Time Series Correlated Error's Simulation Scheme with the Application to Simulate the Ephemerides Error of CHAMP

Computer simulation experiment is very important in the phase of project design, the availability of simulated result highly depends on the scheme of error simulation. Time series observations are normally correlated. This paper first discusses the formula of correlated error propagation, then derives the formula of simulating time series correlated errors. This formula is then used to simulate correlated ephemerides errors of CHAMP, then the ephemerides are used to recover the gravity vector at satellite altitude with finite differential formula. The formulae derived in this paper are verified with the difference between the recovered gravity vectors and the `true values’ which are directly computed with the same gravity model as that generating the ephemerides.

Application of Accelerometer Data in Precise Orbit Determination of GRACE-A and-B

We investigate how well the GRACE satellite orbits can be determined using the on- board GPS data combined with the accelerometer data. The preprocessing of the accelerometer data and the methods and models used in the orbit determination are presented. In order to assess the orbit accuracy, a number of tests are made, including external orbit comparison, and through Satellite Laser Ranging （SLR） residuals and K-band ranging （KBR） residuals. It is shown that the standard deviations of the position differences between the so-called precise science orbits （PSO） produced by GFZ, and the single-difference （SD） and zero-difference （ZD） dynamic orbits are about 7 cm and 6 cm, respectively. The independent SLR validation indicates that the overall root-mean-squared （RMS） errors of the SD solution for days 309 - 329 of 2002 are about 4.93cm and 5.22cm, for GRACE-A and B respectively; the overall RMS errors of the ZD solution are about 4.25 cm and 4.71 cm, respectively. The relative accuracy between the two GRACE satellites is validated by the KBR data to be on a level of 1.29cm for the SD, and 1.03 cm for the ZD solution.

Secular Increase in the Earth’s LOD Strongly Implies that the Earth Might Be Expanding Radially on a Global Scale

Exactly 101 years ago, German scientist—Alfred Lothar Wegener, sailed against the prevailing wisdom of his day when he posited that not only have the Earth’s continental plates receded from each other over the course of the Earth’s history, but that they are currently in a state of motion relative to one another. To explain this, Wegener set forth the hypothesis that the Earth must be expanding as a whole. Wegener’s inability to provide an adequate explanation of the forces and energy source responsible for continental drift and the prevailing belief that the Earth was a rigid solid body resulted in the acrimonious dismissal of his theories. Today, that the continents are receding from each other is no longer a point of debate but a sacrosanct pillar of modern geology and geophysics. What is debatable is the energy source driving this phenomenon. An expanding Earth hypothesis is currently an idea that is not accepted on a general consensus level. Antiproponent of the expanding Earth mercilessly dismiss it as a pseudo or fringe science with their main point of rejection being the energy source to power this supposed expansion. Be that asit may, we show herein that from the well accepted law of conversation of spin angular momentum, Stephenson [1]’s result that over the last 2700 years or so, the length of the Earth’s day has undergone a change of about +17.00 μs/yr, this result invariably leads to the plausibility the Earth may very be expanding radially at a paltry rate of about +0.60 mm/yr. If correct, this simple fact, automatically move the expanding Earth hypothesis from the realm of pseudo or fringe science, to that of plausible science.

Satellite Clock Error and Orbital Solution Error Estimation for Precise Navigation Applications

Global Positioning System (GPS) is a satellite-based navigation system that provides a three-dimensional user position (x,y,z), velocity and time anywhere on or above the earth surface. The satellite-based position accuracy is affected by several factors such as satellite clock error, propagation path delays and receiver noise due to which the GPS does not meet the requirements of critical navigation applications such as missile navigation and category I/II/III aircraft landings. This paper emphasizes on modelling the satellite clock error and orbital solution (satellite position) error considering the signal emission time. The transmission time sent by each satellite in broadcast ephemerides is not accurate. This has to be corrected in order to obtain correct satellite position and in turn a precise receiver position. Signal transmission time or broadcast time from satellite antenna phase center is computed at the receiver using several parameters such as signal reception time, propagation time, pseudorange observed and satellite clock error correction parameters. This corrected time of transmission and broadcast orbital parameters are used for estimation of the orbital solution. The estimated orbital solution was validated with the precise ephemerides which are estimated by Jet Propulsion Laboratory (JPL), USA. The errors are estimated for a typical day data collected on 11th March 2011 from dual frequency GPS receiver located at Department of Electronics and Communication Engineering, Andhra University College of Engineering, Visakhapatnam (17.73°N/83.319°E).

