Sentinel-6A precise orbit determination using a combined GPS/Galileo receiver

The Sentinel-6 (or Jason-CS) altimetry mission provides a long-term extension of the Topex and Jason-1/2/3 missions for ocean surface topography monitoring. Analysis of altimeter data relies on highly-accurate knowledge of the orbital position and requires radial RMS orbit errors of less than 1.5 cm. For precise orbit determination (POD), the Sentinel-6A spacecraft is equipped with a dual-constellation GNSS receiver. We present the results of Sentinel-6A POD solutions for the first 6 months since launch and demonstrate a 1-cm consistency of ambiguity-fixed GPS-only and Galileo-only solutions with the dual-constellation product. A similar performance (1.3 cm 3D RMS) is achieved in the comparison of kinematic and reduced-dynamic orbits. While Galileo measurements exhibit 30–50% smaller RMS errors than those of GPS, the POD benefits most from the availability of an increased number of satellites in the combined dual-frequency solution. Considering obvious uncertainties in the pre-mission calibration of the GNSS receiver antenna, an independent inflight calibration of the phase centers for GPS and Galileo signal frequencies is required. As such, Galileo observations cannot provide independent scale information and the estimated orbital height is ultimately driven by the employed forces models and knowledge of the center-of-mass location within the spacecraft. Using satellite laser ranging (SLR) from selected high-performance stations, a better than 1 cm RMS consistency of SLR normal points with the GNSS-based orbits is obtained, which further improves to 6 mm RMS when adjusting site-specific corrections to station positions and ranging biases. For the radial orbit component, a bias of less than 1 mm is found from the SLR analysis relative to the mean height of 13 high-performance SLR stations. Overall, the reduced-dynamic orbit determination based on GPS and Galileo tracking is considered to readily meet the altimetry-related Sentinel-6 mission needs for RMS height errors of less than 1.5 cm.

Uncovering the orbit of the hercules dwarf galaxy

ABSTRACT We present new chemo-kinematics of the Hercules dwarf galaxy based on Keck II-DEIMOS spectroscopy. Our 21 confirmed members, including 9 newly confirmed members, have a systemic velocity of vHerc = 46.4 ± 1.3 km s−1 and a velocity dispersion $\sigma _{v,\mathrm{Herc}}=4.4^{+1.4}_{-1.2}$ km s−1, consistent with previous studies. From the strength of the Ca ii triplet, we obtain a metallicity of [Fe/H] = −2.48 ± 0.19 dex and dispersion of $\sigma _{\rm {[Fe/H]}}= 0.63^{+0.18}_{-0.13}$ dex. This result is within 1σ of previous measurements, and makes Hercules a particularly metal-poor galaxy, placing it slightly below the standard mass–metallicity relation. Previous photometric and spectroscopic evidence suggests that Hercules is tidally disrupting and may be on a highly radial orbit. From our identified members, we measure no significant velocity gradient. By cross-matching with the second Gaia data release, we determine an uncertainty-weighted mean proper motion of $\mu _{\alpha }^*=\mu _{\alpha }\cos (\delta)=-0.153\pm {0.074}$ mas yr−1, μδ = −0.397 ± 0.063 mas yr−1. This proper motion is slightly misaligned with the elongation of Hercules, in contrast to models which suggest that any tidal debris should be well aligned with the orbital path. Future observations may resolve this tension.

The Three Hundred project: shapes and radial alignment of satellite, infalling, and backsplash galaxies

ABSTRACT Using 324 numerically modelled galaxy clusters, we investigate the radial and galaxy–halo alignment of dark matter subhaloes and satellite galaxies orbiting within and around them. We find that radial alignment depends on distance to the centre of the galaxy cluster but appears independent of the dynamical state of the central host cluster. Furthermore, we cannot find a relation between radial alignment of the halo or galaxy shape with its own mass. We report that backsplash galaxies, i.e. objects that have already passed through the cluster radius but are now located in the outskirts, show a stronger radial alignment than infalling objects. We further find that there exists a population of well radially aligned objects passing very close to the central cluster’s centre that were found to be on highly radial orbit.

Discreteness effects, N-body chaos and the onset of radial-orbit instability

ABSTRACT We study the stability of a family of spherical equilibrium models of self-gravitating systems, the so-called γ models with Osipkov–Merritt velocity anisotropy, by means of N-body simulations. In particular, we analyse the effect of self-consistent N-body chaos on the onset of radial-orbit instability. We find that degree of chaoticity of the system associated with its largest Lyapunov exponent Λmax has no appreciable relation with the stability of the model for fixed density profile and different values of radial velocity anisotropy. However, by studying the distribution of the Lyapunov exponents λm of the individual particles in the single-particle phase space, we find that more anisotropic systems have a larger fraction of orbits with larger λm.

