In our calculations we used the following models: GEM-T3, GRIM4-S4 (preliminary,
1995 year version), TEG-2B, JGM-2 and JGM-3. We calculated predicted positions for
the near-circular orbits with different inclinations ranged from 0° to 180° and with altitudes
corresponding to Space Station (400 km altitude), NOAA satellites (800 km) and
TOPEXIPOSEIDON (1330 km). Figs. 1 - 3 show differences in predicted satellite positions after the time interval Lit equal 24 hours calculated applying three different levels of
the ana1ytical theory, which included:
(I) the secular perturbations (the influence of all even zonal harmonic coefficients of a
given model is included),
(IT) the long-period perturbations due to zonal harmonic (the influence all zonal harmonic
is included, the main value of perturbations is due to odd zonal harmonic
coefficients),
(llI) the zonal and the tesseral harmonic perturbations except for the long-period
perturbations due to zonal harmonics ( the influence of all zonal and tesseral harmonic
coefficients.
Presented at the figs. 1 - 3 differences between two satellite position r(t1) and r(t]) were
calculated from the same mean orbital elements for the time epoch to using two different
gravity models and are plotted against the orbital inclination I
DISCUSSION
The results for orbits with the altitude of 400 km presented on the fig. 1 show that after 24
hours differences in satellite positions calculated using two gravity models can reach 100
meters or more. Even for the more recent and probably the best contemporary models
JGM-2 and JGM-3 differences are on a level of several dozens meters for some inclinations. For the orbits on the higher altitudes (figs. 2 and 3) these differences are smaller, but
still are on the level of 20 - 50 meters for some inclinations. For all the models the differences are much higher for orbits close to the equator (with inclinations close to 0° and
180°) than for other inclinations. Since the secular perturbations are linear functions of
time, presented differences are functions of time as well and for longer than 24 hours time
intervals are higher than those on figs. 1 - 3. Note that the peaks near 63° and 116° in the
case of the long-period perturbations due to zonal harmonic are not real. They are effects
of singularities of formulas for the long-period perturbations for the critical inclination.
CONCLUSIONS
Presented results show that uncertainties in the determination of the future satellite
positions due to uncertainties in models of the Earth's gravity field are very large and for
some orbits may exceed 100 meters.
Results presented on figs. 1 - 3 also indicate differences in particular parts of gravity models coefficients and their influence on orbits with different inclinations. For example, the
differences calculated using secular perturbations only (even zonal harmonic coefficients
are included only) for TEG-2B and JGM-3 models are very small for inclinations from
40° to 140° and large for the other ones. Very similar picture is in the total case when both
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1995 year version), TEG-2B, JGM-2 and JGM-3. We calculated predicted positions for
the near-circular orbits with different inclinations ranged from 0° to 180° and with altitudes
corresponding to Space Station (400 km altitude), NOAA satellites (800 km) and
TOPEXIPOSEIDON (1330 km). Figs. 1 - 3 show differences in predicted satellite positions after the time interval Lit equal 24 hours calculated applying three different levels of
the ana1ytical theory, which included:
(I) the secular perturbations (the influence of all even zonal harmonic coefficients of a
given model is included),
(IT) the long-period perturbations due to zonal harmonic (the influence all zonal harmonic
is included, the main value of perturbations is due to odd zonal harmonic
coefficients),
(llI) the zonal and the tesseral harmonic perturbations except for the long-period
perturbations due to zonal harmonics ( the influence of all zonal and tesseral harmonic
coefficients.
Presented at the figs. 1 - 3 differences between two satellite position r(t1) and r(t]) were
calculated from the same mean orbital elements for the time epoch to using two different
gravity models and are plotted against the orbital inclination I
DISCUSSION
The results for orbits with the altitude of 400 km presented on the fig. 1 show that after 24
hours differences in satellite positions calculated using two gravity models can reach 100
meters or more. Even for the more recent and probably the best contemporary models
JGM-2 and JGM-3 differences are on a level of several dozens meters for some inclinations. For the orbits on the higher altitudes (figs. 2 and 3) these differences are smaller, but
still are on the level of 20 - 50 meters for some inclinations. For all the models the differences are much higher for orbits close to the equator (with inclinations close to 0° and
180°) than for other inclinations. Since the secular perturbations are linear functions of
time, presented differences are functions of time as well and for longer than 24 hours time
intervals are higher than those on figs. 1 - 3. Note that the peaks near 63° and 116° in the
case of the long-period perturbations due to zonal harmonic are not real. They are effects
of singularities of formulas for the long-period perturbations for the critical inclination.
CONCLUSIONS
Presented results show that uncertainties in the determination of the future satellite
positions due to uncertainties in models of the Earth's gravity field are very large and for
some orbits may exceed 100 meters.
Results presented on figs. 1 - 3 also indicate differences in particular parts of gravity models coefficients and their influence on orbits with different inclinations. For example, the
differences calculated using secular perturbations only (even zonal harmonic coefficients
are included only) for TEG-2B and JGM-3 models are very small for inclinations from
40° to 140° and large for the other ones. Very similar picture is in the total case when both
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