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Ørsted Geomagnetic Mission

Overview   Spacecraft   Launch    Mission Status   Sensor Complement   References

Ørsted is a geomagnetic research microsatellite mission of Denmark [named in honor of the Danish scientist Hans Christian Ørsted (1777-1851) who discovered electromagnetism in 1820]. The Ørsted mission was developed by a consortium of organizations including the NBI (Niels Bohr Institute) of the University of Copenhagen, the Technical University of Denmark (DTU), the Solar-Terrestrial Physics Division of DMI (Danish Meteorological Institute), the Danish Space Research Institute (DSRI) of Copenhagen, Terma A/S, and Computer Resources International (now part of Terma A/S). International contributions were provided by NASA, CNES, DLR and ESA.

Note: In January 2005 DRSI changed its name to DNSC (Danish National Space Center), and in January 2007 it became DTU Space, an institute at the Technical University of Denmark.

The mission objectives are to perform highly accurate and sensitive measurements of the geomagnetic field and global monitoring of the high energy charged particles in the Earth's environment. The data are used to improve geomagnetic models, to study auroral phenomena, and for correlation with Earth-based measurements in order to study the relationship between the external field and the energy coupling of the solar wind-magnetosphere-ionosphere system. 1) 2) 3) 4) 5) 6)


Figure 1: The Ørsted spacecraft illustration


Ørsted is in the low-cost microsatellite class, built by Terma A/S of Lystrup, Denmark as prime contractor. S/C mass = 60.7 kg, power = 54 W (40 W average load), S/C stabilization by a gravity gradient boom (8 m boom containing the star imager and magnetometers) and active magnetic torquing (three-axis magnetorquer coils maintain yaw to within 10º).

Primary attitude determination (sensing) is provided by ASC (Advanced Stellar Compass), a star imager camera, with sun sensors and magnetometers as backup. The satellite has a box-like shape (34 x 45 x 72 cm) and is covered by solar panels (GaAs), 37 W EOL (End of Life) power. NiCd batteries provide power in eclipse (6 Ah). Design life of at least one year (three year goal).

From a programmatic point of view, Ørsted observations are supposed to fill the gap in magnetic measurements after MAGSAT (October 1979 - June 1980) of NASA. The Ørsted satellite and its instrumentation served already as a model for other operational and forthcoming missions like CHAMP and Swarm, since it is the first satellite of the "International Decade of Geopotential Research."


Figure 2: Illustration of the Ørsted spacecraft in orbit (image credit: DRSI)

RF communications: Science data sampling rates: 1 to 100 samples/s. On-board data storage and downlinking every 12 hours or less. Uplink and downlink in S-band (2.114 GHz and 2.296 GHz, respectively). Maximum downlink rate is 256 kbit/s, the uplink date rate is 4 kbit/s. There are three downlink stations in Denmark. The main receiver station is located at DMI in Copenhagen (extra station at AAU in Aalborg). The Science Data Center is at DMI. The satellite is controlled from the Ørsted control center at Terma A/S at Birkerød, Denmark.

S/C body dimensions

340 mm x 450 mm x 720 mm


GaAS body-mounted solar panels, 37 W EOL. Two power control units, two 6-cell NiCd battery packs, 6 Ah

Primary structure

H-beam with honeycomb platforms

Attitude control

Gravity gradient and magnetorquers. ACS


S-band with ESA standard packet TM/TC. Cold redundant TX/RX units

On-board computers

Two, each with 16 MByte storage, 80C186, 16 MHz CPU

Orbit position

Redundant GPS


8 m deployable 3 longerons (the boom is pointing in the zenith direction)

Thermal control


S/C mass

60.7 kg

Table 1: Overview of the Ørsted satellite parameters

Launch: Ørsted was launched Feb. 23, 1999 (after almost two years in storage) as a secondary payload to ARGOS (Advanced Research and Global Observation Satellite) of the US Air Force on a Delta II rocket from VAFB, CA. The other secondary payload on the flight was SUNSAT of Stellenbosch University, South Africa.

Orbit: Slowly drifting elliptical polar orbit, perigee = 655 km km, apogee=857 km, inclination = 96.5º, period = 100 min. Initial local equator crossing local times at 14:39 hours on the ascending node. The orbit is drifting approximately 0.91 minutes in local time each day. Note: after 4 years in space, perigee, apogee, and period decreased to 640 km, 845 km, and 99.7 minutes, respectively.


