## Details

Originalsprache | Englisch |
---|---|

Aufsatznummer | 035015 |

Fachzeitschrift | Classical and quantum gravity |

Jahrgang | 35 |

Ausgabenummer | 3 |

Publikationsstatus | Veröffentlicht - 8 Jan. 2018 |

## Abstract

This paper presents the recent version of the lunar laser ranging (LLR) analysis model at the Institut für Erdmessung (IfE), Leibniz Universität Hannover and highlights a few tests of Einstein's theory of gravitation using LLR data. Investigations related to a possible temporal variation of the gravitational constant, the equivalence principle, the PPN parameters β and γ as well as the geodetic precession were carried out. The LLR analysis model was updated by gravitational effects of the Sun and planets with the Moon as extended body. The higher-order gravitational interaction between Earth and Moon as well as effects of the solid Earth tides on the lunar motion were refined. The basis for the modeled lunar rotation is now a 2-layer core/mantle model according to the DE430 ephemeris. The validity of Einstein's theory was studied using this updated analysis model and an LLR data set from 1970 to January 2015. Within the estimated accuracies, no deviations from Einstein's theory are detected. A relative temporal variation of the gravitational constant is estimated as Ġ /G_{0} = (7.1 ± 7.6) × 10^{-14} yr^{-1}, the test of the equivalence principle gives Δ(m_{g}/m_{i})_{EM} = (-3 ± 5) × 10^{-14} and the Nordtvedt parameter η = (-0.2 ± 1.1) × 10^{-4}, the PPN-parameters β and γ are determined as β - 1 = (-4.5 ± 5.6) × 10^{-5} and γ - 1 = (-1.2 ± 1.2) × 10^{-4} and the geodetic precession is confirmed within 0.09%. The results for selected relativistic parameters are obtained by introducing constraints from an LLR solution without estimating relativistic quantities. The station coordinates are constrained for the estimation of Ġ /G_{0}, β and γ, the initial value of the core rotation vector is constrained to a reasonable model value for the estimation of Ġ /G_{0} and geodetic precession. A constrained z-component of the initial lunar velocity is used for the estimation of the geodetic precession.

## ASJC Scopus Sachgebiete

- Physik und Astronomie (insg.)
**Physik und Astronomie (sonstige)**

## Zitieren

- Standard
- Harvard
- Apa
- Vancouver
- BibTex
- RIS

**Relativistic tests with lunar laser ranging.**/ Hofmann, F.; Müller, J.

in: Classical and quantum gravity, Jahrgang 35, Nr. 3, 035015, 08.01.2018.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

*Classical and quantum gravity*, Jg. 35, Nr. 3, 035015. https://doi.org/10.1088/1361-6382/aa8f7a

*Classical and quantum gravity*,

*35*(3), Artikel 035015. https://doi.org/10.1088/1361-6382/aa8f7a

}

TY - JOUR

T1 - Relativistic tests with lunar laser ranging

AU - Hofmann, F.

AU - Müller, J.

N1 - Funding information: Current LLR data are collected, archived, and distributed under the auspices of the International Laser Ranging Service (ILRS) (Pearlman et al 2002). We acknowledge with thanks that more than 47 years of processed LLR data has been obtained under the efforts of the personnel at the Observatoire de la Côte dAzur in France, the LURE Observatory in Maui, Hawaii, the McDonald Observatory in Texas, the Apache Point Observatory in New Mexico and the Matera Laser Ranging station in Italy. LLR-related research at the University of Hannover was funded by the DFG, the German Research Foundation, within the research unit FOR1503 ‘Space-Time Reference Systems for Monitoring Global Change and for Precise Navigation in Space’. We are also grateful to the two anonymous reviewers for their comments which helped us in improving the paper.

