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Investigation into the rate of changes in Keplerian orbital elements for GPS satellites under solar storming/GPS palydovu orbitu Keplerio elementu kitimo del Saules audru itakos analize.

1. Introduction

The environment in space has significant effects on GPS satellites. Currently, there are 27 active GPS satellites flying in orbit around the Earth. These satellites transmit their predicted position (the broadcast ephemeris) to the users, which is known as a "navigation message". Position predictions are developed by the system control segment based on tracking observations (Kaplan, Hegarty 2006; Leick 1995).

The satellites move predictably according to the laws of physics and do not escape the Earth's gravity that, in fact, holds them in orbit. The location of GPS satellites is given in the navigation message in the form of Keplerian elements.

The Keplerian model presents the satellites orbiting in an ellipse of a constant shape and orientation. Actually, to define a position of a satellite, a minimum set of six time-tagged numbers called satellite orbital elements or Keplerian elements is required. These numbers define an ellipse, orient it about the Earth and place the satellite on the ellipse at a particular time. Six orbital elements used to completely describe the motion of a satellite within orbit are summarized below:

a--semi-major axis;


[OMEGA]--right ascension of the ascending node;

[omega]--argument of perigee;


v--true/mean anomaly.

Keplerian elements provide a mathematical description of satellite orbit. Satellite tracking software reads Keplerian elements. Reality is more complex and the model used includes small corrections called perturbations that are extra parameters (OL 1989; Stewart, Tsakiri 1998).

As already noted, the broadcast ephemeris is obtained from a GPS receiver. Meanwhile, precise ephemerides based on tracking can be obtained from an archive on the World Wide Web (IGS).

2. Description and Assumptions of the Issue

The presented investigation is motivated by solar activity and its effects on GNSS systems. More specifically, the conducted investigation compares solar stormy and stormless days and shows how these events can be seen in the satellite's orbital motion. Logically, orbital motion implies knowledge of a position in orbit. However, significant computations are necessary to take a position in orbit considering Keplerian elements. The question is whether these storm events can be seen directly in variations in Keplerian elements, therefore avoiding extra computations.

Solar storms consist of three major components: solar flares, solar proton events (SPEs) and coronal mass ejection (CMEs). CMEs can interact with the Earth's magnetic field to produce geomagnetic storms. Though not all solar storms produce all three elements, the largest parts of those tend to (Program 2011; Baker 2005).

Solar storms vary in size and impact on GNSS and Earth. The National Oceanographic and Atmospheric Administration (NOAA) delivers space weather impacts on satellite navigation, called NOAA Space Weather Scales. Three categories of descriptive scales of space weather are given:

--geomagnetic storms--disturbances to the geomagnetic field caused by gusts in the solar wind that blows the Earth;

--solar radiation storms--elevated levels of radiation that occur when the number of energetic particles increases;

--radio blackouts--disturbances to the ionosphere caused by X-ray emissions from the Sun (Crosby 2008; Marusek 2007; Koskinen et al. 2001).

Each scale provides the lists of possible effects seen in each category of activity. Five levels of severity from 1 to 5 (from minor to extreme) of space weather are defined and regularly reported in weekly summaries distributed by the Space Environment Centre (SEC). Essentially, geomagnetic storm categories from G2 to G5 and solar radiation storm categories from S2 to S5 can affect satellite navigation and specifically have an effect on altering satellite orbits. The days with particularly significant solar activity were selected as the object for experimentation (Table 1). When using data obtained from SEC and NOAA archives, a priority list of the major solar storms was extracted. The main major event from the list made in October 2003 was chosen for the study and compared with an apparently completely storm free period in October 2010. On 30 October 2003, geomagnetic storms of categories G1 and G5 and a solar radiation storm of category S3 were recorded. Data was collected one day before and one day after the storms. Meanwhile, for comparison purposes, a similar storm free period at was chosen the end of October 2010 (Zubinaite, Preiss 2010).

In some parts of the Nordic countries, including Norway, Denmark, Finland and Sweden, GPS is available with a precision of one centimetre using an auxiliary system Position Accuracy on the Centimetre Level (CPOS). This is Norwegian service for both GPS and GLONASS users who need to determine a position without their own base station. To support this service, a number of permanent tracking stations have been established. Two of those were chosen to carry out this experiment. CPOS station NYA1 is located in Svalbarg (Spitzbergen), the north of Norway, and the second station KRSS is located in the south of Norway. The coordinates of the stations are computed in two independent ways:

Precise point positioning (solution to ITRF2005 transformed to EUREF89).

GNSS baselines from four closest EUREF89 benchmarks. GPS navigation message files of these tracking stations were obtained taking into account two time periods with the help of Norwegian Mapping Authority. At the early stage, six Keplerian elements are clearly required to describe an instantaneous position of the satellite in its orbit. The sixth element, in fact, describes an angular distance of the satellite around its orbit from the perigee of orbit. The previous five Keplerian parameters are necessary to describe the orbit itself. Therefore, five elements for each different time of ephemeris--[t.sub.oe] were extracted from the selected CPOS stations.

Then, the average of all values for each satellite are taken and then subtracted from individual values to get residuals.

3. Data Analysis

The results of the performed investigation are presented in the following graphs (Figs. 1-20), i.e. variations in the Keplerian parameters of GPS satellite orbits regarding solar activity and non-solar activity days.

Figures (1-10) show variations in five parameters during three stormy days in 2003. For comparison purposes, Figures (11-20) indicate variations in stormless days in 2010.





















Each of these figures shows variations in one particular satellite.

Unfortunatelly, at the latest stage of the conducted experiment, serious gaps in data collected in 2010 were discovered. The gaps remain unexplained at the time of writing, however, the available data obtained in 2010 is considered sufficient for the purposes of these experiments.

