34 research outputs found
Range, Doppler and astrometric observables computed from Time Transfer Functions: a survey
Determining range, Doppler and astrometric observables is of crucial interest
for modelling and analyzing space observations. We recall how these observables
can be computed when the travel time of a light ray is known as a function of
the positions of the emitter and the receiver for a given instant of reception
(or emission). For a long time, such a function--called a reception (or
emission) time transfer function--has been almost exclusively calculated by
integrating the null geodesic equations describing the light rays. However,
other methods avoiding such an integration have been considerably developped in
the last twelve years. We give a survey of the analytical results obtained with
these new methods up to the third order in the gravitational constant for a
mass monopole. We briefly discuss the case of quasi-conjunctions, where
higher-order enhanced terms must be taken into account for correctly
calculating the effects. We summarize the results obtained at the first order
in when the multipole structure and the motion of an axisymmetric body is
taken into account. We present some applications to on-going or future missions
like Gaia and Juno. We give a short review of the recent works devoted to the
numerical estimates of the time transfer functions and their derivatives.Comment: 6 pages, 2 figures, proceedings of the Conference "Journ\'ees 2014
Syst\`emes de r\'ef\'erence spatio-temporels (Recent developments and
prospects in ground-based and space astrometry)", 22-24 September 2014,
Pulkovo Observatory, Russi
Direction of light propagation to order G^2 in static, spherically symmetric spacetimes: a new derivation
A procedure avoiding any integration of the null geodesic equations is used
to derive the direction of light propagation in a three-parameter family of
static, spherically symmetric spacetimes within the post-post-Minkowskian
approximation. Quasi-Cartesian isotropic coordinates adapted to the symmetries
of spacetime are systematically used. It is found that the expression of the
angle formed by two light rays as measured by a static observer staying at a
given point is remarkably simple in these coordinates. The attention is mainly
focused on the null geodesic paths that we call the "quasi-Minkowskian light
rays". The vector-like functions characterizing the direction of propagation of
such light rays at their points of emission and reception are firstly obtained
in the generic case where these points are both located at a finite distance
from the centre of symmetry. The direction of propagation of the
quasi-Minkowskian light rays emitted at infinity is then straightforwardly
deduced. An intrinsic definition of the gravitational deflection angle relative
to a static observer located at a finite distance is proposed for these rays.
The expression inferred from this definition extends the formula currently used
in VLBI astrometry up to the second order in the gravitational constant G.Comment: 19 pages; revised introduction; added references for introduction;
corrected typos; published in Class. Quantum Gra
Time-Varying Gravitomagnetism
Time-varying gravitomagnetic fields are considered within the linear
post-Newtonian approach to general relativity. A simple model is developed in
which the gravitomagnetic field of a localized mass-energy current varies
linearly with time. The implications of this temporal variation of the source
for the precession of test gyroscopes and the motion of null rays are briefly
discussed.Comment: 10 pages; v2: slightly expanded version accepted for publication in
Class. Quantum Gra
Accurate light-time correction due to a gravitating mass
This work arose as an aftermath of Cassini's 2002 experiment \cite{bblipt03},
in which the PPN parameter was measured with an accuracy
and found consistent with the prediction
of general relativity. The Orbit Determination Program (ODP) of
NASA's Jet Propulsion Laboratory, which was used in the data analysis, is based
on an expression for the gravitational delay which differs from the standard
formula; this difference is of second order in powers of -- the sun's
gravitational radius -- but in Cassini's case it was much larger than the
expected order of magnitude , where is the ray's closest approach
distance. Since the ODP does not account for any other second-order terms, it
is necessary, also in view of future more accurate experiments, to
systematically evaluate higher order corrections and to determine which terms
are significant. Light propagation in a static spacetime is equivalent to a
problem in ordinary geometrical optics; Fermat's action functional at its
minimum is just the light-time between the two end points A and B. A new and
powerful formulation is thus obtained. Asymptotic power series are necessary to
provide a safe and automatic way of selecting which terms to keep at each
order. Higher order approximations to the delay and the deflection are
obtained. We also show that in a close superior conjunction, when is much
smaller than the distances of A and B from the Sun, of order , say, the
second-order correction has an \emph{enhanced} part of order , which
corresponds just to the second-order terms introduced in the ODP. Gravitational
deflection of the image of a far away source, observed from a finite distance
from the mass, is obtained to .Comment: 4 figure
Radioscience simulations in General Relativity and in alternative theories of gravity
In this communication, we focus on the possibility to test GR with
radioscience experiments. We present a new software that in a first step
simulates the Range/Doppler signals directly from the space time metric (thus
in GR and in alternative theories of gravity). In a second step, a
least-squares fit of the involved parameters is performed in GR. This software
allows one to get the order of magnitude and the signature of the modifications
induced by an alternative theory of gravity on radioscience signals. As
examples, we present some simulations for the Cassini mission in
Post-Einsteinian gravity and with the MOND External Field Effect.Comment: 4 pages; Proceedings of "Les Rencontres de Moriond 2011 - Gravitation
session
A universal tool for determining the time delay and the frequency shift of light: Synge's world function
In almost all of the studies devoted to the time delay and the frequency
shift of light, the calculations are based on the integration of the null
geodesic equations. However, the above-mentioned effects can be calculated
without integrating the geodesic equations if one is able to determine the
bifunction giving half the squared geodesic distance between
two points and (this bifunction may be called Synge's world
function). In this lecture, is determined up to the order
within the framework of the PPN formalism. The case of a stationary
gravitational field generated by an isolated, slowly rotating axisymmetric body
is studied in detail. The calculation of the time delay and the frequency shift
is carried out up to the order . Explicit formulae are obtained for the
contributions of the mass, of the quadrupole moment and of the internal angular
momentum when the only post-Newtonian parameters different from zero are
and . It is shown that the frequency shift induced by the mass
quadrupole moment of the Earth at the order will amount to
in spatial experiments like the ESA's Atomic Clock Ensemble in Space mission.
