Constraints on the location of a putative distant massive body in the Solar System from recent planetary data

Abstract

We analytically work out the long-term variations caused on the motion of a planet orbiting a star by a very distant, pointlike massive object X. Apart from the semi-major axis a, all the other Keplerian osculating orbital elements experience long-term variations which are complicated functions of the orbital configurations of both the planet itself and of X. We infer constraints on the minimum distance d X at which X may exist by comparing our prediction of the long-term variation of the longitude of the perihelion to the latest empirical determinations of the corrections ˙ to the standard Newtonian/Einsteinian secular precessions of several solar system planets recently estimated by independent teams of astronomers. We obtain the following approximate lower bounds on d X for the assumed masses of X quoted in brackets: 150-200 au (Mars), 250-450 au (0.7 m ⊕ ), 3500-4500 au (4 m Jup ).

Planet X revamped after the discovery of the Sedna-like object 2012 VP113?

“…Model-independent, dynamical constraints on d X were inferred by Iorio (2012) for different values of m X from the upper bounds ∆̟ on the anomalous secular precessions of the longitude of perihelion ̟ of some known planets of the Solar System computed with earlier versions of the INPOP ephemerides (Fienga et al 2010). Iorio (2012) (Iorio 2012), it is straightforward to refine such estimates by using the latest results on ∆̟ obtained with more recent planetary ephemerides (Fienga et al 2011;Pitjeva & Pitjev 2013).…”

“…Iorio (2012) (Iorio 2012), it is straightforward to refine such estimates by using the latest results on ∆̟ obtained with more recent planetary ephemerides (Fienga et al 2011;Pitjeva & Pitjev 2013). From Figure 1 of Iorio (2012), it can be noticed that, for a given value of m X and by keeping the ecliptic latitude β X fixed to some low values, the combined use of the perihelia of Earth, Mars and Saturn allows to constrain effectively d X for practically all values of the ecliptic longitude λ X . In the case m X = 0.7m ⊕ (Iorio 2012), the values by Pitjeva & Pitjev (2013) for the perihelion precessions of Mars and Saturn provide us with overall tighter bounds of the order of d X 350 − 400 AU.…”

“…From Figure 1 of Iorio (2012), it can be noticed that, for a given value of m X and by keeping the ecliptic latitude β X fixed to some low values, the combined use of the perihelia of Earth, Mars and Saturn allows to constrain effectively d X for practically all values of the ecliptic longitude λ X . In the case m X = 0.7m ⊕ (Iorio 2012), the values by Pitjeva & Pitjev (2013) for the perihelion precessions of Mars and Saturn provide us with overall tighter bounds of the order of d X 350 − 400 AU. In turn, such revised bounds can be easily extended to the scenario proposed by Trujillo & Sheppard (2014); it turns out that d X 496 − 570 AU for m X = 2m ⊕ and d X 970 − 1111 AU for m X = 15m ⊕ , respectively.…”

“…Since the early work of Lowell (1915), the hypothesis that the remote peripheries of the Solar System may host a still unseen major body is regularly re-emerged over the years (see, e.g., (Raup & Sepkoski 1984;Whitmire & Jackson 1984;Gomes et al 2006;Lykawka & Mukai 2008;Iorio 2009;Melott & Bambach 2010;Matese & Whitmire 2011;Fernández 2011;Lykawka 2012;Gomes & Soares 2012;Iorio 2012Iorio , 2013Trujillo & Sheppard 2014)), supported by a number of more or less sound indirect observational motivations ranging from alleged periodicities detected in paleontological fossil records on the Earth (Melott & Bambach 2013) to certain morphological features of the Edgeworth-Kuiper belt (Lykawka 2012). Such a hypothetical trans-Plutonian object has been variously dubbed so far as Planet X (Lowell 1915), Nemesis (Raup & Sepkoski 1984), Tyche (Matese & Whitmire 2011), Thelisto (Iorio 2013); in the following, we will refer to it as PX.…”

Conservative evaluation of the uncertainty in the LAGEOS-LAGEOS II Lense-Thirring test

“…In Ref. [28] a ≈ 20% test was reported by using the 5 EGM96 [29] Earth gravity model; subsequent analyses showed that such an evaluation of the total error budget was overly optimistic in view of the likely unreliable computation of the total bias due to the even zonals [30][31][32]. An analogous, huge underestimation turned out to hold also for the effect of non-gravitational perturbations [33] like direct solar radiation pressure, the Earth's albedo, various subtle thermal effects depending on the the physical properties of the satellites' surfaces and their rotational state [31,[34][35][36][37][38][39][40], which the perigees of LAGEOS-like satellites are particularly sensitive to.…”