It can be noticed that the range and variation of the presented diagrams is greater under storm (Figs. 1-10) rather than under stormless conditions (Figs. 11-20) (Table 2). However, differences in this particular experiment appear to be marginal.

4. Discussions and Conclusions

1. While the overall differences between 2003 and 2010 (respectively stormy and stormless) appear to be marginal, two of Keplerian elements seem to be significantly affected. These are the semi-major axis of orbit and argument of perigee (see Table 2).

2. The semi-major axis and argument of perigee are more sensitive to solar activity, while orbital inclination for the equatorial plane is relatively unaffected.

3. Meanwhile, the results obtained in the south of Norway are similar to those from northern Norway, i.e. the findings are not accepted to be a function of latitude.

4. The results are received from only one experiment, and therefore significant additional experiments are necessary for drawing valid conclusions.

5. However, unusually a low level of solar storm activity has been noticed within the period of collecting data on GPS tracking in Norway.

A hypothesis that variations in Keplerian elements can be used as indicators for changes in orbit due to solar storm activity has been put forward. There is no doubt that, if a solar event diverts a satellite from its orbit, then, its new orbit will have different Keplerian elements. It is also clear that, at least for GPS, Keplerian elements are immediately available from the navigation message without extensive computing effort.

The practical usefulness of these variations, however, is more debatable, when compared with unexpected changes in satellite coordinates in meters. A departure in meters is much more readily understandable than a small change expressed in a tiny fraction of a radian.

In conclusion, therefore, it seems to be more appropriate to accept additional computing power necessary to produce satellite coordinates change, rather than to rely on changes in Keplerian elements that are probably much more difficult to interpret.

doi: 10.3846/13921541.2011.645342


Baker, N. D. 2005. Specifying and forecasting space weather throuts to Human Technology, in Daglis, I. A. (Ed.). Effects of Space Weather on Technology Infrastructure 176: 1-25. Dordrecht: Springer.

Crosby, N. B. 2008. Space Weather: Science and Effects. Bruges.

Kaplan, E. D.; Hegarty, C. J. 2006. Understanding GPS: Principles and Applications. 2nd edition. Artech House, London, UK.

Koskinen, H.; Tanskanen, E.; Pirjola, R.; Pulkkinen, A.; Dyers, C.; Rodgers, D., et al. 2001. Space Weather Effects Catalogue.

Leick, A. 1995. GPS Satellite Surveying. New York: Wiley.

Marusek, J. A. 2007. Solar Storm Threat Analysis. Indiana.

OL, C. 1989. The dynamics of global positioning orbits and the determination of precise ephemerides, Geophys Res 94(B7): 9167-9182. doi:10.1029/JB094iB07p09167

Program, A. M. 2011. Satellite Navigation & Space Weather: Understanding the Vulnerability & Building Resilience. Washington: American Meteorological Society Policy Workshop Report.

Stewart, M.; Tsakiri, M. 1998. GLONASS Broadcast Orbit Computation, GPS Solutions 2(2): 16-27. doi:10.1007/PL00000032

Zubinaite, V.; Preiss, G. 2010. An initial analysis of the solar storming effects on the determination of coordinates using GNSS, Geodezija ir kartografija [Geodesy and Cartography] 36(3): 97-102. doi:10.3846/gc.2010.16

Vilma zuBINAITE. Doctoral student at the Department of Geodesy and Cadastre, Vilnius Gediminas Technical University, Sauletekio al. 11, LT-10223 Vilnius, Lithuania. Ph +370 5 2744 703, Fax +370 5 2744 705, e-mail: MSc from VGTU (2007). Research interests: calibration of GNSS antennas, investigation into solar storm effects to ground position, satellite movement theory, Building Intelligent Modeling (BIM).

George PREISS. Assist. Prof. at Geomatics Group, Gj0vik University College, Postboks 191 Teknologivn. 22, NO-2802 Gj0vik, Norway. Ph +47 6113 5283, Fax +47 6113 5170, e-mail: Master of Arts (Mechanical Sciences) (1966), University of Cambridge, Master of Science (Geodesy) (1974) University of Oxford. The author of different educational notes and papers concerning GNSS, the theory of errors, adjustment theory and classical geodetic computations. Research interests: examining GNSS error sources, calibrating GNSS systems, Building Intelligent Modeling (BIM).

Vilma Zubinaite (1), George Preiss (2)

(1) Department of Geodesy and Cadastre, Vilnius Gediminas Technical University, Sauletekio al. 11, LT-10223 Vilnius, Lithuania

(2) Geomatics group, Gjovik University College, Post Box 191, NO-2802 Gjovik, Norway

E-mails: (1) (corresponding author); (2)

Received 07 November 2011; accepted 21 November 2011
Table 1. Selected solar activity events as an object for

 Space weather Scale

Date G1 G2 G3 G4 G5 S1 S2 S3 S4 S5

29.10.2003 # # # # # #
30.10.2003 # # # # # #
31.10.2003 # # #

Note: Selected solar activity events indicated with #.

Table 2. The summary of results
showing the range of differences
(The range in this context is
defined as the difference between
the highest and lowest values)

 2003 2010

[OMEGA], KRSS 3.7907 2.382
 radians NYA1 3.665 3.129
i, radians KRSS 3.451 4.537
 NYA1 3.451 1.786
a, meters KRSS 56.797 70.758
 NYA1 52.970 55.441
e, no unit KRSS 0.748 2.180
 NYA1 0.730 0.589
[omega], KRSS 171.286 98.968
 radians NYA1 147.238 153.141
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Author:Zubinaite, Vilma; Preiss, George
Publication:Geodesy and Cartography
Article Type:Report
Geographic Code:4EXNO
Date:Dec 1, 2011
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