Precession of Mercury’s Perihelion from Ranging to the MESSENGER Spacecraft

Abstract

The perihelion of Mercury's orbit precesses due to perturbations from other solar system bodies, solar quadrupole moment (J 2 ), and relativistic gravitational effects that are proportional to linear combinations of the parametrized post-Newtonian parameters β and γ. The orbits and masses of the solar system bodies are quite well known, and thus the uncertainty in recovering the precession rate of Mercury's perihelion is dominated by the uncertainties in the parameters J 2 , β, and γ. Separating the effects due to these parameters is challenging since the secular precession rate has a linear dependence on each parameter. Here we use an analysis of radiometric range measurements to the MESSENGER (MErcury Surface, Space ENvironment, GEochemistry, and Ranging) spacecraft in orbit about Mercury to estimate the precession of Mercury's perihelion. We show that the MESSENGER ranging data allow us to measure not only the secular precession rate of Mercury's perihelion with substantially improved accuracy, but also the periodic perturbation in the argument of perihelion sensitive to β and γ. When combined with the γ estimate from a Shapiro delay experiment from the Cassini mission, we can decouple the effects due to β and J 2 and estimate both parameters, yielding ( ) ( ) b -= -´-1 2.7 3.9 10 5 and J 2 =(2.25±0.09)×10 −7. We also estimate the total precession rate of Mercury's perihelion as 575.3100±0.0015″/century and provide estimated contributions and uncertainties due to various perturbing effects.

Are we close to putting the anomalous perihelion precessions from Verlinde’s emergent gravity to the test?

“…due to the Sun's quadrupole mass moment J 2 , which was recently determined by Park et al [29] to 4% as…”

“…On the other hand, our analysis shows that the perspectives of effectively putting the Verlinde-type emergent gravity to the test in the Solar System seems promising, especially if Mars is considered in view of the steady improvements in its orbit determination allowed by the accurate tracking of the remarkable number of present and future landers and orbiters [17]. Furthermore, also the orbit of Mercury should be improved in the next years thanks to the steady analysis of the entire data record of the MESSENGER spacecraft, of which the work by Park et al [29] is a first step, 4 and the future BepiColombo mission [3,32], scheduled to be launched in 2018.…”

“…Another potential source of major systematic uncertainty is represented by the N-body perturbations due to the other planets, especially Jupiter and Saturn. We will, now, demonstrate that, luckily, they can be modeled with sufficiently 2 Park et al [29] use the symbol for the in-plane, unbroken angle ω + cos I . high accuracy.…”

“…Recently, Park et al [29] considered the in-plane precession 2ω +˙ cos I of the pericenter of Mercury by constraining it to the 1.5 mas cty −1 level. It is still 2.1 times larger than the Verlinde-type in-plane precession which coincides with Eq.…”

“…All the figures quoted here for the precessions, both theoretical and experimental, are in milliarcseconds per century (mas cty −1 ). Recently, Park et al [29] constrained the secular precession of the orbital element ω+ cos I of Mercury to an accuracy of 1.5 mas cty −1 . About Saturn, Hees et al [13], in looking for possible anomalous effects on it due to a certain version of MOND, managed to constrain its perihelion precession to the 0.43 mas cty −1 level.…”