Selected Accelerations and Orbital Elements of the Goce Satellite in the Time Domain
2009; Volume: 12; Issue: -1 Linguagem: Inglês
10.2478/v10022.009-0010-y
ISSN2083-4527
Autores Tópico(s)GNSS positioning and interference
ResumoWYBRANE PRZYŚPIESZENIA I ELEMENTY ORBITALNE SATELITY GOCE W DZIEDZINIE CZASU Andrzej Bobojc Instytut Geodezji Uniwersytet Warminsko-Mazurski w Olsztynie S l o w a k l u c z o w e: orbita satelity GOCE, przyśpieszenia satelity, elementy orbitalne, geopotencjal. A b s t r a k t Praca zawiera wyniki symulacji orbity satelity GOCE. Orbite satelity GOCE przedstawiono w aspekcie zmian czasowych wybranych przyśpieszen i elementow keplerowskich. Przyśpieszenia satelity spowodowane przez: geopotencjal, plywy skorupy, plywy oceaniczne (skladowa radialna dla obu), grawitacje Slonca i grawitacje Ksiezyca, przedstawiono w funkcji czasu. Pokazane zmiany w elementach orbity obejmują poloś wielką, mimośrod, nachylenie, argument perygeum i rektascensje wezla wstepującego. Do wyznaczenia orbity uzyto calkowania numerycznego metodą Cowella osmego rzedu. Geopotencjal opisano modelem EGM96. Opisano wspomniane zmiany czasowe wybranych przyśpieszen i elementow orbity. Wiekszośc z nich zawiera charakterystyczne skladowe okresowe, ktore są zblizone do okresu orbitalnego satelity, okresu rotacji Ziemi oraz okresu synodycznego Ksiezyca. Introduction One of the ESA’s missions is the Gravity Field and Steady – State Ocean Circulation Explorer Mission (GOCE). The GOCE mission has been started on 17 March 2009. The main goal of this mission is to determine the geopotential model up to 200 degree and order of the spherical harmonic coefficients. The mentioned model will allow to obtain the gravity acceleration with an accuracy of 1 mGal and to estimate of the geoid with an accuracy of 1 cm. Such accuracies will be realized at spatial scales down to 100 km (Gravity Field... 1999, DRINKWATER et al. 2003, MEGIE, READINGS 2000). A gradiometric satellite is a key component of the GOCE mission. This satellite is placed into almost circular and sun-synchronous orbit with an average altitude of about 250 km (Gravity Field... 1999). The non-gravitational forces acting on the satellite are compensated by a drag-free control system (DRINKWATER et al. 2003). The GOCE satellite is planned to provide two types of measurements: the gravity gradients (Satellite Gravity Gradiometry data – SGG data) and the high-low Satellite to Satellite tracking data (SST data). They will be obtained by two on-board devices: an electrostatic gravity gradiometer and a GPS/GLONASS receiver, respectively (JOHANESSEN et al. 2003). Both the SGG data and the SST data will be subject of a joint inversion to estimate the Earth’s gravity field model (DITMAR, KLEES 2002, DITMAR et al. 2003). The knowledge of the satellite orbit is one of the key factors in the estimation of Earth’s gravity field. GPS measurements (SST data) are the basic data for the GOCE satellite orbit estimation. Advanced algorithms were prepared to determine the aforementioned orbit in the form of a reduceddynamic and a kinematic orbit solution (BOCK et al. 2006, VISSER et al. 2006). Basically, the SGG data (i.e. gravity gradients) will be used to obtain the Earth’s gravity field model. However, these observations also carry the information about the position and velocity of a satellite. Thus they can be used in the process of satellite orbit improvement. This process requires the computation of approximated gravity gradients along a approximated orbit. The description of planned GOCE satellite orbit using the temporary changes in the selected accelerations and in keplerian elements, can be helpful in the computation of aforementioned approximated orbit. Selected Accelerations and Orbital... 105 Simulations To obtain the GOCE satellite orbit, the Cowell numerical integration method of the eighth order was used. The computed orbit was expressed with respect to the J2000.0 reference frame (LAING 1991, ANDERSON et al. 2002). This frame can be described in the following way: the origin at the Earth’s mass centre, the X-axis is directed towards the mean vernal equinox of the standard epoch J2000.0 (at noon on January 1, 2000), the Z-axis points out from the Earth’s mass centre along the Earth’s mean rotational axis of the standard epoch J2000.0, the Y-axis completes the frame to the right-handed frame. The following initial elements of the GOCE orbit were taken into the computation: the epoch: 54313.0 MJD, semi-major axis: 6634.7711 km, eccentricity: 0.001, inclination: 96.5 deg., argument of perigee: 0.00 deg., right ascension of ascending node: 45.00 deg., mean anomaly: 0.00 deg., the orbital period T= 89.64 min. (Gravity Field... 