Gravitomagnetism and the Earth–Mercury range

Abstract

We numerically work out the impact of the general relativistic Lense-Thirring effect on the Earth-Mercury range | ρ| caused by the gravitomagnetic field of the rotating Sun. The peak-to peak nominal amplitude of the resulting time-varying signal amounts to 1.75 × 10 1 m over a temporal interval ∆t = 2 yr. Future interplanetary laser ranging facilities should reach a cm-level in ranging to Mercury over comparable timescales; for example, the BepiColombo mission, to be launched in 2014, should reach a 4.5 − 10 cm level over 1 − 8 yr. We looked also at other Newtonian (solar quadrupole mass moment, ring of the minor asteroids, Ceres, Pallas, Vesta, Trans-Neptunian Objects) and post-Newtonian (gravitoelectric Schwarzschild solar field) dynamical effects on the Earth-Mercury range. They act as sources of systematic errors for the Lense-Thirring signal which, in turn, if not properly modeled, may bias the recovery of some key parameters of such other dynamical features of motion. Their nominal peak-to-peak amplitudes are as large as 4 × 10 5 m (Schwarzschild), 3 × 10 2 m (Sun's quadrupole), 8 × 10 1 m (Ceres, Pallas, Vesta), 4 m (ring of minor asteroids), 8 × 10 −1 m (Trans-Neptunian Objects). Their temporal patterns are different with respect to that of the gravitomagnetic signal.

History of the attempts to measure orbital frame-dragging with artificial satellites

“…Professor Doug Currie from the University of Maryland (USA), who had long been involved with the design of retroreflec-tors for satellite and lunar laser ranging, recommended to have this relativity-testing Lageos follow-on be called WEBER-SAT in honor of Dr. Joseph Weber who built a pioneering gravitational wave detector at the University of Maryland about 1961. The tests with the Mars Global Surveyor (MGS) spacecraft and Mars [18][19][20][21], and the Sun-planets scenario [22][23][24][25][26][27] will be left aside as well; a recent, comprehensive overview can be found in [28]. Another general relativistic orbital effect caused by the rotation of a central body is the so-called gravitomagnetic clock effect [29][30][31][32][33][34].…”

A Test of Gravitational Theories Including Torsion with the BepiColombo Radio Science Experiment

“…• the "relativity" parameters, which are the PPN parameters γ, β, α 1 , α 2 and the Nordtvedt parameter η, which characterize the expansion of the spacetime metric in the limit of slow motion and weak field (see, e.g., [8,18]) 1 , together with some related parameters, such as the oblateness of the Sun J 2 , the solar gravitational mass µ = GM (where G is the gravitational constant and M the mass of the Sun), possibly its time derivative ζ = 1/µ dµ /dt, and the solar angular momentum GS which appears in the Lense-Thirring effect on the orbit of Mercury (see, e.g., [19][20][21] for a general discussion; moreover, the topic has been addressed by the authors in the case of MORE in [22]).…”

Local tests of gravitation with Gaia observations of Solar System Objects

“…Such a direct measurement would provide a new way to estimate the Sun angular momentum, an important quantity to assess interior models of the Sun (Pijpers 2006). Possibilities to measure the Sun Lense-Thirring effect has been mentioned in (Iorio et al 2011;Iorio 2011Iorio , 2012b. Nevertheless, as mentioned in (Folkner et al 2014), planetary ephemerides analysis does not allow to disentangle the Sun Lense-Thirring from the Sun J 2 (even with the latest Messenger data).…”