Figure 3: The Ørsted satellite mounted for vibration tests (photo: Per L. Thomsen)

Legend to Figure 3. Photo of the Ørsted satellite mounted for vibration test at IABG (Industrie-Anlagen Betriebs-Gesellschaft) in Germany. At the front is seen the top of the cylinder holding the Overhauser magnetometer at the end of the 8 m coilable boom stowed inside the satellite body. Four of the CPD detectors are looking upward through the cut-out at the top panel. The remaining two detectors are looking to the side through the cut-out in the side solar panel. The TRSR antenna is mounted at the upper right edge of this panel.



Status of the Ørsted mission:

Regular operations of the Ørsted spacecraft operations were halted in January 2014. Since then, the project made contact with the spacecraft on an occasional basis, the last time was in November 2014. Currently there are no plans to restart operations, also because there are now better data available from the Swarm mission of ESA. 7)

• On Feb. 23, 2014, the Ørsted spacecraft will be on-orbit for 15 years. Since 2005, Ørsted only measures the magnetic field intensity (but not its vector components). There is, however, no sign of degradation of the measurements of magnetic field intensity which is still of excellent quality. 8)

• In 2012, the Ørsted spacecraft and its main instruments (CSC and Overhauser magnetometers) are operational (except the star tracker), scalar magnetic and charged particle measurements are still being collected. However, the funding for operating the satellite has not been secured (Ref. 9). In February 2012, the spacecraft is completing 13 years on orbit.

• In 2011, the Ørsted spacecraft and its main instruments (CSC and Overhauser magnetometers) are still operational. However, the star camera (attitude sensor) and attitude control are disabled. Hence the satellite can only make absolute magnetic measurements (this has been the situation for the past ~5-6 years). There are presently problems with the telemetry receiver state (and budgets). This situation might limit operations beyond mid-2012 (Ref. 9).

• In February of 2010, the Ørsted spacecraft and its main instruments are still operational; they completed their 11th year in orbit on Feb. 23, 2010. In spite of the mission's age (design life of 1 year with a goal of 3 years), a major part of the satellite instrumentation and systems is still functional. 9)

The aging has reduced the power delivered from its solar panels and has diminished the efficiency of the batteries needed for satellite operations in Earth's shadow. One of the instruments, the ASC (Advanced Stellar Compass), a star sensor needed for precise spacecraft attitude information, has experienced considerable degradation of the commercial-grade CCD, accumulated during many years of exposure in the space environment - and has ceased to provide attitude information by the end of 2005.

In spite of the unavailability of the star sensor data since 2006, great care is being exercised to nurse the satellite and the remaining instruments. The Ørsted satellite still supplies valuable data from its measurements in space. However, only high precision scalar magnetic data based on the joint operation of the CSC and Overhauser magnetometers, are currently available, not the high precision vector data.

In 2010, the prime objective for the Ørsted science mission is the continuation of the collection of high precision scalar magnetic data in order to provide an overlap with the coming ESA mission, SWARM. The SWARM mission comprises 3 satellites equipped with high-precision magnetometers to be launched in 2011 into complementary low orbits. The potential overlap between Ørsted and SWARM will provide a unique possibility for a precise intercalibration between the two missions. The Ørsted satellite systems, including back-up or redundancy units and software revival procedures, have given the mission far more endurance than expected. The lessons learned are considered very useful for future space missions and have in fact proven most useful for the instrumentation of the SWARM satellites (Ref. 9).

Some of the results of the Ørsted mission are: 10)

- Insight in the vortex-like flows in the Earth's core of fluid metal

- Information on the electrical properties of the viscous mineral mass in the Earth's mantle

- Estimates of the crustal thickness and its remnant magnetism

- Calculation of the heat flow from Earth's interior to the bottom of ice caps

- Measurements of large-scale ocean currents

- Sounding of the temperature and humidity profiles in the atmosphere

- Mapping of the electron content in the upper atmosphere

- Scaling of the electric currents in outer space

- Detection of the high-energy particles in the radiation belts

- Estimates of the electric fields in the solar wind.