1999). The computations were performed using the TOP package (DROŻYNER 1995). The TOP package determines a satellite orbit in the Earth’s gravity field taking into account selected perturbing forces. Several models were used to the orbit computation. The EGM96 model (LEMOINE et al. 1998) was taken for the geopotential. The Earth and ocean tides were modelled by the MERIT Standards (MELBOURNE et al. 1983). Both, the IAU1976 Theory of Precession and the IAU1980 Theory of Nutation (the Wahr nutation) were included to the computation. Additionally, the following data were taken into the computation: the Sun, Moon and planet ephemerides DE200/LE200 (epoch J2000.0). The pole coordinates were equal to zero. It was assumed that the GOCE satellite motion is determined by the geopotential and by the following forces: the gravitation of the Moon, the gravitation of the Sun, the gravitation of the planets, the Earth tides and the ocean tides. Additionally, the relativity effects was taken into account in the satellite motion model. The relativity effects generate the corresponding satellite acceleration. Taking into account the aforementioned assumptions, a 30-day arc of the GOCE orbit with an integration step 60 s was obtained. The chosen satellite accelerations due to thementioned above forces and the chosen keplerian elements, were computed along this orbit. The obtained temporary changes of the selected accelerations and keplerian elements were expressed with respect to the J2000.0 reference frame. Description of the obtained temporary changes The presented below graphs were prepared for the 30-day arc of the GOCE orbit. The initial epoch (denoted as 0) and the last given epoch (number 21600) correspond to 54313.0 MJD and 54343.0 MJD, respectively. A sampling Andrzej Bobojc 106 interval is 2 minutes. For most presented below figures, the main graph and additional small graphs were prepared. These small graphs zoom in the main graph in the chosen epoch ranges of the 30-day orbital arc. The width of these ranges is 400 minutes with the exception of Figure 9b, where the mentioned width is equal to 200 minutes. The term “amplitude” used in this work, refers to the difference between a given maximum and a neighbouring minimum (so called peak-to-peak amplitude). Changes in selected accelerations The temporary changes of the satellite acceleration due to the geopotential are presented in Figure 1. The continuous oscillations of the mentioned acceleration result from this figure. The acceleration oscillates around the value of ~ 9.062 m s (Fig. 1a). These oscillations have the periodic behavior with the increasing amplitude. At the start of the orbital arc, this amplitude is equal to about 0.04 m s. Next, it decreases to approx. 0.03 m s (at ~ one-fifth of the orbital arc) and increases to about 0.09 m s at the end of the orbital arc. An occurrence of the oscillation of the geopotential-derived acceleration is in relation with the non-zero value of eccentricity (for the initial epoch 0.001). As the additional research showed, the increasing trend of the eccentricity appears together with the mentioned increase of the oscillating amplitude of the acceleration. Two periods of the acceleration changes can be seen in Figure 1. The first period visible in four small graphs of Figure 1 is equal to about 90 minutes and coincides with the satellite orbital period. The second period is equal to about 1 day and is close to the Earth’s rotation period. This period concerns the changes of the maximum values of acceleration and is visible in Figure 1a. The occurrence of the aforementioned period is in relation with the Earth’s rotation with respect to the used J2000.0 frame. In the first three small graphs (Fig. 1b-1d), the characteristic small peaks between the main peaks of the oscillating acceleration, are shown. The mentioned peaks appear in the middle of the satellite orbital period. Taking into account Figure 1b, the explanation of such acceleration changes can be performed. The satellite experiences the maximum acceleration at the perigee, being simultaneously at the equatorial plane, near the equatorial bulge (the acceleration at the epoch 0 in Fig. 1b). Next, the acceleration decreases when the satellite moves around the Earth. When the satellite reaches the maximum altitude above the equatorial plane, after the quarter of the orbital period, the acceleration decreases to the minimum value. From this point, the experienced acceleration increases when the satellite returns to the equatorial plane. After half the orbital period, the satellite is again at the equatorial plane, near the Selected Accelerations and Orbital... 107
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