Analyzing shell structure from Babylonian and modern times

We investigate ``shell structure'' from Babylonian times: periodicities and beats in computer-simulated lunar data corresponding to those observed by Babylonian scribes some 2500 years ago. We discuss the mathematical similarity between the Babylonians' recently reconstructed method of determining one of the periods of the moon with modern Fourier analysis and the interpretation of shell structure in finite fermion systems (nuclei, metal clusters, quantum dots) in terms of classical closed or periodic orbits.Comment: LaTeX2e, 13pp, 8 figs; contribution to 10th Nuclear Physics Workshop "Marie and Pierre Curie", 24 - 28 Sept. 2003, Kazimierz Dolny (Poland); final version accepted for J. Mod. Phys.

Gamma-ray halo around 3C 279: looking through the Sun on the 8th of October

We discuss how the solar occultations of bright sources of energetic gamma rays can be used to extract non-trivial physical and astrophysical information, including the angular size of the image when it is significantly smaller than the experiment's angular resolution. We analyze the EGRET data and discuss prospects for other instruments. The Fermi Gamma Ray Space Telescope will be able to constrain the size of a possible halo around 3C~279 from observations it makes on the 8th of October each year.Comment: 6 pages, 4 eps figures, mn2e.cls style; v.2: numerous but minor changes to match the published versio

Reconsidering the galactic coordinate system

Initially defined by the IAU in 1958, the galactic coordinate system was thereafter in 1984 transformed from the B1950.0 FK4-based system to the J2000.0 FK5-based system. In 1994, the IAU recommended that the dynamical reference system FK5 be replaced by the ICRS, which is a kinematical non-rotating system defined by a set of remote radio sources. However the definition of the galactic coordinate system was not updated. We consider that the present galactic coordinates may be problematic due to the unrigorous transformation method from the FK4 to the FK5, and due to the non-inertiality of the FK5 system with respect to the ICRS. This has led to some confusions in applications of the galactic coordinates. We tried to find the transformation matrix in the framework of the ICRS after carefully investigating the definition of the galactic coordinate system and transformation procedures, however we could not find a satisfactory galactic coordinate system that is connected steadily to the ICRS. To avoid unnecessary misunderstandings, we suggest to re-consider the definition of the galactic coordinate system which should be directly connected with the ICRS for high precise observation at micro-arcsecond level.Comment: 10 pages, 3 figures, accepted for publication in A&

Prospects in the orbital and rotational dynamics of the Moon with the advent of sub-centimeter lunar laser ranging

Lunar Laser Ranging (LLR) measurements are crucial for advanced exploration of the laws of fundamental gravitational physics and geophysics. Current LLR technology allows us to measure distances to the Moon with a precision approaching 1 millimeter. As NASA pursues the vision of taking humans back to the Moon, new, more precise laser ranging applications will be demanded, including continuous tracking from more sites on Earth, placing new CCR arrays on the Moon, and possibly installing other devices such as transponders, etc. Successful achievement of this goal strongly demands further significant improvement of the theoretical model of the orbital and rotational dynamics of the Earth-Moon system. This model should inevitably be based on the theory of general relativity, fully incorporate the relevant geophysical processes, lunar librations, tides, and should rely upon the most recent standards and recommendations of the IAU for data analysis. This paper discusses methods and problems in developing such a mathematical model. The model will take into account all the classical and relativistic effects in the orbital and rotational motion of the Moon and Earth at the sub-centimeter level. The new model will allow us to navigate a spacecraft precisely to a location on the Moon. It will also greatly improve our understanding of the structure of the lunar interior and the nature of the physical interaction at the core-mantle interface layer. The new theory and upcoming millimeter LLR will give us the means to perform one of the most precise fundamental tests of general relativity in the solar system.Comment: 26 pages, submitted to Proc. of ASTROCON-IV conference (Princeton Univ., NJ, 2007

Astrometric Control of the Inertiality of the Hipparcos Catalog

Based on the most complete list of the results of an individual comparison of the proper motions for stars of various programs common to the Hipparcos catalog, each of which is an independent realization of the inertial reference frame with regard to stellar proper motions, we redetermined the vector $\omega$ of residual rotation of the ICRS system relative to the extragalactic reference frame. The equatorial components of this vector were found to be the following: $\omega_x = +0.04\pm 0.15$ mas yr$^{-1}$, $\omega_y = +0.18\pm 0.12$ mas yr$^{-1}$, and $\omega_z = -0.35\pm 0.09$ mas yr$^{-1}$.Comment: 8 pages, 1 figur

