A comment on "Can observations inside the Solar System reveal the gravitational properties of the quantum vacuum?" by D.S. Hajdukovic
aa r X i v : . [ phy s i c s . g e n - ph ] A ug A comment on “Can observations inside the Solar System reveal thegravitational properties of the quantum vacuum?” by D.S. Hajdukovic
Lorenzo Iorio Ministero dell’Istruzione, dell’Universit`a e della Ricerca (M.I.U.R.)-IstruzionePermanent address for correspondence: Viale Unit`a di Italia 68, 70125, Bari (BA), Italy [email protected]
Received ; accepted 2 –
Abstract
The modified gravitational theory by Hajdukovic, based on the idea that quantumvacuum contains virtual gravitational dipoles, predicts, among other things, anomaloussecular precessions of the planets of the Solar System as large as ≃ − ,
1. Introduction
Some years ago, Hajdukovic (2013) put forth the hypothesis that quantum vacuum wouldcontain virtual gravitational dipoles. He argued that this hypothesis, which would have thepotential to simultaneously solve the Dark Matter and Dark Energy problems, might be testedwithin the Solar System. The key point in his proposal consists of the fact that the quantumvacuum (“enriched” with the gravitational dipoles) would induce a retrograde precession of theperihelion because of an additional constant radial acceleration of gravitational origin. In hisTable 1, Hajdukovic (2013) calculated the amount of such a putative anomalous precession forthe planets of the Solar System finding values ranging from −
690 milliarcseconds per century (cid:16) mas cty − (cid:17) for Mercury to − ,
980 mas cty − for Neptune. Hajdukovic (2013) did not comparehis theoretical predictions with the very tight bounds, already existing at the time of his writing,on any anomalous perihelion precessions for the inner planets of the Solar System and Saturnreleased by teams led by the astronomers E.V. Pitjeva and A. Fienga. Instead, he decided to limithimself just to Uranus and Neptune by citing, e.g., a paper of the present author, published inthe context of the Pioneer Anomaly and relying upon Pitjeva (2005a) who used the EPM2004ephemerides, by stating that “the current ephemerides of planets do not preclude the illustrativevalues” of his Table 1. In fact, the bounds on the perihelion precessions of the outer planets ofthe Solar System (Pitjeva 2010) were and, to our knowledge, are still too weak to rule out withconfidence even e ff ects as large as those listed by Hajdukovic (2013) in his Table 1. As a result,Hajdukovic (2013) suggested to look at the pericenter precession of the orbital motion of thenatural satellite Dysnomia around its primary which is the dwarf planet Eris.
2. A comparison with the EPM and INPOP ephemerides
Actually, the anomalous e ff ects predicted by Hajdukovic (2013) for the telluric planetsshould have been deemed as completely incompatible even with the planetary data processed 3 –with the EPM2004 ephemerides and available since 2005. Indeed, Table 3 of Pitjeva (2005b)states that the uncertainties in the perihelion precessions of the inner planets were as little as5 mas cty − (Mercury), 0 . − (Earth), and 0 . − (Mars); Table 1 of Hajdukovic(2013) predicts anomalous precessions as large as about ≃ − ,
000 mas cty − for the Earth andMars. Later, the situation became even worse. Su ffi ce it to say that the INPOP10a ephemeridesallowed Fienga et al. (2011) to obtain bounds on the inner planets of the Solar System as tiny as0 . − (Mercury), 0 . − (Earth), and 0 .
15 mas cty − (Mars), while Pitjev & Pitjeva(2013) and Pitjeva & Pitjev (2013) obtained 3 mas cty − (Mercury), 0 .
19 mas cty − (Earth),and 0 .
037 mas cty − (Mars) with the EPM2011 ephemerides. Moreover, while Table 1 ofHajdukovic (2013) predicts a perihelion precession of − ,
360 mas cty − for Saturn, the INPOP10a(Fienga et al. 2011) and EPM2011 (Pitjev & Pitjeva 2013; Pitjeva & Pitjev 2013) ephemeridesyielded uncertainties of 0 .
65 mas cty − and 0 .
47 mas cty − , respectively.
3. Conclusions
Thus, we conclude that the exotic secular rates of change predicted by Hajdukovic (2013) areneatly ruled out by the planetary observations, and not even the most recent ones. 4 –
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