Gravitational wave sensitivity curve of pulsar timing arrays affected by correlated noises

The detection of gravitational waves(GWs)by pulsar timing arrays(PTAs)is not only a very important supplementation of the verification of general relativity but also a new window to study the evolution of supermassive binary black holes and the early universe.However,so far the detection sensitivity of PTAs is not good enough to catch signals of GWs due to the disturbance of various noises.In this paper we explore the influences of the correlated noises caused by the reference clock errors and solar system ephemeris errors in pulsar timing on the detection of stochastic gravitational waves background(GWB).We demonstrate the power-law integrated sensitivity curves of GWB detection under the impacts from these correlated noises.From the simulated data,we find that the influence of different reference timescale is non-negligible,and the influence is even quite huge if one uses a very old version of solar system ephemeris.However,the impact from these correlated noises on the sensitivity curve is very limited for the real observational data released by international pulsar timing arrays(IPTA).We also calculate the signalto-noise ratios based on the theoretical GW amplitude permitted by observations.Moreover,we study how the detection sensitivity increases with more pulsar number and longer observation.

Nereid's orbit based on new precise observations

A new orbit of Triton was provided by our previous work, benefitted by new Gaia Data, both in a new precise reduction of charge-coupled device observations and in the planetary ephemeris INPOP19 a.In this paper, we provide a new ephemeris for another main Neptunian satellite, Nereid. The orbit is fitted for the newest observations, including 2 075 ground-based observations during the period 1949-2018 and 83 space observations acquired by the Voyager 2 spacecraft in 1989. The dynamical model used here is consistent with that of our previous work. For the ground-based absolute observations of Nereid, the rootmean-square deviations are 0.201′′in right ascension and 0.189′′in declination. Finally, a comparison with the HORIZONS ephemeris is made and discussed.

New upper limit on the cosmological constant from solar system dynamics

The cosmological constant A is the simplest model for explaining the dark energy which supposedly drives the observed accelerated expansion rate of the Universe. Together with the concept of cold dark matter, it satisfactorily accommo- dates a wealth of observations related to cosmology. Due to its assumed constancy throughout the Universe, A might also affect the dynamics of the planets in the so- lar system, although with extremely small effects. However, modern high-precision ephemerides provide a promising tool for constraining it. Using the supplementary advances in the perihelia provided by current INPOP10a and EPM2011 ephemerides, we obtain a new upper limit on A in the solar system when the Lense-Thirring ef- fect due to the Sun＇s angular momentum and the uncertainty of the Sun＇s quadrupole moment are properly taken into account. These two factors were mostly absent in pre- vious works dealing with A. We find that INPOP10a yields an upper limit of A = （0.26±1.45） × 10^-43 m^-2 and EPM2011 gives A = （-0.44 4±8.93） × 10^-43 m^-2. Such bounds are about 10 times less than previously estimated results.

