MG15 - Talk detail

Back to previous page

 Participant

Institution

Session

Accepted

Yes

Order

Time

Talk

Title

Abstract

We analytically calculate the time series for the perturbations induced by a general disturbing acceleration on the mutual range and range-rate of two test particles orbiting the same spinning body. We apply it to the general relativistic Lense-Thirring effect, due to the primary's spin, and the classical perturbation arising from its quadrupole mass moment for arbitrary orbital geometries and orientation of the source's symmetry axis. The Earth-Mercury range and range-rate are nominally affected by the Sun's gravitomagnetic field to the 10 m, 10^-3 cm s^-1 level, respectively, during the extended phase (2026-2028) of the forthcoming BepiColombo mission to Mercury whose expected tracking accuracy is of the order of 0.1 m, 2 X 10^-4 cm s^-1. The competing signatures due to the solar quadrupole, if modelled at the $10^-9 level of the latest planetary ephemerides INPOP17a, are nearly 10 times smaller than the relativistic gravitomagnetic effects.

Pdf file

Session

Accepted

Yes

Order

Time

Talk

Title

Abstract

One of the directly measured quantities used in monitoring the orbits of many of the S stars revolving around the Supermassive Black Hole in the Galactic Center is their radial velocity obtained with near-infrared spectroscopy. Here, we devise a general approach to calculate both the instantaneous variations and the net shifts per revolution induced on such an observable by some post-Keplerian accelerations. In particular, we look at the general relativistic Schwarzschild (gravitoelectric) and Lense-Thirring (gravitomagnetic frame-dragging) effects, and the mass quadrupole. It turns out that we may be on the verge of measuring the Schwarzschild-type 1pN static component of the SMBH's field with the star S2 for which RV measurements accurate to about $30-50 km s^-1 dating back to t_0 = 2003.271 are currently available, and whose orbital period amounts to P_b = 16 yr. Indeed, while its expected general relativistic RV net shift per orbit amounts to just -11.6 km s^-1, it should reach a peak value as large as 551 km s^-1 at t_max = 2018.35. Current uncertainties in the S2 and SMBH's estimated parameters yield a variation range from 505 km s^-1 (2018.79) to 575 km s^-1 (2018.45). The periastron shift of S2 over the same time span will not be larger than 0.2 deg, while the current accuracy in estimating such an orbital element for this star is of the order of 0.6 deg. The frame-dragging and quadrupole-induced RV shifts are far smaller for S2, amounting to, at most, 0.19 km s^-1, 0.0039 km s^-1, respectively.

Pdf file

Session

Accepted

Yes

Order

Time

Talk

Title

Abstract

Recently, the launch of a new cannonball geodetic satellite in 2019 with the VEGA C rocket was announced. It is planned to be injected in an essentially circular path with the same semimajor axis of the LAGEOS satellite, in orbit since 1976, and an inclination of its orbital plane supplementary with respect to that of its existing cousin. According to their proponents, the sum of the precessions of the longitudes of their ascending nodes should allow to test the general relativistic Lense-Thirring effect to a 0.2% accuracy level, with a contribution of the mismodelling in the even zonal harmonics of the geopotential to the total error budget as little as 0.1%. We will critically discuss such an ambitious goal.

Pdf file

Session

Accepted

Yes

Order

Time

Talk

Title

Abstract

Independent tests aiming to constrain the value of the cosmological constant Lambda are usually difficult because of its extreme smallness (Lambda < 1 X 10^-52 m^-2). Bounds on it from Solar System orbital motions determined with spacecraft tracking are currently at the < 10^-43-10^-44 m^-2 level, but they may turn out to be somewhat optimistic since Lambda has not yet been explicitly modeled in the planetary data reductions. Accurate (1-10 microseconds) timing of expected pulsars orbiting the Black Hole at the Galactic Center, preferably along highly eccentric and wide orbits, might, at least in principle, improve the planetary constraints by several orders of magnitude. By assuming for such a hypothetical pulsar the orbit of, say, the very far star S85, characterized by an eccentricity as large as e = 0.78 and an orbital period as long as P_b=3580 +/- 2550 yr, the cosmological constant would induce an instantaneous timing orbital shift as large as just 1-10 microseconds for some given values of its eccentric anomaly at different epochs. By looking at the average time shift per orbit of closer pulsars, a S2-like orbital configuration with e=0.8839, P_b=16 yr would allow to obtain an upper bound as little as |Lambda|< 9 x 10^-47 m^-2. Our results can be easily extended to modified models of gravity using Lambda-type parameters.

Pdf file

Back to previous page