A new laser-ranged satellite for General Relativity and space geodesy: III. De Sitter effect and the LARES 2 space experiment
Eur. Phys. J. C
A new laser-ranged satellite for General Relativity and space geodesy: III. De Sitter effect and the LARES 2 space experiment
Ignazio Ciufolini 1 2
Richard Matzner 0
Vahe Gurzadyan 4
Roger Penrose 3
0 Theory Group, University of Texas at Austin , Austin , USA
1 Centro Fermi , Rome , Italy
2 Dip. Ingegneria dell'Innovazione, Università del Salento , Lecce , Italy
3 Mathematical Institute, University of Oxford , Oxford , UK
4 Center for Cosmology and Astrophysics, Alikhanian National Laboratory and Yerevan State University , Yerevan , Armenia
In two previous papers we presented the LARES 2 space experiment aimed at a very accurate test of framedragging and at other tests of fundamental physics and measurements of space geodesy and geodynamics. We presented the error sources of the LARES 2 experiment, its error budget and Monte Carlo simulations and covariance analyses confirming an accuracy of a few parts in one thousand in the test of frame-dragging. Here we discuss the impact of the orbital perturbation known as the de Sitter effect, or geodetic precession, in the error budget of the LARES 2 frame-dragging experiment. We show that the uncertainty in the de Sitter effect has a negligible impact in the final error budget because of the very accurate results now available for the test of the de Sitter precession and because of its very nature. The total error budget in the LARES 2 test of frame-dragging remains at a level of the order of 0.2%, as determined in the first two papers of this series.
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The LARES 2-LAGEOS space experiment is designed to
achieve a new, accurate measurement of the General
Relativistic frame-dragging due to the rotation of the Earth.
Analytical estimates, covariance studies, and Monte Carlo
simulations concur that the expected error level in this effect is
of order 0.2%, as shown in Refs. [
1,2
].
The two LAGEOS (Laser GEOdynamics Satellite) and
the two LARES (Laser RElativity Satellite) are laser-ranged
satellites. Satellite Laser Ranging (SLR) is the most accurate
technique for measuring distances to the Moon [
3
] and to
artificial satellites such as the LAGEOS and LARES satellites
[
4–6
]. Short-duration laser pulses are emitted, with
different elevations, from lasers on the Earth towards a satellite
and then reflected back to the emitting laser-ranging
stations by the retro-reflectors on the satellite. The tracking
data collected by the SLR network are analysed, organized
and distributed by the International Laser Ranging Service
(ILRS) [
7
]. By measuring the total round-trip travel time we
are today able to determine the instantaneous distance of a
retro-reflector on the LAGEOS and LARES satellites with a
precision of a few millimetres [
8
]. Then, using orbital
estimators, such as GEODYN, EPOSOC and UTOPIA, the orbit
of the satellite is reconstructed and its six Keplerian orbital
elements are determined with extremely high accuracy. For
example the longitude of the ascending node can be
determined with an uncertainty of a fraction of milliarcsecond
that, over a long period of time, allows for extremely high
accuracy in the measurement of the total nodal precession of
a laser-ranged satellite. The LAGEOS satellites (LAGEOS
and LAGEOS 2) [
4
] are spherical, made of heavy brass and
aluminium, with a radius of 300 mm and about 406 kg in
weight, completely passive and covered with retro-reflectors.
LAGEOS and LAGEOS 2 have an essentially identical
structure but they have different orbits. The semimajor axis of
LAGEOS is a = 12270 km, the eccentricity e = 0.004 and
the inclination I = 109.9◦. The semimajor axis of LAGEOS
2 is aI I = 12163 km, the eccentricity eI I = 0.014 and the
inclination II I = 52.65◦. The LARES satellite [
5
], launched
in 2012 by the Italian Space Agency (ASI) and ESA with
the VEGA launch vehicle of ASI, ESA, AVIO and ELV, is
spherical with a radius of 182 mm and a total mass of 386.8
kg. It is a single spherical piece of a very dense tungsten
alloy and it is covered with 92 retro-reflectors. The LARES
orbital elements are semimajor axis aL AR E S = 7820 km,
orbital eccentricity eL A R E S = 0.0008, and orbital
inclination IL A R E S = 69.5◦.
The LARES 2 satellite is planned for launch in 2019 with
the new VEGA C launch vehicle of ASI, ESA, AVIO and
ELV. It will be spherical with a radius of about 200 mm and
a total mass of about 300 kg. Its orbital elements will be
semimajor axis aL A R E S 2 = 12270 km, orbital inclination
IL A R E S 2 = 70.16◦ (supplementary to that of LAGEOS) and
approximately null orbital eccentricity.
In addition to the frame-dragging, gravitomagnetic effect,
whose test is the main objective of the LARES 2-LAGEOS
space experiment, there is another general relativistic
perturbation of an orbiting gyroscope, relative to an asymptotic
inertial frame: the de Sitter or geodetic (or geodesic)
precession [
9
] (see also [
10
]). This precession is due to the coupling
between the velocity of a gyroscop (...truncated)