Satellite Orbit and Ephemeris Determination using Inter Satellite Links
Satellite Orbit and Ephemeris Determination using Inter Satellite Links
Satellite Orbit and Ephemeris Determination using Inter Satellite Links
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<strong>Inter</strong> <strong>Satellite</strong> <strong>Links</strong><strong>Orbit</strong> Computation4.3 Force Model ErrorsA given force model will only be accurate to a certain degree. This lead to a divergence of thepredicted trajectory, <strong>and</strong> the actual one. On the other h<strong>and</strong>, if computational recourses arerare, the orbit arc is short or the required accuracy is not that dem<strong>and</strong>ing, it is necessary toassess the impact of simplifying the force model. This section deals with the impact of theseforce model simplifications, as well as force model errors on the orbit prediction error.4.3.1 Earth's GravityAs shown in chapter 4.2.1, the impact of the higher order spherical harmonics of the earth'sgravity field decreases with orbit altitude. Neglecting higher order terms will therefore lead toprediction errors, but depending on orbit altitude. Another error source is the imperfection ofthe harmonic coefficients. To assess the impact of neglecting higher order terms, as well as animperfect gravity model, a reference trajectory has been computed <strong>using</strong> the full JGM-3,being a state of the art gravity model. Degree <strong>and</strong> order of the model has been decreasedsuccessively <strong>and</strong> the resulting trajectory has been compared to the reference orbit.Furthermore the reference trajectory has been compared to orbits computed with other fullgravity models. The following gravity models have been compared:Gravity ModelJGM-3 (ReferenceModel)Maximum Degree xOrder70 x 70JGM-2 70 x 70GEM-T3 50 x 50GRIM4-S4 66 x 66Table 4-4 Assessed Gravity ModelsAll these models have been derived by satellite measurements. To show the impact of theorbit altitude, different reference orbit have been computed:• a low earth orbit (LEO) with 1250 km orbit altitude• a GPS like orbit (MEO) with 20200 km orbit altitude• a geostationary orbit (GEO) with approximately 36 000 km orbit altitudeThe following figure indicates the prediction errors if a 1250 km LEO is predicted <strong>using</strong> onlya 15 x 15 gravity model. The errors shows a periodic behaviour reflecting the orbital period ofR. Wolf Page 39
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