Paper ID No.SO96.5.18

POSSIBLE MODIFICATION OF GEOPOTENTIAL COEFFICIENTS TO IMPROVE PROPAGATION ACCURACY OF POLAR ORBIT

H.Dosho*, S.Mori*, T.Tajima*, A.Suzuki*, Y.Fujita*, M.Horii*, T.Babauchi* & H.Nozawa**
* National Space Development Agency of Japan (NASDA), 2-1-1,Sengen Tsukuba Ibaraki,305 Japan
Fax: 81-298-51 2326. E-mail:mori.shigehiro@tkjv01.nnet.nasda.go.jp
** Daiko Denshi Tsushin Ltd., 2-1,Ageba-cho Shinjuku Tokyo,162 Japan
Fax: 81-298-52 7188. E-mail:dkm01072@niftyserve.or.jp

ABSTRACT. The MOS-1, the first Japanese Marine Observation Satellite, had been operated in a sun-synchronous polar orbit with a recurrent period of 17 days. From the early stage of its operation, we noticed an along-the-track prediction error having periods of 8.5 days and 17 days, and reported the phenomenon and the evaluation results of the resonant terms of the geopotential model GEM10B in 1989. After completing 8 years of the mission operation, the semi-major axis of the orbit was slightly shortened in order to change the recurrent period to 18 days. Then the same study has been carried out again based on the tracking data gathered for the following two months. Consequently, we could verify that our method which improve the geopotential model by the successive orbit determinations is applicable not only to satellites on the orbit with a recurrent period of 17 days, but to the other recurrent orbit satellites.

1.INTRODUCTION
The MOS-1 was the first Japanese marine observation satellite launched from the NASDA Tanegashima Space Center on February 19, 1987, and had been operated in a sun-synchronous polar orbit with a recurrent period of 17 days. After completing 8 years of the mission operation, the semi-major axis of the orbit was slightly shortened in order to change the recurrent period to 18 days. After gathering the tracking data for the following two months, the satellite was re-orbited using all the remaining fuel and the satellite operations were terminated on November 29, 1995. From the early stage of its operation, we noticed an along-the-track prediction error having periods of 8.5 days and 17 days, and reported the phenomenon and the evaluation results of the resonant terms of the Goddard Earth Model 10B (GEM10B) in 1989***.

The same study has been carried out again based on the above-mentioned orbit data. Following the estimation of the high order resonance terms of the GEM10B from MOS-1's new orbit, was the modification of its specific terms for optimizing model to the orbit of MOS-1. After these procedures, we evaluated the GEMT3, which is going to be introduced in new NASDA Orbit Computation System 2 *** Reference 3.

2.OBSERVED PHENOMENON AND CONDITION
Comparision between the previous values and the new values of the MOS-1 orbital parameters, which reflect their sun-synchronous recurrent orbit conditions, are shown in Table 1. The mathematical models and the basic parameters employed in the NOCS are shown in Table 2. The tracking data used in this analysis were acquired during the period from August 3 to October 1 in 1995 (about the time of three. The arc length of the data used in each orbit determination way of the data are shown in Table 3. The data arcs selection There were two advantages of the data usage in this analysis. One was that the MOS-1 had no jet firing in its normal attitude control mode, and the other was the tracking data which had been gathered in a time period of very low solar activity. Table 1. MOS-1 orbital parameters
Description Previous valueNew value
Nodal period 103.2 min 103.1 min
Semi-major axis 7286.9 km 7285.6 km
Eccentricity 0.001 0.001
Inclination 99.1 deg 99.0 deg
Altitude 908.8 km 907.5 km
Recurrent period 17 days 18 days
Local sun time of descending node 10h:05m 9h:50m
Table 2. Force models and constants
Parameter Value or Comment
Speed of light 299792.458 km/s
Love number for second-order k2= 0.25
solid erath tides phase=2.5 deg
Ephemeris for sun and moon DE200(JPL)
Polar motion and UT1 variations IERS
Precession and nutation Force Models Woolard
Earth gravitational GEM10B
Atmosphere model Jacchia-Nicolet
Radiation pressure board
Table 3. MOS-1 range data summary
StationKTDSMTDSOTDSTOTAL
Number of passes 63 65 55 183

5_18_01.GIF
Figure 1. The data arcs and prediction arcsThe pattern of the difference in the semi-major axis (DIFF.a) and the along-track direction (DIFF.M) between the predicted and the determined orbit, are shown in Figure 2 and Figure 3 respectively. The difference in the semi-major axis, which also includes J2 short periodic perturbation due to displacement in the along-track direction, needs a correction. Thus, this correction has already been applied in the Figure 2. Obviously these two figures show periodic changes and both periods show good coincidence, similar to the previous analysis which we reported in 1989.
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Figure 2. The pattern of the difference in the semi-major axis between the predicted and determined orbit
5_18_03.GIF
Figure 3. The pattern of the difference in the along-track direction between the predicted and determined orbit

