Limitations to testing the equivalence principle with satellite laser ranging |
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Authors: | A M Nobili G L Comandi D Bramanti Suresh Doravari D M Lucchesi F Maccarrone |
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Institution: | (1) Department of Physics “E. Fermi”, University of Pisa, Largo B. Pontecorvo 3, 56127 Pisa, Italy;(2) INFN-Istituto Nazionale di Fisica Nucleare, Sezione di Pisa, Largo B. Pontecorvo 3, 56127 Pisa, Italy;(3) Department of Physics, University of Bologna, Bologna, Italy;(4) INAF-Istituto Nazionale di Astrofisica, IFSI, Via Fosso del Cavaliere 100, 00133 Rome, Italy |
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Abstract: | We consider the possibility of testing the equivalence principle (EP) in the gravitational field of the Earth from the orbits
of LAGEOS and LAGEOS II satellites, which are very accurately tracked from ground by laser ranging. The orbital elements that
are affected by an EP violation and can be used to measure the corresponding dimensionless parameter η are semimajor axis and argument of pericenter. We show that the best result is obtained from the semimajor axis, and it is
limited—with all available ranging data to LAGEOS and LAGEOS II—to η ≃ 2 × 10−9, more than 3 orders of magnitude worse than experimental results provided by torsion balances. The experiment is limited
because of the non uniformity of the gravitational field of the Earth and the error in the measurement of semimajor axis,
precisely in the same way as they limit the measurement of the product GM of the Earth. A better use of the pericenter of LAGEOS II can be made if the data are analyzed searching for a new Yukawa-like
interaction with a distance scale of one Earth radius. It is found that the pericenter of LAGEOS II is 3 orders of magnitude
more sensitive to a composition dependent new interaction with this particular scale than it is to a composition dependent
effect expressed by the η parameter only. Nevertheless, the result is still a factor 500 worse than EP tests with torsion balances in the gravitational
field of the Earth (i.e. at comparable distance), though a detailed data analysis has yet to be performed. While EP tests
with satellite laser ranging are not competitive, laser ranging to the Moon has been able to provide a test of the EP almost
1 order of magnitude better than torsion balances. We show that this is due to the much greater distance of the test masses
(the Earth and the Moon) from the primary body (the Sun) and the correspondingly smaller gradients of its gravity field. We
therefore consider a similar new experiment involving the orbit of LAGEOS: testing LAGEOS and the Earth for an EP violation
in the gravitational field of the Sun. We show that this test may be of interest, though it is a factor 300 less sensitive
than in the case of the Moon due to the fact that LAGEOS is closer to the Earth than the Moon and consequently its orbit is
less affected by the Sun. The limitations we have pointed out for laser ranging can be overcome by flying in low Earth orbit
a spacecraft carrying concentric test masses of different composition with the capability, already demonstrated in ground
laboratories, to accurately sense in situ any differential effects between them.
An erratum to this article can be found at |
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