PY - 2018/1/8

Y1 - 2018/1/8

N2 - This paper presents the recent version of the lunar laser ranging (LLR) analysis model at the Institut für Erdmessung (IfE), Leibniz Universität Hannover and highlights a few tests of Einstein's theory of gravitation using LLR data. Investigations related to a possible temporal variation of the gravitational constant, the equivalence principle, the PPN parameters β and γ as well as the geodetic precession were carried out. The LLR analysis model was updated by gravitational effects of the Sun and planets with the Moon as extended body. The higher-order gravitational interaction between Earth and Moon as well as effects of the solid Earth tides on the lunar motion were refined. The basis for the modeled lunar rotation is now a 2-layer core/mantle model according to the DE430 ephemeris. The validity of Einstein's theory was studied using this updated analysis model and an LLR data set from 1970 to January 2015. Within the estimated accuracies, no deviations from Einstein's theory are detected. A relative temporal variation of the gravitational constant is estimated as Ġ /G0 = (7.1 ± 7.6) × 10-14 yr-1, the test of the equivalence principle gives Δ(mg/mi)EM = (-3 ± 5) × 10-14 and the Nordtvedt parameter η = (-0.2 ± 1.1) × 10-4, the PPN-parameters β and γ are determined as β - 1 = (-4.5 ± 5.6) × 10-5 and γ - 1 = (-1.2 ± 1.2) × 10-4 and the geodetic precession is confirmed within 0.09%. The results for selected relativistic parameters are obtained by introducing constraints from an LLR solution without estimating relativistic quantities. The station coordinates are constrained for the estimation of Ġ /G0, β and γ, the initial value of the core rotation vector is constrained to a reasonable model value for the estimation of Ġ /G0 and geodetic precession. A constrained z-component of the initial lunar velocity is used for the estimation of the geodetic precession.

AB - This paper presents the recent version of the lunar laser ranging (LLR) analysis model at the Institut für Erdmessung (IfE), Leibniz Universität Hannover and highlights a few tests of Einstein's theory of gravitation using LLR data. Investigations related to a possible temporal variation of the gravitational constant, the equivalence principle, the PPN parameters β and γ as well as the geodetic precession were carried out. The LLR analysis model was updated by gravitational effects of the Sun and planets with the Moon as extended body. The higher-order gravitational interaction between Earth and Moon as well as effects of the solid Earth tides on the lunar motion were refined. The basis for the modeled lunar rotation is now a 2-layer core/mantle model according to the DE430 ephemeris. The validity of Einstein's theory was studied using this updated analysis model and an LLR data set from 1970 to January 2015. Within the estimated accuracies, no deviations from Einstein's theory are detected. A relative temporal variation of the gravitational constant is estimated as Ġ /G0 = (7.1 ± 7.6) × 10-14 yr-1, the test of the equivalence principle gives Δ(mg/mi)EM = (-3 ± 5) × 10-14 and the Nordtvedt parameter η = (-0.2 ± 1.1) × 10-4, the PPN-parameters β and γ are determined as β - 1 = (-4.5 ± 5.6) × 10-5 and γ - 1 = (-1.2 ± 1.2) × 10-4 and the geodetic precession is confirmed within 0.09%. The results for selected relativistic parameters are obtained by introducing constraints from an LLR solution without estimating relativistic quantities. The station coordinates are constrained for the estimation of Ġ /G0, β and γ, the initial value of the core rotation vector is constrained to a reasonable model value for the estimation of Ġ /G0 and geodetic precession. A constrained z-component of the initial lunar velocity is used for the estimation of the geodetic precession.

KW - equivalence principle

KW - geodetic precession

KW - gravitational constant

KW - lunar laser ranging

KW - PPN parameters

UR - http://www.scopus.com/inward/record.url?scp=85040647834&partnerID=8YFLogxK

U2 - 10.1088/1361-6382/aa8f7a

DO - 10.1088/1361-6382/aa8f7a

M3 - Article

AN - SCOPUS:85040647834

VL - 35

JO - Classical and quantum gravity

JF - Classical and quantum gravity

SN - 0264-9381

IS - 3

M1 - 035015

ER -