Numerical Evaluation of Post-Newtonian Perturbations on the Global Navigation Satellite System

Roh, Kyoung-Min

doi:10.2514/1.a33980

Cited by 4 publications

(8 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Again we obtain the expected order of magnitude for the effects considered in this paper: the greatest effect on GNSS satellites is mainly due to Earth's oblateness (see the book Teunissen and Montenbruck (2015) and Roh (2018)). That is, effects at kilometre level are obtained.…”

Section: Adding the Earth Oblatenesssupporting

confidence: 53%

“…Therefore, our method is working properly because the order of magnitude computed in preceding works with the GNSS approximation is obtained (see for instance Teunissen andMontenbruck (2015), Chap. 3, Montenbruck andGill (2005) and Roh (2018)). The RPS methods are more exact than GNSS classical procedures, even when the last ones incorporate relativity corrections.…”

Section: Discussionmentioning

confidence: 99%

“…The order of magnitude obtained is the one expected for every quantity computed in this paper as (see the book Teunissen and Montenbruck (2015), Chap. 3, andRoh (2018)):…”

Section: Sun and Moon Effectsmentioning

confidence: 99%

“…In Kostić et al (2015) a model of RPS is presented in a more realistic spacetime near the Earth with all important gravitational effects: Earth multipoles up to 6th order, the Moon, the Sun, Jupiter, Venus, solid and ocean tides, and Kerr effect. A recent approach was proposed by Roh et al (2016), Roh (2018). They implemented a full set of first-order Post-Newtonian (PN) corrections in the high-fidelity orbit propagation KASIOP (Korea Astronomy and Space Science Institute Orbit Propagator).…”

Section: Introductionmentioning

confidence: 99%

“…The metric taken into account considers the effect of the Earth, the Moon, the Sun and the Earth oblateness. Solar radiation pressure and other non-gravitational effects are not considered although some of them have important contributions (see for instance Roh et al (2016), Roh (2018). However, the order of magnitude of their contributions depends on the distance to the Earth.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Relativistic positioning: including the influence of the gravitational action of the Sun and the Moon and the Earth’s oblateness on Galileo satellites

Colmenero

Córdoba

Alfonso

2021

Astrophys Space Sci

View full text Add to dashboard Cite

Uncertainties in the satellite world lines lead to dominant positioning errors. In the present work, using the approach presented in Puchades and Sáez (Astrophys. Space Sci. 352, 307–320, 2014), a new analysis of these errors is developed inside a great region surrounding Earth. This analysis is performed in the framework of the so-called Relativistic Positioning Systems (RPS). Schwarzschild metric is used to describe the satellite orbits corresponding to the Galileo Satellites Constellation. Those orbits are circular with the Earth as their centre. They are defined as the nominal orbits. The satellite orbits are not circular due to the perturbations they have and to achieve a more realistic description such perturbations need to be taken into account. In Puchades and Sáez (Astrophys. Space Sci. 352, 307–320, 2014) perturbations of the nominal orbits were statistically simulated. Using the formula from Coll et al. (Class. Quantum Gravity. 27, 065013, 2010) a user location is determined with the four satellites proper times that the user receives and with the satellite world lines. This formula can be used with any satellite description, although photons need to travel in a Minkowskian space-time. For our purposes, the computation of the photon geodesics in Minkowski space-time is sufficient as demonstrated in Puchades and Sáez (Adv. Space Res. 57, 499–508, 2016). The difference of the user position determined with the nominal and the perturbed satellite orbits is computed. This difference is defined as the U-error. Now we compute the perturbed orbits of the satellites considering a metric that takes into account the gravitational effects of the Earth, the Moon and the Sun and also the Earth oblateness. A study of the satellite orbits in this new metric is first introduced. Then we compute the U-errors comparing the positions given with the Schwarzschild metric and the metric introduced here. A Runge-Kutta method is used to solve the satellite geodesic equations. Some improvements in the computation of the U-errors using both metrics are introduced with respect to our previous works. Conclusions and perspectives are also presented.

show abstract

Section: Adding the Earth Oblatenesssupporting

confidence: 53%

Section: Discussionmentioning

confidence: 99%

“…The order of magnitude obtained is the one expected for every quantity computed in this paper as (see the book Teunissen and Montenbruck (2015), Chap. 3, andRoh (2018)):…”

Section: Sun and Moon Effectsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Relativistic positioning: including the influence of the gravitational action of the Sun and the Moon and the Earth’s oblateness on Galileo satellites

Colmenero

Córdoba

Alfonso

2021

Astrophys Space Sci

View full text Add to dashboard Cite

show abstract

A comparison between Runge-Kutta and Adems-Bashforth methods for determining the stability of the satellite's orbit

Ibrahim¹,

Saleh²

2020

International Conference of Numerical Analysis and Applied Mathematics Icnaam 2019

View full text Add to dashboard Cite

Re-Evaluation Solution Methods for Kepler's Equation of an Elliptical Orbit

Ibrahim

Saleh

2019

eijs

View full text Add to dashboard Cite

An evaluation was achieved by designing a matlab program to solve Keplerâ€™s equation of an elliptical orbit for methods (Newton-Raphson, Danby, Halley and Mikkola). This involves calculating the Eccentric anomaly (E) from mean anomaly (M=0Â°-360Â°) for each step and for different values of eccentricities (e=0.1, 0.3, 0.5, 0.7 and 0.9). The results of E were demonstrated that Newtonâ€™s- Raphson Danbyâ€™s, Halleyâ€™s can be used for e between (0-1). Mikkolaâ€™s method can be used for e between (0-0.6).The term that added to Danbyâ€™s method to obtain the solution of Keplerâ€™s equation is not influence too much on the value of E. The most appropriate initial Gauss value was also determined to be (En=M), this initial value gave a good result for (E) for these methods regardless the value of e to increasing the accuracy of E. After that the orbital elements converting into state vectors within one orbital period within time 50 second, the results demonstrated that all these four methods can be used in semi-circular orbit, but in case of elliptical orbit Danbyâ€™s and Halleyâ€™s method use only for e â‰¤ 0.7, Mikkolaâ€™s method for e â‰¤ 0.01 while Newton-Raphson uses for e < 1, which considers more applicable than others to use in semi-circular and elliptical orbit. The results gave a good agreement as compared with the state vectors of Cartosat-2B satellite that available on Two Line Element (TLE).

show abstract

Numerical Evaluation of Post-Newtonian Perturbations on the Global Navigation Satellite System

Cited by 4 publications

References 13 publications

Relativistic positioning: including the influence of the gravitational action of the Sun and the Moon and the Earth’s oblateness on Galileo satellites

Relativistic positioning: including the influence of the gravitational action of the Sun and the Moon and the Earth’s oblateness on Galileo satellites

A comparison between Runge-Kutta and Adems-Bashforth methods for determining the stability of the satellite's orbit

Re-Evaluation Solution Methods for Kepler's Equation of an Elliptical Orbit

Contact Info

Product

Resources

About