The optimal design of co-orbiter space missions for Earth's gravity modeling


1 Associate Professor, College of Surveying and Geomatics Engineering, Faculty of Engineering, University of Tehran, Iran

2 Ph.D. Student, College of Surveying and Geomatics Engineering, Faculty of Engineering, University of Tehran, Iran


In recent years, strong scientific interest has been generated in a better understanding of the physical system of the Earth. It has been heightened the need for improving our knowledge of the gravity field of the Earth, both in terms of accuracy and spatial resolution. this could be globally and homogeneously possible only by means of space gravity missions. Nowadays, it is becoming increasingly difficult to ignore the widely used applications of the satellite gravity mission's information in studying the Earth system. For example, the application of the gravity information in geophysical and geotechnical research, is a new dimension for geodynamic research and seismology, Oceanography and determining ocean circulation, Hydrological research, Ice mass balance and sea level study.
There have been many motivations behind launching the space gravity missions. After the first gravity mission CHAllenging Minisatellite Payload (CHAMP) launched in 2000 for the gravity and atmosphere applications, Gravity Recovery And Climate Experiment (GRACE) mission was launched to improve the temporal and spatial resolution for hydrological and geophysical studies. As a new space-born gravity mission, Gravity field and steady-state Ocean Circulation Explorer (GOCE) was designed based on the gradiometry observation in height about 250km. Because of the short life-time of GOCE, this mission was designed to determine static gravity field and the temporal gravity field modeling was assigned to other space-born missions like GRACE. The GRACE was designed to determine and interpret the temporal gravity variations. By the help of GRACE monthly solutions, it is easily possible to extract the periodic and quasi-periodic signals of the gravity. It allows researchers to interpret the time gravity variation as the mass redistribution in the Earth dynamic system. The temporal gravity variation might be caused the global water cycle, ice mass loss in the poles, the glacial isostatic adjustment, the earthquake subsequences and geodynamic activities.
A follow-on mission to GRACE is desirable to bridge the gap in the time-series of the monthly gravity models. After the successful GRACE mission, in order to minimize the cost and technical risk, the same space mission has been proposed to measure the gravity field variations. Then, the GRACE follow-on mission will be a rebuild of the original GRACE with a few developments. Laser interferometry will be tested as a new experiment to improve the ranging precision whereas, the mission will be equipped with the microwave ranging system similar to the GRACE. As the first mission in the planetary science, the lunar GRAIL mission was proposed as a pair co-orbiting spacecraft similar GRACE. GRAIL that was launched in 2011 to improve our knowledge about the moon's gravity field.
In this study, we investigate the role of various parameters of the co-orbiter mission design to improve the gravity field modeling for post-GRACE missions. A proper definition of these parameters will have a large effect to improve the gravity field modeling. The redesign has been carried out based on the science and technology developments in recent years. Using laser ranging system instead of K-band ranging system, and decreasing the satellite height (assuming the use of active propulsion system) are new suggestions. The mission could not only improve the quality of the gravity modeling, but also bridge the gap in the time-series of the monthly solutions. In the co-orbit missions, the mission design commonly consists of designing the orbit and satellite separation. Assuming the mission is equipped with an active propulsion system, the height of the satellite pair will be reduced to 350 km. Laser interferometry will be tested as a new experiment to improve the ranging precision by considering its advantage and disadvantages. The results show that using the mission equipped with laser ranging system could not improve the quality of the gravity modeling, because of the limitation in average range< 100 km.


Main Subjects

Becker, S., Brockmann, J. and Schuh, W. D., 2014, Mean dynamic topography estimates purely based on goce gravity field models and altimetry. Geophysical Research Letters 41(6):2063–2069.
Blandino, J. J., Marchetti, P. and Demetriou, M. A., 2008, Electric propulsion and controller design for drag-free spacecraft operation. Journal of Spacecraft and Rockets, 45(6), 1303-1315.
Chambers, D. P., 2006, Observing seasonal steric sea level variations with GRACE and satellite altimetry. Journal of Geophysical Research: Oceans (1978–2012), 111(C3).
Case, K., Kruizinga, G. and Wu, S., 2002, GRACE level 1B data product user handbook. JPL Publication D-22027.
Chen, J., Wilson, C., Tapley, B., Famiglietti, J. and Rodell, M., 2005, Seasonal global mean sea level change from satellite altimeter, grace and geophysical models. Journal of Geodesy 9(9):532—539.
Chen, J., Wilson, C., Blankenship, D. and Tapley, B., 2006, Antarctic mass rates from grace. Geophysical Research Letters 33(11).
Fatolazadeh, F., Voosoghi, B. and Naeeni, M. R., 2016, Wavelet and Gaussian approaches for estimation of groundwater variations using GRACE data. Groundwater, 54(1), 74-81.
Han, S.C., Ray, R. D. and Luthcke, S. B., 2007, Ocean tidal solutions in antarctica from grace inter-satellite tracking data. Geophysical Research Letters 34(21).
Heki, K. and Matsuo, K., 2010, Coseismic gravity changes of the 2010 earthquake in central chile from satellite gravimetry. Geophysical Research Letters 37(24).
Knudsen, P., Bingham, R., Andersen, O. and Rio, M. H., 2011, A global mean dynamic topography and ocean circulation estimation using a preliminary goce gravity model. Journal of Geodesy 85(11):861-879.
Klinger, B., Baur, O. and Mayer-Gürr, T., 2014, GRAIL gravity field recovery based on the short-arc integral equation technique: simulation studies and first real data results. Planetary and Space science, 91, 83-90.
Kroes, R., Montenbruck, O., Bertiger, W. and Visser, P., 2005, Precise GRACE baseline determination using GPS. GPS Solutions, 9(1), 21-31.
Liu, X., 2008, Global gravity field recovery from satellite-to-satellite tracking data with the acceleration approach (Doctoral dissertation, TU Delft, Delft University of Technology).
Mayer-Gürr, T., Savcenko, R., Bosch, W., Daras, I., Flechtner, F. and Dahle, C., 2012, Ocean tides from satellite altimetry and GRACE. Journal of Geodynamics, 59, 28-38.
Reubelt, T., Sneeuw, N. and Sharifi, M. 2010, Future mission design options for spatio-temporal geopotential recovery. In: Gravity, Geoid and Earth Observation, Springer, pp 163–170
Rietbroek, R., Brunnabend, S. E., Kusche, J. and Schröter, J., 2012, Resolving sea level contributions by identifying fingerprints in time-variable gravity and altimetry. Journal of Geodynamics, 59, 72-81.
Schaub, H. and Junkins, J. L., 2003, Analytical mechanics of space systems. Aiaa.
Sheard, B. S., Heinzel, G., Danzmann, K., Shaddock, D. A., Klipstein, W. M. and Folkner, W. M., 2012, Intersatellite laser ranging instrument for the GRACE follow-on mission. Journal of Geodesy, 86(12), 1083-1095.
Tapley, B. D., Bettadpur, S., Ries, J. C., Thompson, P. F. and Watkins, M. M., 2004, Grace measurements of mass variability in the earth system. Science 305(5683):503–505
Wiese, D. N., Nerem, R. S. and Lemoine, F. G., 2012, Design considerations for a dedicated gravity recovery satellite mission consisting of two pairs of satellites. Journal of Geodesy, 86(2), 81-98.
Wu, S. C., Kruizinga, G. and Bertiger, W., 2006, Algorithm theoretical basis document for grace level- 1b data processing v1. 2. Jet Propulsion Laboratory, California Institute of Technology