Other contributions are briefly discussed.Comment: 18 pages, To appear in: "Lasers, Clocks and Drag-Free control:
Exploration of Relativistic Gravity in Space", Springer Series on
Astrophysics and Space Science Library, vol 349, p 15
Application of Time Transfer Function to McVittie Spacetime: Gravitational Time Delay and Secular Increase in Astronomical Unit
We attempt to calculate the gravitational time delay in a time-dependent
gravitational field, especially in McVittie spacetime, which can be considered
as the spacetime around a gravitating body such as the Sun, embedded in the
FLRW (Friedmann-Lema\^itre-Robertson-Walker) cosmological background metric. To
this end, we adopt the time transfer function method proposed by Le
Poncin-Lafitte {\it et al.} (Class. Quant. Grav. 21:4463, 2004) and Teyssandier
and Le Poncin-Lafitte (Class. Quant. Grav. 25:145020, 2008), which is
originally related to Synge's world function and enables to
circumvent the integration of the null geodesic equation. We re-examine the
global cosmological effect on light propagation in the solar system. The
round-trip time of a light ray/signal is given by the functions of not only the
spacial coordinates but also the emission time or reception time of light
ray/signal, which characterize the time-dependency of solutions. We also apply
the obtained results to the secular increase in the astronomical unit, reported
by Krasinsky and Brumberg (Celest. Mech. Dyn. Astron. 90:267, 2004), and we
show that the leading order terms of the time-dependent component due to
cosmological expansion is 9 orders of magnitude smaller than the observed value
of , i.e., ~[m/century]. Therefore, it is not possible
to explain the secular increase in the astronomical unit in terms of
cosmological expansion.Comment: 13 pages, 2 figures, accepted for publication in General Relativity
and Gravitatio
Gaia Data Release 2 Mapping the Milky Way disc kinematics
Context. The second Gaia data release (Gaia DR2) contains high-precision positions, parallaxes, and proper motions for 1.3 billion sources as well as line-of-sight velocities for 7.2 million stars brighter than G(RVS) = 12 mag. Both samples provide a full sky coverage. Aims. To illustrate the potential of Gaia DR2, we provide a first look at the kinematics of the Milky Way disc, within a radius of several kiloparsecs around the Sun. Methods. We benefit for the first time from a sample of 6.4 million F-G-K stars with full 6D phase-space coordinates, precise parallaxes (sigma((omega) over bar)/(omega) over bar Results. Gaia DR2 allows us to draw 3D maps of the Galactocentric median velocities and velocity dispersions with unprecedented accuracy, precision, and spatial resolution. The maps show the complexity and richness of the velocity field of the galactic disc. We observe streaming motions in all the components of the velocities as well as patterns in the velocity dispersions. For example, we confirm the previously reported negative and positive galactocentric radial velocity gradients in the inner and outer disc, respectively. Here, we see them as part of a non-axisymmetric kinematic oscillation, and we map its azimuthal and vertical behaviour. We also witness a new global arrangement of stars in the velocity plane of the solar neighbourhood and in distant regions in which stars are organised in thin substructures with the shape of circular arches that are oriented approximately along the horizontal direction in the U - V plane. Moreover, in distant regions, we see variations in the velocity substructures more clearly than ever before, in particular, variations in the velocity of the Hercules stream. Conclusions. Gaia DR2 provides the largest existing full 6D phase-space coordinates catalogue. It also vastly increases the number of available distances and transverse velocities with respect to Gaia DR1. Gaia DR2 offers a great wealth of information on the Milky Way and reveals clear non-axisymmetric kinematic signatures within the Galactic disc, for instance. It is now up to the astronomical community to explore its full potential.Peer reviewe
Gaia Data Release 2 Observations of solar system objects
CONTEXT: The Gaia spacecraft of the European Space Agency (ESA) has been securing observations of solar system objects (SSOs)
since the beginning of its operations. Data Release 2 (DR2) contains the observations of a selected sample of 14,099 SSOs. These
asteroids have been already identified and have been numbered by the Minor Planet Center repository. Positions are provided for each
Gaia observation at CCD level. As additional information, complementary to astrometry, the apparent brightness of SSOs in the unfiltered
G band is also provided for selected observations.
AIMS: We explain the processing of SSO data, and describe the criteria we used to select the sample published in Gaia DR2. We then
explore the data set to assess its quality.
METHODS: To exploit the main data product for the solar system in Gaia DR2, which is the epoch astrometry of asteroids, it is necessary
to take into account the unusual properties of the uncertainty, as the position information is nearly one-dimensional. When this aspect
is handled appropriately, an orbit fit can be obtained with post-fit residuals that are overall consistent with the a-priori error model that
was used to define individual values of the astrometric uncertainty. The role of both random and systematic errors is described. The
distribution of residuals allowed us to identify possible contaminants in the data set (such as stars). Photometry in the G band was
compared to computed values from reference asteroid shapes and to the flux registered at the corresponding epochs by the red and blue
photometers (RP and BP).
RESULTS: The overall astrometric performance is close to the expectations, with an optimal range of brightness G ∼ 12 − 17. In this
range, the typical transit-level accuracy is well below 1 mas. For fainter asteroids, the growing photon noise deteriorates the performance.
Asteroids brighter than G ∼ 12 are affected by a lower performance of the processing of their signals. The dramatic improvement
brought by Gaia DR2 astrometry of SSOs is demonstrated by comparisons to the archive data and by preliminary tests on the detection
of subtle non-gravitational effects