Advancing Tests of Relativistic Gravity via Laser Ranging to Phobos

Phobos Laser Ranging (PLR) is a concept for a space mission designed to advance tests of relativistic gravity in the solar system. PLR's primary objective is to measure the curvature of space around the Sun, represented by the Eddington parameter $\gamma$, with an accuracy of two parts in $10^7$, thereby improving today's best result by two orders of magnitude. Other mission goals include measurements of the time-rate-of-change of the gravitational constant, $G$ and of the gravitational inverse square law at 1.5 AU distances--with up to two orders-of-magnitude improvement for each. The science parameters will be estimated using laser ranging measurements of the distance between an Earth station and an active laser transponder on Phobos capable of reaching mm-level range resolution. A transponder on Phobos sending 0.25 mJ, 10 ps pulses at 1 kHz, and receiving asynchronous 1 kHz pulses from earth via a 12 cm aperture will permit links that even at maximum range will exceed a photon per second. A total measurement precision of 50 ps demands a few hundred photons to average to 1 mm (3.3 ps) range precision. Existing satellite laser ranging (SLR) facilities--with appropriate augmentation--may be able to participate in PLR. Since Phobos' orbital period is about 8 hours, each observatory is guaranteed visibility of the Phobos instrument every Earth day. Given the current technology readiness level, PLR could be started in 2011 for launch in 2016 for 3 years of science operations. We discuss the PLR's science objectives, instrument, and mission design. We also present the details of science simulations performed to support the mission's primary objectives.Comment: 25 pages, 10 figures, 9 table

On the effect of ocean tides and tesseral harmonics on spacecraft flybys of the Earth

[EN] The so-called flyby anomaly has encouraged several authors to analyse in detail the minor perturbative contributions to the trajectory of spacecraft performing a flyby manoeuvre. This anomaly consist of an unexplained increase or decrease of the asymptotic velocity of the spacecraft after a flyby of the Earth in the range of a few mm per second. Some order of magnitude estimations have been performed in recent years to dismiss many possible conventional effects as the source of such an anomaly but no explanation has been found yet. In this paper we perform a study of the perturbation induced by ocean tides in a flybying spacecraft by considering the time dependence of the location of the high tide as the Moon follows its orbit. We show that this effect implies a change of the spacecraft velocity of a few micrometres per second. We also consider the coupling of tesseral harmonics inhomogeneities and the rotation of the Earth and its impact on the spacecraft outgoing velocity. Significant corrections to the observed asymptotic velocities are found in this case but neither their sign nor their magnitude coincide with the anomalies. So, we can also rule this out as a conventional explanation.Acedo Rodríguez, L. (2016). On the effect of ocean tides and tesseral harmonics on spacecraft flybys of the Earth. Monthly Notices of the Royal Astronomical Society. 463(2):2119-2124. doi:10.1093/mnras/stw2135S21192124463

Celestial pole offsets from lunar laser ranging and comparison with VLBI

Context. The analysis of lunar laser ranging (LLR) observations is based on determining the round- trip travel times of light pulses between stations on the Earth and reflectors on the surface of the Moon. Several works have demonstrated that this technique is powerful in various domains including astronomy, geodynamics and gravitational physics. Aims. In the field of geodynamics, LLR contributes to the realization of a dynamical celestial reference frame, in contrast to very long baseline interferometry (VLBI) that determines a kinematical celestial reference frame. In this paper, we have determined corrections to the celestial pole coordinates, denoted X, Y, using LLR observations. This determination is of particular interest for comparison with the one obtained from VLBI observations. The main purpose is to study the benefits of LLR for the determination of the celestial pole coordinates and second how to best combine the time series obtained from both techniques. Methods. For these determinations, data acquired by LLR tracking stations since 1969 were analyzed and corrections to the nutation terms estimated using a weighted least square fit. Finally, LLR data were combined with the IVS combined VLBI series of 23-year duration. Results. We have demonstrated the possibility of determining the celestial pole offsets from LLR data even though the results are not as accurate nor as dense as those obtained with VLBI. This work provides some external constraints to the celestial pole coordinates derived from VLBI observations. Moreover, the LLR determination of the long periodic nutation terms shows an improvement with respect to previous studies. The combination of LLR and VLBI series may indicate that the combined series reveal details that do not appear in the VLBI series alone