The Earth’s center of mass – as a whole planet – cannot be measured directly. However, precise knowledge about its motion is crucial both in engineering practice and the study of the environmental changes in the planet Earth. To find the Earth’s center of mass, we have to use indirect techniques and universal laws of physics. One of Kepler’s laws says that all celestial bodies orbit in circles or ellipses, with the main body at one of the two foci. Therefore, satellites orbiting the Earth and precise observations of their motion can be used to measure the center of the Earth, the so-called geocenter coordinates. In the latest article in GPS Solutions, scientists from the Institute of Geodesy and Geoinformatics UPWr used for the first time in the world observations of up to 80 artificial navigational satellites (GNSS, Global Navigational Satellite Systems) to determine geocenter coordinates. Three constellations of satellites were used, including GPS, GLONASS, and Galileo. To date, such research was not feasible because Galileo reached the number of 24 active satellites at the end of 2018. That makes the research innovative and breakthrough in determining the center of the Earth’s center of mass with a millimeter level accuracy.

Formal errors of the GCC-Z estimates in mm. The β angles for all the orbital planes of the corresponding GNSS constellations are shown using dashed gray lines. Vertical cyan lines point to the epochs of minimum and maximum errors for each of the GPS, GLONASS, and Galileo. Note a different vertical axis scale for GLO

Origin of the geocenter motion

Most of the processes in the Earth’s atmosphere, oceans, and ice cover are connected with the transport of huge masses. Along with the movement of masses in the Earth system, their natural center, the so-called geocenter, also moves. The precise description of the movement of the natural center of the Earth’s masses is crucial for orbit modeling of artificial satellites and the interpretation of the climate changes on Earth. One should keep in mind that all artificial satellites of the Earth orbit around the same natural Earth’s center of mass. In attempting to imagine the practical consequences of incorrect interpretation of the geocenter motion, we can point out that an error in the determination of the geocenter equal to 3 mm translates into an inaccurate estimate of the loss of mass of glaciers in Antarctica equivalent to 200 billion tons of ice.

Problems with the geocenter motion in GNSS research

The description of the geocenter motion using the GPS system has been a research problem for years. It is worth noting that we describe the millimeter movement of the center of the planet’s masses, observing the motion of the satellites about 20 000 km above the Earth’s surface. The main problem is to model the forces acting in space on a satellite and to separate them from the movement of the geocenter. Satellites are susceptible to the non-gravitational perturbing forces – mainly solar radiation pressure, which acts on the solar panels and the satellite’s body. In this article IGiG scientists described how the orbit modeling of GPS, GLONASS and the latest Galileo system influences the determination of geocenter coordinates. The most problematic component of the geocenter coordinates turned out to be the Z-axis component, which is directed to the North Pole. When satellite orbit and solar radiation pressure are not well modeled, the Z component of the geocenter motion contains more errors than the actual geophysical signal caused by the circulation of masses between the northern and southern hemispheres. Researchers also pointed out that precise metadata on the satellites’ optical and physical parameters, which has been officially published in 2017 by the European Space Agency, improve the quality of orbit modeling and the possibility to describe the geocenter motion.

The failure at the start of Galileo proves to be crucial in the determination of the geocenter

In the case of the Galileo constellation, a very unusual phenomenon can be observed. One pair of the Galileo satellites have been launched into highly eccentric orbit instead of circular. These satellites have never been classified as fully operational but transmit signals, which can be tracked by the ground stations. Interestingly, a pair of satellites in an incorrect orbit improves the determination of the geocenter coordinates using the Galileo constellation.

The analysis also revealed that the geocenter coordinates are best determined using two constellations: GPS and Galileo. The article shows that the GLONASS constellation is currently not suitable for determining the geocenter motion because regardless of the adopted orbit modeling strategy, the errors resulting from solar radiation pressure modeling are more significant than the movement of the geocenter itself.

For more information about the GNSS-derived geocenter coordinates, please refer to the latest article published in GPS Solutions:

Zajdel, R.; Sośnica, K.; Bury, G. (2021) Geocenter coordinates derived from multi-GNSS: a look into the role of solar radiation pressure modeling. GPS Solut 25, 1 (2021).