• Figure 4 shows the local time of the orbit plane in the top half and the availability of magnetic and attitude data in the bottom half. From mid July 2006 through June 2007, a big gap in the data occurred due to the lack of attitude control which resulted in an almost total lack of GPS timing information in this period. Possibly, data from this period may be recovered at a later time. 11)




Figure 4: Local time evolution of the Ørsted orbit (top) and data availability (bottom), image credit: DRSI

• The Ørsted observations opened in effect a decade of geopotential field research by an international team (the first satellite to measure with high precision the three components of the Earth's magnetic field since MAGSAT). 12) 13) 14) 15) 16)

• The Ørsted data are a major source to update the IGRF (International Geomagnetic Reference Field) model. For instance, the IGRF2000 field model was based entirely on Oersted data. In the meantime, a variety of magnetic field models have been derived from Ørsted observations. 17) 18) 19)

• Although the main objective of Ørsted is the precise mapping of Earth's internal field, the satellite has contributed to improved understanding of ionospheric and magnetospheric current systems. A much more detailed determination of their variability with season and local time is possible due to the greatly improved data distribution compared to previous missions. 20) 21)



Sensor complement: (Scalar & Vector Magnetometers, CPD, ASC, TRSR)

Scalar Magnetometer (OVM):

The scalar magnetometer was built by LETI (Laboratoire d'Electronique de Technologie et d'Instrumentation) of Grenoble and funded by CNES, France -and referred to as OVM (Overhauser Magnetometer). The objective of the proton-precession OVM [coils for proton resonance excitation and detection, and a resonator for Electronic Spin Resonance (ESR) pumping of a nitro-oxide solution] is to measure magnetic field scalar values (field strength) with an absolute measurement error of < 0.5 nT. Measurement range: 16,000 - 64,000 nT; sampling rate = 1 Hz. Provides in-flight calibration for the vector magnetometer. Sensor mass = 1 kg. The instrument is boom-mounted at a distance of 8 m. The instrument mass is 2.5 kg, power = 3 W.

Measurement principle: The underlying idea of this scalar magnetometer is based on the principle of proton magnetic resonance. If a proton-rich liquid is exposed to a DC magnetic field, the protons will start to precess around the field direction with a frequency strictly proportional to the applied field magnitude. In principle there is no dependency on field direction, on temperature and no drift. By exactly measuring the precession frequency (0.8 - 3 kHz) an absolute figure of the ambient magnetic field strength can be derived.

The OVM samples continuously the ambient field strength at a rate of 1 Hz. It can cope with fields from any direction. There are no dead zones as often encountered with instruments of this type. The deviation from omni-directionality is less than 0.2 nT. The internal crystal oscillator is regularly checked against GPS clock to ensure a precise determination of the proton precession frequency.

Instrument design: The first point to consider for any given scalar magnetometer is the choice of the method for the initial signal amplification. Here the nuclear magnetic resonance signal is amplified thanks to a dynamic nuclear polarization process: the sample consists of a solvent whose nuclear spins are coupled to the electronic spins of a free radical in solution. A saturation of the electronic transitions first leads to an increased electronic polarization, which in turn results in a nuclear polarization amplified by a factor of about 3000. By properly choosing the RF frequency for a given solvent/radical pair, one can obtain either positive or negative polarization of the solvent's nuclear spins. This feature is exploited to build a CW oscillator around two flasks with opposite polarities, as illustrated on Figure 5, so that the resonance signal generated in each flask and picked-up by the detection coils is amplified, while the common mode signal resulting from the injection is rejected by the differential amplifier. 22)


Figure 5: Architecture of the Overhauser nuclear magnetic resonance autooscillator (image credit: LETI)

The sensor's omnidirectionality on the other hand is ensured by the coils design: they create highly inhomogeneous RF injection signals in such a way that, regardless of the direction of the static magnetic field, a constant fraction of the cells volume is submitted to the proper excitation and detection conditions. (Figure 6).

Such magnetometers have been operated for many years in various environments, in particular for aeromagnetic surveys for which the operational constraints are similar in many ways to the ones met in satellite applications. However, as mentioned previously, several design evolutions were nevertheless necessary to comply with the mass and power budgets allocated to the OVM.


Figure 6: Schematic view of the NMR (Nuclear Magnetic Resonance) sensor head (image credit: LETI)


Figure 7: Photo of the OVM instrument (image credit: LETI)

Note: The same OVM instrument of LETI/CNES was also flown on the CHAMP mission (2000-2010).


