The Influence of Dynamic Solar Oblateness on Tracking Data Analysis from Past and Future Mercury Missions

Abstract

When the BepiColombo spacecraft arrives at Mercury in late 2025, it will be able to measure the orbit of the planet with unprecedented accuracy, allowing for more accurate measurements of the perihelion advance of the planet, as predicted by the Theory of General Relativity (GR). A similar effect is produced by the gravitational oblateness of the Sun through the zonal coefficient J2⊙. The gravitational field of the Sun has been hard to determine despite centuries of observations, causing great uncertainties in experiments on GR. Recent publications in heliophysics suggest that J2⊙ is not a constant, but a dynamic value that varies with solar magnetic activity. The aim of this paper is to analyse what the effect is of suggested higher-order effects of the solar gravitational field on experiments of the perihelion advance of Mercury as predicted by GR. The orbit of Mercury and observations of the MESSENGER and BepiColombo spacecraft are simulated, and parameters corresponding to gravitational theory, as well as the oblateness J2⊙ including a time-variable component are estimated using a least-squares approach. The result of the estimation is that the amplitude of a periodic component can be found with an uncertainty of 3.7×10−11, equal to 0.017% the value of J2⊙. From analysis of published experiments that used MESSENGER tracking data, it can already be deduced that the amplitude of the periodic variation cannot be higher than 5% of the value of J2⊙. It is also found that if a periodic component exists with an amplitude greater than 0.04% the value of J2⊙ and it is not considered, it can lead to errors in the experiments of GR using BepiColombo data to the point that results falsely confirm or contradict the Theory of General Relativity.

Might the 2PN Perihelion Precession of Mercury Become Measurable in the Next Future?

“…The ongoing mission to Mercury BepiColombo [41] aims, among other things, to accurately determine β and γ; according to [42] Table 5, p. 21, an extended mission may reach just the 10 −7 accuracy level in constraining such PPN parameters. The same conclusion is shown also in [43] Table 2, p. 12; see also references therein. However, it should be remarked that most of the scenarios examined in [41,43] envisage an accuracy in constraining β and γ of the order of 10 −6 .…”

“…The same conclusion is shown also in [43] Table 2, p. 12; see also references therein. However, it should be remarked that most of the scenarios examined in [41,43] envisage an accuracy in constraining β and γ of the order of 10 −6 . Be that as it may, perhaps, we may not be so far away from having to include, one day, also the 2PN terms in Solar System's dynamics.…”

Testing theories of gravity with planetary ephemerides

“…This mission will orbit Mercury for more than a year and will provide unprecedented accurate measures of the Mercury-Earth distance, and consequently, will produce stringent new limits on deviations from general relativity. A lot of publications propose to include Bepi-Colombo range simulations in order to provide possible new constraints on classic general relativity tests, such as advance of the Mercury perihelion, PPN parameter estimations, SEP or alternative tests (Milani et al 2002;Ashby et al 2007;De Marchi et al 2016;Imperi et al 2018;De Marchi and Cascioli 2020;van der Zwaard and Dirkx 2022;Fienga et al 2021a. As previously explained, a specific care should be taken on the consistency between the definition of the considered framework (e.g.…”