidt, SLALOM mission/ system definition. Final Report (1987). 9. D. P. Hajela, Recovery of 5 mean gravity anomalies in local areas from ATS6/GEOS3 satellite to satellite range rate observation. J. geophys. Res. 84, 6884 (1979). 10. Ch. Reigber, S. Hieber and E. Achtermann, Popsat, an active solid Earth monitoring system. Proceedings of lAG Symposium, Symposium D "The Future of Terrestrial and Space Methods for Positioning", Hamburg (1983). 11. Ph. Hartl, N. Gieschen, K.-M. Mussener, W. Schafer and C.-M. Wende, High accuracy global time transfer via geosynchronous telecommunication satellites with MITREX. Zfw 7, 335 (1983). 12. E. Grafarend, Map projection for non-standard manifolds with special emphasis on the tri-axial ellipsoid (manuscript), Geodetic Institute, Univeristy of Stuttgart (1987). 13. C. A. Wagner, Gravitational spectre from the tracking of planetary orbiters. J. geophys. Res. 84, 6891 (1979). 14. W. Schafer and H. Wilmes, Precise range and range rate equipment (PRARE)--system design and status of development. Workshop on Advances in Satellite Radio Tracking, Austin, Tex.
0094-5765/90 $3.00+ 0.00 Copyright © 1990PergamonPress pie
MARS GLOBAL DYNAMICS ANALYSIS (MAGDA) PROJECTt PH. HARTL and W. SCH.~.FER Institute of Navigation, Stuttgart University, Keplerstrasse 11, 7000 Stuttgart 1, F.R.G. and J. B. ZIELIlqSKI Space Research Centre, Polish Academy of Sciences, Bartycka 18, 00-716 Warsaw, Poland (Received 26 January 1989; revised version received 6 October 1989)
Abstract--In view of the forthcoming interplanetary missions to Mars, especiallythe impressiveprogram of investigations of Mars announced by the Academy of Sciences of the U.S.S.R., we propose to undertake the complex study of the gravity field and the kinematics of Mars. By means of range and range rate ratio measurements and with the help of dedicated vehicles (Mars orbiter, subsatellite, Mars ground stations) the following scientific objectives can be achieved: (1) Improvement of the Mars gravity field up to 3° x 3° resolution (spherical harmonics development 60,60). (2) Determination of the Martian geoid with accuracy of + 1-2 m. (3) Establishment of the reference system on the surface of Mars with an accuracy of approx. 10 cm. (4) Determination of the rotation parameters of Mars. (5) Provision of high accuracy orbitography data for the Mars Orbiter. The envisioned measuring system will be the modified version of PRARE (precise range and range rate equipment), the extremely precise two-way microwave tracking system. The pseudo-noise coded signal in S-band emitted from the master station and retransmitted by the remote transmitter will allow one to measure the distance with a precision of 1 cm and the range rate with a precision of 0.003 cm/s. In the paper the scenario of the proposed mission is described and an accuracy analysis of measurements and solution is presented.
I. INTRODUCTION A detailed model of the Mars gravity field is essential for the study of the internal structure of the planet and the verification of any hypothesis concerning its evolution. For the topography mapping of Mars the reference system is necessary, consisting of normal figure parameters, geoid (areoid) and some ground fixed bench marks. Since the Viking mission, some Martian gravity models have been published[I-4], however, their accuracy and resolution is not satisfactory[5]. The Mars rotation model has also been improved thanks to Viking data[6] but there is still much room for further improvement of the rotation parameters. Geodesy gathered many experiences in investigating the Earth gravity field. One of the methods developed recently is that of satellite-to-satellite tracking. The Polish Project DIDEX was elaborated some years ago[7] and a number of theoretical and numerical analyses were made. In Germany and France a number of works have been done in connection with the proposed SLALOM Project[8]. Experimental results in this domain have been
obtained in the U.S.A.[9]. All the abovementioned results and analysis confirm the validity of the satellite-to-satellite tracking method for gravity field investigations. Point positioning via satellite ratio signals has been analysed and realised in Germany in connection with the POPSAT Project[10]. The microwave positioning system PRARE, a follow-on project of the MITREX experiment[11] has been developed in the Institute of Navigation, University of Stuttgart and is scheduled for the 1990 ERS-1 Mission. In the proposed M A G D A Project we are going to exploit all of the abovementioned methods and analyses. 2. GENERAL OUTLINE OF THE MAGDA PROJECT
The M A G D A measuring system will consist of the following elements:
tPaper IAF-88-401 presented at the 39th Congress o f the International Astronautical Federation, Bangalore, India, 8-15 October 1988. 197
(1) Orbiter station (OS). A transmitter and receiver located on-board the Mars Orbiter. Assumed orbit: polar, circular, altitude of about 500-550 km. (2) Subsatellite transponder (ST). Located on the small compact subsatellite with an orbit coplanar to the main Orbiter and an altitude of about 200-250 km.