Vector Magnetometer:

The vector magnetometer is of the DTU (Danish Technical University) and the DRSI (Danish Space Research Institute). The instrument is a CSC (Compact Spherical Coil) triaxial fluxgate magnetometer which measures magnetic field vectors at an angular resolution of 1 arcsec and an absolute measurement error of less than 1 nT. Dynamic range: ±65,536 nT; resolution: < 0.25 nT; 100 vector samples/s in burst mode over polar latitudes are collected, or 20 vector samples/s in normal mode; the resolution obtained is < 0.1 nT and is calibrated using the absolute intensity measured by the OVH. After calibration, the agreement between the two magnetometers is better than 0.33 nT rms (corresponding to better than ±1 nT for 98% of the data). Sensor mass = 300 g. The sensor is boom-mounted in a cylindrical container (gondola) at a distance of 6 m from the satellite body. The instrument mass is 2.1 kg, power consumption = 1.1 W. - The advanced sensor technology is based on stress-annealed amorphous magnetic metal. 23) 24) 25)


Figure 8: Illustration of the CSC fluxgate magnetometer (image credit: DRSI)


CPD (Charged Particle Detector):

The CPD experiment was built by DMI (Danish Meteorological Institute). The instrument consists of six solid-state particle detectors for measurements of high energy electrons (50 keV - 1 MeV), protons (250 keV - 30 MeV), and alpha-particles (1-100 MeV). Detectors look in different directions with a FOV of 15-45º. The instrument has a mass of 2.3 kg, power consumption of 1 W, and a size of 260 mm x 199 mm x 113 mm. 26)


Figure 9: Illustration of the CPD device (image credit: DMI)


ASC (Advanced Stellar Compass):

The ASC was developed at DTU, Lyngby, Denmark [ASC is also referred to as SIM (Star IMager)]. The objective is to provide an attitude reference instrument with a precision of a few arcseconds aboard the satellite [the greatest limitation of the vector data accuracy is the star imager accuracy]. The instrument is a CCD star imager for determining the pointing vector for the CSC fluxgate magnetometer with a resolution of 6 arcsec or less.

The ASC consists of a camera head unit (CHU) using a 752 x 588 pixel CCD device. The CHU is mechanically fixed to the vector magnetometer on a common optical bench in the boom-mounted gondola. The CHU is connected to a DPU (Data Processing Unit), i.e. a microcomputer fitted to a frame-grabber, mounted in the satellite body. The CHU acquires star images within its FOV, while the DPU provides the processing power to perform image analysis, pattern recognition, data reduction, and communication. The total mass of ASC is 1.647 kg, the power consumption is 4.5 W. ASC is also being flown on the following missions: Astrid-2, TEAMSAT, CHAMP, SAC-C, ADEOS-II, GRACE, and PROBA. 27) 28) 29) 30)


Figure 10: Illustration of the ASC/SIM instrument (image credit: DTU)


TRSR (TurboRogue Space Receiver):

TRSR is a special GPS receiver provided by NASA/JPL (in fact, 2 receivers consisting of: Trimble Tans II + modified JPL Turbo Rogue). The objective is to: a) accurately determine the position of the satellite, and b) the instrument observes in parallel ionospheric electron content, and provides atmospheric soundings permitting the derivation of atmospheric profiles of density, pressure, and temperature (refractive occultation monitoring). TRSR supports both C/A and P code and P-codeless (cross-correlation) operation. It provides parallel dual-frequency code and cross-correlation tracking, and data output of up to eight GPS satellites simultaneously. The TRSR sampling rate is 10 Hz. The instrument has a mass of 4 kg, power = 7-15 W.


Figure 11: Illustration of the TRSR instrument (image credit: JPL)


Some results from the Ørsted mission:

The results from the Ørsted satellite mission can be summarized in the following list: 31)

• The precise magnetic measurements conducted from the Ørsted satellite have provided a basis for International Geomagnetic Reference Field (IGRF) models, which are used for many technical and scientific tasks, among other, to develop models for the internal geo-dynamo and its secular variations, to provide mapping of magnetic anomalies in the crust, and to estimate geothermal heat flux to the bottom of ice caps.

• The accurate magnetic measurements made at high time resolution have provided detailed mapping of electric currents in space and have been used to study the coupling of the solar wind to the Earth's magnetosphere.