A new class of galaxy models with a central BH – I. The spherical case

ABSTRACTThe dynamical properties of spherically symmetric galaxy models, where a Jaffe stellar density profile is embedded in a total mass density decreasing as r−3 at large radii, are presented. The orbital structure of the stellar component is described by the Osipkov–Merritt anisotropy; the dark matter halo is isotropic, and a black hole is added at the centre of the galaxy. First, the conditions for a nowhere negative and monotonically decreasing dark matter halo density profile are derived; this profile can be made asymptotically coincident with an NFW profile at the centre and large radii. Then, the minimum value of the anisotropy radius for phase-space consistency is derived as a function of the galaxy parameters. The Jeans equations for the stellar component are solved analytically; the projected velocity dispersion at the centre and large radii is also obtained, for generic values of the anisotropy radius. Finally, analytical expressions for the terms entering the Virial Theorem are derived, and the fiducial anisotropy limit required to prevent the onset of Radial Orbit Instability is determined as a function of the galaxy parameters. The presented models, built following an approach already adopted in our previous works, can be a useful starting point for a more advanced modelling of the dynamics of elliptical galaxies, and can be easily implemented in numerical simulations requiring a realistic dynamical model of a galaxy.

The retrograde orbit of the globular cluster FSR1758 revealed with Gaia DR2

ABSTRACT We report the first radial velocity measurements of the recently identified globular cluster FSR1758. From the two member stars with radial velocities from the Gaia Radial Velocity Spectrograph reported in Gaia DR2, we find FSR1758 has a radial velocity of 227 ± 1$\, \textrm{km}\, \textrm{s}^{-1}$. We also find potential extra-tidal star lost from the cluster in the surrounding 1 deg. Combined with Gaia proper motions and photometric distance estimates, this shows that FSR1758 is on a relatively retrograde, radial orbit with a pericentre of $3.8_{-0.9}^{+0.9}$ kpc, an apocentre of $16_{-5}^{+8}$ kpc, and eccentricity of $0.62_{-0.04}^{+0.05}$. Although it is currently at a Galactocentric distance of $3.8_{-0.9}^{+0.9}$ kpc – at the edge of the bulge – it is an intruder from the halo. We investigate whether a reported ‘halo’ of stars around FSR1758 is related to the cluster, and find that most of these stars are likely foreground dwarf stars. We conclude that FSR1758 is not a dwarf galaxy, but rather a globular cluster.

The shape of the dark matter halo revealed from a hypervelocity star

A recently discovered young, high-velocity giant star J01020100-7122208 is a good candidate of hypervelocity star ejected from the Galactic center, although it has a bound orbit. If we assume that this star was ejected from the Galactic center, it can be used to constrain the Galactic potential, because the deviation of its orbit from a purely radial orbit informs us of the torque that this star has received. Based on this assumption, we estimate the flattening of the Galactic dark matter halo by using the Gaia DR2 data and the circular velocity data. Our Bayesian analysis shows that the orbit of J01020100-7122208 favors a prolate halo within ~ 10 kpc from the Galactic center. The posterior distribution of the density flattening q shows a broad distribution at q ≳ 1 and peaks at q ≃ 1.5. Also, 98.5% of the posterior distribution is located at q > 1, highly disfavoring an oblate halo.

Linear stability of stellar rotating spheres

Recent observations of globular clusters encourage to revise some aspects of the traditional paradigm, in which they were considered to be isotropic in velocity space and non-rotating. However, the theory of collisionless spheroids with some kinematic richness has seldom been studied. We present here a further step in this direction, owing to new results regarding the linear stability of rotating Plummer spheres, with varying anisotropy in velocity space and total amount of angular momentum. We extend the well-known radial orbit instability to rotating systems, and discover a new regime of instability in fast rotating, tangentially anisotropic systems.

A linear stability study of stellar rotating spheres

Recent observations of globular clusters imposed major revisions to the previous paradigm, in which they were considered to be isotropic in velocity space and non-rotating. However, the theory of collisionless spheroids with some kinematic richness has seldom been studied. We present here a first step in this direction, owing to new results regarding the linear stability of rotating Plummer spheres, with varying anisotropy in velocity space and total amount of angular momentum. We extend the well-known radial orbit instability to rotating systems, and discover a new regime of instability in fast rotating, tangentially anisotropic systems.

Analysis of Precise Orbit Predictions for a Hy-2A Satellite with Three Atmospheric Density Models Based on Dynamic Method

HY-2A (Haiyang 2A) is the first altimetry satellite in China, and it was designed to be in a repeated ground track orbit to achieve the mission targets. Maneuvers are necessary to keep the satellite on the designed orbit according to the dynamic precise orbital prediction. Atmospheric density models are essential for predicting the low Earth orbit (LEO) satellites, such as HY-2A. Nevertheless, it is a complex process to determine the optimal atmospheric density model for orbit prediction. In this paper, short-term and long-term orbit predictions based on the dynamic method using three different atmospheric density models are tested. Detailed comparisons and evaluation of the accuracy of the predicted results are performed. Furthermore, to assess the results for the ground tracking of the satellite, the interpolation method especially for a spherical surface is introduced. The results show that among the three models, the Jacchia 1971 model is in the closest agreement with Multi-Mission Ground Segment for Altimetry precise positioning and Orbitography (SSALTO) precise orbits. The root-mean-squares (RMSs) of radial orbit differences between the predicted and precise orbits are 0.016 m, 0.091 m, 0.176 m, 0.573 m, and 1.421 m for predicted 1-h, 12-h, 1-day, 3-day, and 7-day arcs, respectively.