198
PH. HARTLeta/. /4
Earth
/ / /
/
/
\\ \
/
\
/
\
/
\
/ / /
" sT
\ \
/ / L
For satisfying coverage a 3-month observation campaign is necessary at least, and with more observations we can obtain more accurate results. The OS-MG link will function in parallel. The most favourable position for the MG would be in the polar region. Then many orbital passes of the Orbiter could be controlled by this station. Two stations in two opposite polar regions would bring optimal results. However, the location of the MG can be accommodated to the mission constraints. The a S - T O link will work as long as Mars-Earth communication is assured. We plan to use this data as an enhancement of measurements made on Mars. It is expected that this data will be used by other experimentors also in the areas of celestial mechanics, relativity physics, space physics, etc. 3. SYSTEM DESCRIPTION
A MG
Fig. 1. Scheme of the MAGDA Project.
(3) Martian ground stations (MG). Minimum one, but if more could be deployed this would improve the measurement capabilities. (4) Terrestrial observing stations (TO). The crucial element of the experiment will be the satellite-to-satellite tracking from the a S to ST. The tracking will consist of range and range rate measurements along the line of sight between two satellites. Similar measurements will also be performed between MG and aS. Eventually a S will be tracked by TO on the Earth (Fig. 1 illustrates the scheme.). We assume that the link a S - T O (Orbiter-Earth) will be independent from the routine orbit control system, so some redundancy in the orbiter orbit determination is expected. The measurement precisions assumed are given in Table 1. The following experiment scenario is proposed: After insertion of ST into the low orbit, the range rate measurements in a S - S T link began. Because of the difference in heights and velocities the period of common visibility between two satellites is comparable to the period of revolution of the lower satellite (approx. 100 min). Then the time of nonvisibility is about six times longer. So, during one Martian day, two measurement periods occur.
Table 1. Assumed measurement precisions
OS-ST OS-MG OS-TO
Range (em)
Range rate (cm/s)
I 1 4
0.003 0.003 0.05
The instrument's primary operation mode is satellite-to-satellite tracking between a S and ST. Both range and range rate measurements are performed. The main part of the equipment will be contained in the aS, where the instrumentation in the ST shall be limited to those which are necessary. This automatically leads to a maste~slave concept, the master located in a S and the slave being a suitable transponder on the ST, both performing in a two-way tracking mode. All transmissions are initiated on the aS, then relayed by the ST. After signal conditioning in the a S the received signals are compared in time and phase against the original transmission. All measurement data are taken in the aS, stored in the instrument's own memory, and are finally handed over to the aS-telemetry system on request, whereas the ST consists of a relatively simple "dumb transponder". This two-way tracking system eliminates all firstorder errors induced by frequency uncertainties of the local clock. During visibility between satellites, the equipment operates continuously and data points (both range and range rate) are taken once per second. The a S part of the instrument consists of a relatively self-contained unit. It is housed in one box to which the antenna is connected via one coaxial cable. The antenna itself uses a crossed dipole system of approx. 4cm in height above a slightly grooved metallic ground plane. The field of view of the instrument's antenna will not be obstructed by other parts of the satellite in order to reduce the possibility of multipath effects. Besides these mechanical interfaces, only a few electrical interfaces exist: primary power, 3 command and 4 status lines and I serial link for data exchange. For precise orbit observation of the a S from Earth, there is an additional output providing a pn-modulated r.f.-signal phase-locked to the internal reference. This signal is injected into the lowpower section of the a S transmitter chain within its bandwidth, amplified in the satellite's high power
199
MAGDA Project amplifier and makes use of the main Earth-pointing high-gain antenna of the Orbiter. Multipath effects on this link are not likely to occur because of the small bandwidth of the antenna. On Earth an antenna of approx. 25 m in dia is used for reception. The carrier phase and the time of arrival of the modulation are compared to an atomic clock generating doppler and pseudo range information. The instrument's drift is < 1 cm of pseudo-range per day and is much smaller than external influences along the propagation path such as plasma and the Earth's ionosphere and troposphere. A network of Earth stations normally used for deep space operations (e.g. Wettzell, ESA stations and some Soviet stations) in receive only mode will allow for continuous observations and monitoring of the on-board rubidium clock.