• The detection of high-energy particles from Ørsted have helped the science community to understand the properties of the radiation belts and the effects of high-energy radiation on spaceborne computer circuits.

• The precise detection of the phases and amplitudes of GPS signals have helped the development of satellite-based methods to measure the atmospheric temperature and humidity profiles, which are essential parameters in meteorology.

• Ørsted has provided basis for more than 200 scientific publications in international journals and for more than 400 talks or posters presented at international scientific conferences.

The construction of the satellite and the analysis of data have been accomplished through a close collaboration between three universities (Danish Technical University, University of Copenhagen, Aalborg University), eight private companies (Terma A/S, CRI, Copenhagen Optical Company, DDC International, Innovision, Per Udsen Co., Rescom, and Ticra), and two institutes (DNSC and DMI). The international collaboration has included the space agencies NASA, ESA, CNES and DLR, and more than 40 universities and research institutes all over the world. This successful collaboration is perhaps the most valued and meaningful accomplishment in the Ørsted satellite project.


Figure 12: Illustration of the geomagnetic field of two periods: 2000 and 1980 (image credit: DRSI) 32)

Legend to Figure 12: The top figure displays a color-coded global image (in Mollweide projection) of the magnetic fieldstrength in the year 2000 as modelled from the Oersted data. The scale spans from 20000 - 70000 nT (nanoTesla). The bottom field displays the differences between Oersted results from 2000 and results from the Magsat mission (1979-1980). The scale spans here from -2400 nT to +1800 nT. The changes in field strength over the 20 years span between the two missions are mostly negative and ranges up to almost 10% of the total field.


Figure 13: Illustration of the magnetization in the Earth's crust (image credit: NASA, DRSI) 33)

Legend to Figure 13: A vertically-integrated magnetization model of induced and remanent magnetization that explains the satellite magnetic field observations. The model also incorporates information from near-surface magnetic field observations. Areas of negative magnetization are dominated by magnetizations in directions oblique and opposite to that of the present Earth's field. The model shows the long-wavelength magnetizations (dominated by the continent-ocean contrast) in color and the short wavelength magnetizations (dominated by seafloor spreading) as a gray-scale shaded relief. The map is shown on an orthographic projection centered at 90º West, 30º North.


1) P. Lundahl Thomsen, F. Hansen, "Danish Ørsted Mission In-Orbit Experiences and Status of the Danish Small Satellite Program," Proceedings of the 13th Annual AIAA/USU Conference on Small Satellites, Aug. 23-26, 1999, Logan UT, SSC99-I-8

2) Information provided by F. Primdahl of DTU, Lyngby, Denmark

3) P. Donaldson, "Mapping Magnetism," Space, April 1993



6) "Focus- Our magnetic Earth," NordicSpace, Vol. 15, No 2, 2007, URL:

7) Information provided by Peter Hoffmeyer of Terma A/S, Birkeroed, Denmark.

8) Information provided by Nils Olsen, DNSC (Danish National Space Center), Copenhagen, Denmark.

9) Information provided by Peter Stauning of DMI (Danish Meteorological Institute), Copenhagen, Denmark

10) Peter Stauning, "Ørsted Satellite - The Danish Miracle in Space," Nordic Space, Volume 15, No 2, 2007, pp. 4-8, URL:

11) Information provided by Lars Tøffner-Clausen of DTU Space

12) T. Neubert, M. Mandea, G. Hulot, R. von Frese, F. Primdahl, J. L. Jørgensen, E. Friis-Christensen, P. Stauning, N. Olsen, T. Risbo, "Ørsted Satellite Captures High-Precision Geomagnetic Field Data," EOS Transaction of AGU, Vol. 82, No. 7, p. 81, 87, and 88, Feb. 13, 2001

13) N. Olsen, L. Tøffner-Clausen, T. J. Sabaka, P. Brauer, J. M. G. Merayo, J. L. Jørgensen, J.-M. Léger, O. V. Nielsen, F. Primdahl, T. Risbo, "Calibration of the Ørsted Vector Magnetometer," Earth, Planets and Space, Vol. 55, pp. 11-18, 2003

14) The satellite project, its background and many of the results are presented in: Proceedings of the 4th Oersted International Science Team Conference, eds. P. Stauning et al., Narayana press, Copenhagen 2003