3.MODELING OF THE DIFFERENCE

We assume an periodic motion DM(t) in the along-track direction by following equation, DM(t) = DMn * sin [ wn * t + n ] --------------------------------------------- (1)
where, wn is an apriori determined angular velocity having a resonance period of n days from the MOS-1 orbit. Theobserved difference in the along-track direction at time ti is; dDM(ti) = DM(ti-1) + Dni-1 * ( ti - ti-1 ) - DM(ti) --------------------------- (2) where, Dni-1 is the change in the mean motion within arci-1; time span Ti-1 (see Figure 4). Here, we assumeDM(t) again as following equation considering that the MOS-1 orbit gets deep resonant perturbation from termsof 14th and 28th order having two periods of 17 days and 8.5 days respectively, and that these two orderterms have some errors. DM(t) = DM14 * sin [ w14 * t + b14 ] + DM28 * sin [ w28 * t + b28 ] --- (3) According to the above equations, we can empirically determine 4 parameters, namely 2 amplitudes and 2 phaseangles, which give a good fitness with the observed difference shown in Figure 2 and Figure 3. The estimatedparameters are shown in Table 4 with the parameters from MOS-1's previous orbit. It shows that both2 amplitudes and the phase angle b14 are much the same respectively, however both the phase angle b28 show quite different.
5_18_04.GIF
Figure 4. The difference in the along-track direction between the predicted and determined element Table 4. The estimated and analytical derived parameters
Estimated parametersDM14DM28 b14b28
New orbit 1.651e-3 9.622e-4 90 173
Previous orbit 1.432e-3 9.167e-4 102 311
Unit : deg

4.GRAVITY MODEL MODIFICATION
Based upon the above-mentioned results, we have tried to modify the GEM10B in order to get the best fitted geopotential model for the MOS-1 orbit. We had to select two adequate terms which cause resonant perturbation, because only four parameters could be estimated from the observed MOS-1 orbit. So, we selected two terms, namely (33,14) and (30,28), to modify. They had been selected in the previous analysis and were easily estimated by using the equation derived by Kaura. The estimated values are shown in Table 5 with the values from MOS-1's previous orbit. Table 5. The estimated values of (33,14) and (30,28)
Estimated valuesC33,14S33,14 C30,28S30,28
New orbit -0.1342e-6 0.0302e-6 -0.0027e-6 -0.0129e-6
Previous orbit -0.0862e-6 0.0175e-6 0.0022e-6 -0.0115e-6


In order to verify the effects of the improved geopotential model, several orbit determination computations have been repeated using the same data arcs with the original processing with the GEM10B. The improved pattern of the difference in the semi-major axis (DIFF.a) and the along-track direction (DIFF.M) between the predicted and the determined orbit, are shown in Figure 5 and Figure 6 respectively. They show the effects of the improved geopotential models.
5_18_05.GIF
Figure 5. The improved pattern of the difference in the semi-major axis between the predicted and determined orbit

5_18_06.GIF
Figure 6. The improved pattern of the difference in the along-track direction between the predicted and determined orbit


5.EVALUATION OF THE GEMT3
We have evaluated the GEMT3, which is going to be introduced in new NASDA Orbit Computation System 2 (NOCS2). We have determined MOS-1's orbit with the same conditions including the data arcs by only changing the gravity model. The pattern of the difference in the semi-major axis (DIFF.a) and the along-track direction (DIFF.M) between the predicted and the determined orbit, are shown in Figure 7 and Figure 8 respectively. From these figures, we are understood that the GEMT3 is about twice as accurate as the GEM10B for the MOS-1's orbit determination and prediction.
5_18_07.GIF
Figure 7. The pattern of the difference in the semi-major axis between the predicted and determined orbit with the GEMT3

5_18_08.GIF
Figure 8. The pattern of the difference in the along-track direction between the predicted and determined orbit with the GEMT3


At present, we are modifying the GEMT3 in order to get the best fitted geopotential model for the MOS-1 orbit, and are verifying the effects of the improved GEMT3.

6.CONCLUSION
As shown in this paper, we ACKNOWLEDGMENT The authors wish to thank Ms. J.Mitsuhashi, Mr. Y.Toda, et al. of Daiko Denshi Tsushin Ltd. for their assistance in computer runs.

REFERENCES

1. A.Yamamoto, T.Shimizu, et al. "NASDA's Operational Orbit Computation System for Late'80's, ESA SP-255,Dec., 1986 2. A.Yamamoto, S.Mori, K.Ueno, T.Yamamoto, T.Tajima, "Gravity Model Comparison by MOS-1 " 16thISTS, C-2-6, May., 1988 3. A.Yamamoto, K.Ueno, T.Tajima, M.Horii, "Gravity Model Modification for MOS-1 Tracking Data" Intl. Symposiumof Space Dynamics, Toulouse, Nov., 1989. 4. Kaula, W.M., "Theory of Satellite Geodesy", Waltham, Massachusetts, Blaisdell Publishing Company, 1966 5. Y.Kozai "Satellite Orbit (Japanese)", Tracking and Control Div. NASDA, Feb., 1979 6. F.J.Lerch, et al., "Goddard Earth Models for Oceanographic Applications (GEM10B and 10C), Marine Geodesy,vol.5, No.2, Feb., 1981 7. F.J.Lerch, et al., "Geopotential Models of The Earth from Satellite Tracking, Altimeter and SurfaceGravity Observations : GEM-T3 and GEM-T3S", NASA Goddard Space Flight Center, Greenbelt MD, 1992