Table 2. Physicalcharacteristics OS ST Mass
Power 11W stby/19Woper Data rate 2 kB/s r.f. Power 1W r.f. Frequency 2.0 GHz Antennagain 5dB
(2)
(3) Main modules of the S T and MG units The ST transponder regenerates the r.f.-carrier and transmits the received signal after noise reduction and frequency translation back to OS. For telemetry purposes (temperature, internal signals, etc.) up to 2 kBit/s are modulated on the same signal. In addition to the range unit a battery with associated charger and a small housekeeping module are mounted in a sphere of 30 cm dia which is covered by the solar array and the conformational antenna array. The ST itself is gravity gradient stabilized by an appropriate boom. Some other methods of stabilization are also being considered. The batteries are charged continuously during sunlight, whereas the transmitter section providing 1 W of r.f.-power is operating during satellite-tosatellite visibility periods only. The duty-cycle allows for the relatively high r.f.-power compared with the solar array capabilities. The M G unit consists essentially of the same transponder section as it is used in ST, but rough electrical power is assumed to be available from the carrier (i.e. Mars Lander), for different codes for signal discrimination in the OS. Simultaneous observation of two of these transponders is possible. All carriers and modulation signals are generated coherently to the master oscillator. A combination of pseudo-noise codes and discrete tones is used for coarse (ambiguity) and fine resolution at the same time. In addition there is a data transmission capability on all RF-links which handles 2 kBit/s for instrument control and telemetry exchange between OS and ST, OS and MG and vice versa. The physical characteristics are given in Table 2. 4. SCIENTIFICOBJECTIVES The objectives of M A G D A are stated as follows: (1) Improvement of the Mars gravity field model up to 3° x 3° spatial resolution equivalent to the spherical harmonics development 60, 60. AA 2 L/3----D
6 kg
(4)
(5)
MG
3 kg
2 kg
0.3 W/4W -1W 2.2 GHz 5 dB
0.3 W/4W -1W 2.3 GHz 5dB
The best known model developed by Balmino et al.[l] is 18, 18. We propose to improve this resolution by a factor of 3. Determination of the Martian geoid (areoid) with accuracy of + 1-2 m. Currently the level surface of Mars is known to within an accuracy of several or tens of metres. For any morphological analysis of remote sensing data of the surface this radical improvement is necessary. Establishment of the reference system on the surface of Mars with an accuracy of approx + 10 cm. This is important for the operation of future missions and for the guidance of landing or travelling vehicles as well as for topographical mappings. Determination of the Mars rotation parameters. The long period parameters are known relatively well, but we know practically nothing about the rotation changes, polar motion or short period nutation of Mars. The project will enable one to start these investigations. Provision of high accuracy orbitography data for the Mars Orbiter. With M A G D A data the orbit determination of the Mars Orbiter can be improved by at least a factor of 100 in the areocentric as well as in heliocentric and geocentric coordinate systems. This last feature is especially interesting for studies in relativity. 5. ACCURACYESTIMATIONS
Now we will calculate the sensitivity of the system described above with respect to the gravity field signal. Suppose we are able to determine the motion of the subsatellite with an accuracy of +0.01 cm/s for the velocity vector and of + 3 cm in the position vector every 10 s. This is a rather conservative supposition compared to the technical assumption of the measurement precision of the system. Nevertheless, it permits us to determine the acceleration along the orbit with an accuracy of +0.001 cm/s 2 = + 1 mgal. Now, 10 s of motion along the orbit 200 km above the surface of Mars is equivalent to the track of about 33 km or 0.5 ° of the central angle. Along an orbital arc of 3° (proposed resolution) we will have 6 measurement points. This can occur twice a day, thus during the 3-month duration of the experiment we will have about 1000 measurements in one 3 ° x 3° compartment. The results must be projected on the sphere (or other normal figure) with the mean radius
200
PH. HARTLet al.
of Mars by a downward continuation of the potential field, but fortunately on Mars the attenuation of gravity anomalies with height is twice as small, than on the Earth. Preliminary calculations lead to the conclusion that the expected accuracy of the anomaly in one compartment will be within + 0 . 2 - 0 . 3 m g a l which corresponds to + 1-2 m in areoid undulation. As well as a precision of measurement, equally important is the accuracy of modelling. Most of the forces acting on the system can be modelled with sufficient accuracy, but the atmospheric drag can present a problem. Requirements must be made so that the error induced by the atmosphere will be smaller than the measurement noises (+0.003 cm/s for the velocity). The atmospheric pressure on Mars is only 0.8% of that on the Earth and the density at 200 km altitude on Mars is comparable to 500 km on the Earth. Unfortunately the model of the Martian atmosphere is rather poor and the dispersion in density approaches two orders of magnitude. In this situation the 200 km orbit must be considered as a lower bound for the gravity field determination if a drag-free system will not be applied. Now, let us estimate the volume of observing data. Every 10 s the following measurements will be made: ~ i s t a n c e and velocity between OS and ST, --distance and velocity between M G and OS, - - v e l o c i t y from TO to OS. During one revolution ( ~ 6 5 0 0 s) there will be about 650 observation points which makes 650 x 5 = 3250 observations. In 1 day we should have two revolutions with inter-satellite visibility which makes 6500 observations a day. Thus with the 90-day duration of the experiment we will have approx. 600,000 data set. The number of unknowns will be on the order of 3600 as it is the number of coefficients of spherical harmonics up to a degree and order 60, 60. Acknowledgements--This project has been prepared during the stay of the third author at the Institute of Geodesy, Stuttgart University. The financial support of the Alexander von Humboldt Foundation is gratefully acknowledged. Valuable discussions with Professor E. Grafarend and
Professor B. Schaffrin from the Stuttgart Univeristy, Professor Ch. Reigber from the German Geodetic Research Institute and Professor V. M. Linkin and Dr N. A. Eismont from the Space Research Institute of the Academy of Sciences of the U.S.S.R. contributed essentially to the formulation of the project.
REFERENCES
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