Gravitomagnetism and the Earth

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Gravitomagnetism and the Earth–Mercury range

Iorio, Lorenzo

Abstract We numerically work out the impact of the general relativistic Lense–Thirring effect on the Earth–Mercury range $| \vec{ρ} |$ caused by the gravitomagnetic field of the rotating Sun. The peak-to-peak nominal amplitude of the resulting time-varying signal amounts to 1.75×10¹ m over a temporal interval Δt =2yr. 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 4.5–10cm level over 1−8yr. 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 4×10⁵ m (Schwarzschild), 3×10² m (Sun’s quadrupole), 8×10¹ m (Ceres, Pallas, Vesta), 4m (ring of minor asteroids), 8×10⁻¹ m (Trans-Neptunian Objects). Their temporal patterns are different with respect to that of the gravitomagnetic signal.