15) P. Stauning, "Oersted Results. 5 years in Space", DMI Report 04-12, Copenhagen 2004

16) N. Olsen, "Ørsted," in 'Encyclopedia of Geomagnetism and Paleomagnetism,' edited by D. Gubbins and Emilio Herrero-Bervera, Kluwer Academic Publishers (Earth Sciences Series)

17) N. Olsen, R. Holme, G. Hulot, T. Sabaka, T. Neubert, et al., "Ørsted Initial Field Model,". Geophysical Research Letters, Vol. 27, No. 22, pp. 3607-3610, 2000

18) G. Hulot, C. Eymin, B. Langlais, M. Mandea, N. Olsen, "Small-Scale Structure of the Geodynamo Inferred from Ørsted and Magsat Satellite Data," Nature, Vol. 416, pp. 620-623, Apr. 11, 2002.

19) M. Purucker, B. Langlais, N. Olsen, G. Hulot, M. Mandea, "The Southern Edge of Cratonic North America: Evidence from New Magnetic Satellite Observations," Geophysical Research Letters, Vol. 29, No 15, 2002.

20) V. O. Papitashvili, F. Christiansen, T. Neubert, "A New Model of Field-Aligned Currents Derived from High-Precision Satellite Magnetic Field Data," Geophysical Research Letters, Vol. 29, No. 14, 10.1029, 2002.

21) P. Stauning, "Field-aligned ionospheric current systems observed from the Magsat and Ørsted satellites during northward IMF," Geophysical Research Letters, 2001GL013961, 2002

22) Jean-Michel Leger, Francois Bertrand, Thomas Jager, Isabelle Fratter, "Spaceborne scalar magnetometers for Earth's field studies," Proceedings of IAC 2011 (62nd International Astronautical Congress), Cape Town, South Africa, Oct. 3-7, 2011, paper: IAC-11-B1.3.9

23) Information provided by Peter Stauning of DMI and by Nils Olsen of DRSI




27) J. L. Joergensen, C. C. Liebe, "The Advanced Stellar Compass, Development and Operations," Acta Astronautica, Vol. 39, No. 9-12, 1996, pp. 775-783

28) A. Eisenman, C. C. Liebe, "Operation and Performance of a Second Generation, Solid-State, Star Tracker, The ASC, Acta Astronautica, Vol. 39, No 9-12, 1996, pp. 697-705

29) J. L. Joergensen, "In Orbit Performance of a fully Autonomous Star Tracker," 4th ESA International Conference on Spacecraft Guidance, Navigation and Control Systems, Oct. 18-21, 1999, pp. 103-110, ESA/ESTEC, Noordwijk, The Netherlands, (ESA SP-425, Feb. 2000)

30) T. Bak, M. Blanke, R. Wisniewski, "Flight Results and Lessons Learned from the Ørsted Attitude Control System," 4th ESA International Conference on Spacecraft Guidance, Navigation and Control Systems, Oct. 18-21, 1999, pp.87-94, ESA/ESTEC, Noordwijk, The Netherlands

31) Peter Stauning, "The Ørsted Satellite Project," January 22, 2008, URL:

32) N. Olsen, R. Holme, G. Hulot, T. Sabaka, T. Neubert, L. Tøffner-Clausen, F. Primdahl, J. Joergensen, J.-M. Leger, D. Barraclough, J. Bloxham, J. Cain, C. Constable, V. Golovkov, A. Jackson, P. Kotze, B. Langlais, S. Macmillan, M. Mandea, J. Merayo, L. Newitt, M. Purucker, T. Risbo, M. Stampe, A. Thomson, C. Voorhies, "Ørsted Initial Field Model," Geophysical Research Letters, Nov. 15, 2000, Vol. 27, No 22, pp. 3607-3610

33) M. Purucker, B. Langlais, N. Olsen, G. Hulot, M. Mandea, "The Southern Edge of Cratonic North America: Evidence from New Satellite Magnetometer Observations," Geophysical Research Letters, Vol. 29, No. 15, Aug. 1, 2002, URL:

The information compiled and edited in this article was provided by Herbert J. Kramer from his documentation of: "Observation of the Earth and Its Environment: Survey of Missions and Sensors" (Springer Verlag) as well as many other sources after the publication of the 4th edition in 2002. - Comments and corrections to this article are always welcome for further updates(

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