Details
| Original language | English |
|---|---|
| Pages (from-to) | 921-934 |
| Number of pages | 14 |
| Journal | Advances in Space Research |
| Volume | 62 |
| Issue number | 4 |
| Early online date | 24 May 2018 |
| Publication status | Published - 15 Aug 2018 |
Abstract
Accurate orbit modeling plays a key role in contemporary and future space missions such as GRACE and its successor GRACE-FO, GNSS, and altimetry missions. To fully exploit the technological capabilities and correctly interpret measurements, relativistic orbital effects need to be taken into account. Within the theory of General Relativity, equations of motion for freely falling test objects, such as satellites orbiting the Earth, are given by the geodesic equation. We analyze and compare different solution methods in a spherically symmetric background, i.e. for the Schwarzschild spacetime, as a test bed. We investigate satellite orbits and use direct numerical orbit integration as well as the semi-analytical Lie-series approach. The results are compared to the exact analytical reference solution in terms of elliptic functions. For a set of exemplary orbits, we determine the respective accuracy of the different methods. Within the post-Newtonian approximation of General Relativity, modified orbital equations are obtained by adding relativistic corrections to the Newtonian equations of motion. We analyze the accuracy of this approximation with respect to the general relativistic setting. Therefore, we solve the post-Newtonian equation of motion using the eXtended High Performance Satellite dynamics Simulator. For corresponding initial conditions, we compare orbits in the Schwarzschild spacetime to those in its post-Newtonian approximation. Moreover, we compare the magnitude of relativistic contributions to several typical perturbations of satellite orbits due to, e.g., solar radiation pressure, Earth's albedo, and atmospheric drag. This comparison is done for our test scenarios and for a real GRACE orbit to highlight the importance of relativistic effects in geodetic space missions. For the considered orbits, first-order relativistic contributions give accelerations of about 20 nm/s 2 and are dominant in the radial direction.
Keywords
- Orbit propagation, Post-Newtonian theory, Relativistic effects, Relativistic geodesy, Satellite orbits
ASJC Scopus subject areas
- Engineering(all)
- Aerospace Engineering
- Physics and Astronomy(all)
- Astronomy and Astrophysics
- Earth and Planetary Sciences(all)
- Geophysics
- Earth and Planetary Sciences(all)
- Atmospheric Science
- Earth and Planetary Sciences(all)
- Space and Planetary Science
- Earth and Planetary Sciences(all)
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In: Advances in Space Research, Vol. 62, No. 4, 15.08.2018, p. 921-934.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Modeling approaches for precise relativistic orbits: Analytical, Lie-series, and pN approximation
AU - Philipp, Dennis
AU - Wöske, Florian
AU - Biskupek, Liliane
AU - Hackmann, Eva
AU - Mai, Enrico
AU - List, Meike
AU - Lämmerzahl, Claus
AU - Rievers, Benny
N1 - Funding Information: The present work was supported by the Deutsche Forschungsgemeinschaft (DFG) through the Sonderforschungsbereich (SFB) 1128 Relativistic Geodesy and Gravimetry with Quantum Sensors (geo-Q) and the Research Training Group 1620 Models of Gravity. We also acknowledge support by the German Space Agency DLR with funds provided by the Federal Ministry of Economics and Technology (BMWi) under Grant No. DLR 50WM1547 .
PY - 2018/8/15
Y1 - 2018/8/15
N2 - Accurate orbit modeling plays a key role in contemporary and future space missions such as GRACE and its successor GRACE-FO, GNSS, and altimetry missions. To fully exploit the technological capabilities and correctly interpret measurements, relativistic orbital effects need to be taken into account. Within the theory of General Relativity, equations of motion for freely falling test objects, such as satellites orbiting the Earth, are given by the geodesic equation. We analyze and compare different solution methods in a spherically symmetric background, i.e. for the Schwarzschild spacetime, as a test bed. We investigate satellite orbits and use direct numerical orbit integration as well as the semi-analytical Lie-series approach. The results are compared to the exact analytical reference solution in terms of elliptic functions. For a set of exemplary orbits, we determine the respective accuracy of the different methods. Within the post-Newtonian approximation of General Relativity, modified orbital equations are obtained by adding relativistic corrections to the Newtonian equations of motion. We analyze the accuracy of this approximation with respect to the general relativistic setting. Therefore, we solve the post-Newtonian equation of motion using the eXtended High Performance Satellite dynamics Simulator. For corresponding initial conditions, we compare orbits in the Schwarzschild spacetime to those in its post-Newtonian approximation. Moreover, we compare the magnitude of relativistic contributions to several typical perturbations of satellite orbits due to, e.g., solar radiation pressure, Earth's albedo, and atmospheric drag. This comparison is done for our test scenarios and for a real GRACE orbit to highlight the importance of relativistic effects in geodetic space missions. For the considered orbits, first-order relativistic contributions give accelerations of about 20 nm/s 2 and are dominant in the radial direction.
AB - Accurate orbit modeling plays a key role in contemporary and future space missions such as GRACE and its successor GRACE-FO, GNSS, and altimetry missions. To fully exploit the technological capabilities and correctly interpret measurements, relativistic orbital effects need to be taken into account. Within the theory of General Relativity, equations of motion for freely falling test objects, such as satellites orbiting the Earth, are given by the geodesic equation. We analyze and compare different solution methods in a spherically symmetric background, i.e. for the Schwarzschild spacetime, as a test bed. We investigate satellite orbits and use direct numerical orbit integration as well as the semi-analytical Lie-series approach. The results are compared to the exact analytical reference solution in terms of elliptic functions. For a set of exemplary orbits, we determine the respective accuracy of the different methods. Within the post-Newtonian approximation of General Relativity, modified orbital equations are obtained by adding relativistic corrections to the Newtonian equations of motion. We analyze the accuracy of this approximation with respect to the general relativistic setting. Therefore, we solve the post-Newtonian equation of motion using the eXtended High Performance Satellite dynamics Simulator. For corresponding initial conditions, we compare orbits in the Schwarzschild spacetime to those in its post-Newtonian approximation. Moreover, we compare the magnitude of relativistic contributions to several typical perturbations of satellite orbits due to, e.g., solar radiation pressure, Earth's albedo, and atmospheric drag. This comparison is done for our test scenarios and for a real GRACE orbit to highlight the importance of relativistic effects in geodetic space missions. For the considered orbits, first-order relativistic contributions give accelerations of about 20 nm/s 2 and are dominant in the radial direction.
KW - Orbit propagation
KW - Post-Newtonian theory
KW - Relativistic effects
KW - Relativistic geodesy
KW - Satellite orbits
UR - http://www.scopus.com/inward/record.url?scp=85048577153&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1708.04609
DO - 10.48550/arXiv.1708.04609
M3 - Article
VL - 62
SP - 921
EP - 934
JO - Advances in Space Research
JF - Advances in Space Research
SN - 0273-1177
IS - 4
ER -