Fundamental Physical Basis for Maxwell-Heaviside Gravitomagnetism

Gravitomagnetism is universally and formally recognised in contemporary physics as being the linear first-order approximation of Einstein’s field equations emerging from the General Theory of Relativity (GTR). Herein, we argue that, as has been done by others in the past, gravitomagnetism can be viewed as a fully-fledged independent theory of gravitomagnetism that can be divorced from Professor Einstein’s GTR. The gravitomagnetic theory whose exposition we give herein is exactly envisioned by Professor Maxwell and Dr. Heaviside. The once speculative Maxwell-Heaviside Gravitomagnetic theory now finds full justification as a fully fledged theory from Professor José Hera’s Existence Theorem which states that all that is needed for there to exist the four Max-well-type field equations is that a mass-current conservation law be obeyed. Our contribution in the present work, if any, is that we demonstrate conclusively that like electromagnetism, the gravitomagnetic phenomenon leads to the prediction of gravitomagnetic waves that travel at the speed of light. Further, we argue that for the gravitational phenomenon, apart from the Newtonian gravitational potential, there are four more potentials and these operate concurrently with the Newtonian potential. At the end of it, it is seen that the present work sets the stage for a very interesting investigation of several gravitational anomalies such as the ponderous Pioneer Anomaly, the vexing Flyby Anomalies, the mysterious Anomalous Rotation Curves of Spiral Galaxies and as well, the possibility of the generation of stellar magnetic fields by rotating gravitational masses.

On the Gravitational Bending of Light <br/>—Was Sir Arthur Stanley Eddington Right?

The paramount British-Led (May 29, 1919) Solar Eclipse Result of Eddington et al. has been tremendous if not an arcane effect in persuading scientists, philosophers and the general public, to accept Einstein’s esoteric General Theory of Relativity (GTR) thereby “deserting” Newtonian gravitation altogether, especially in physical domains of extreme gravitation where Einstein’s GTR is thought or believed to reign supreme. The all-crucial factor “2” predicted by Einstein’s GTR has been “verified” by subsequent measurements, more so by the most impressive and precision modern technology of VLBA measurements using cosmological radio waves to within 99.998% accuracy. From within the most well accepted provinces, confines and domains of Newtonian gravitational theory, herein, we demonstrate that the gravitational to inertial mass ratio of photons in Newtonian gravitational theory where the identities of the inertial and gravitational mass are preserved, the resulting theory is very much compatible with all measurements made of the gravitational bending of light. Actually, this approach posits that these measurements of the gravitational bending of light not only confirm the gravitational bending of electromagnetic waves, but that, on a much more subtler level;rather clandestinely, these measurements are in actual fact a measurement of the gravitational to inertial mass ratio of photons. The significant 19% scatter isseen in the measurements where white-starlight is used, according to the present thesis, this scatter is seen to imply that the gravitational to inertial ratio of photons may very well be variable quantity such that for radio waves, this quantity must—to within 99.998% accuracy, be unity. We strongly believe that the findings of the present reading demonstrate or hint to a much deeper reality that the gravitational and inertial mass, may—after all;not be equal as we have come to strongly believe.

Four Poission-Laplace Theory of Gravitation (I)

The Poisson-Laplace equation is a working and acceptable equation of gravitation which is mostly used or applied in its differential form in Magneto-Hydro-Dynamic (MHD) modelling of e.g. molecular clouds. From a general relativistic standpoint, it describes gravitational fields in the region of low spacetime curvature as it emerges in the weak field limit. For non-static gravitational fields, this equation is not generally covariant. On the requirements of general covariance, this equation can be extended to include a time-dependent component, in which case one is led to the Four Poisson-Laplace equation. We solve the Four Poisson-Laplace equation for radial solutions, and apart from the Newtonian gravitational component, we obtain four new solutions leading to four new gravitational components capable (in-principle) of explaining e.g. the Pioneer anomaly, the Titius-Bode Law and the formation of planetary rings. In this letter, we focus only on writing down these solutions. The task showing that these new solutions might explain the aforesaid gravitational anomalies has been left for separate future readings.

On the Expanding Earth and Shrinking Moon

Exactly 101 years ago, German scientist Alfred Lothar Wegener, sailed against the prevailing wisdom of his day when he posited that not only have the Earth’s continental plates receded from each other over the course of the Earth’s history, but that they are currently in a state of motion relative to one another. To explain this, Wegener set forth the hypothesis that the Earth must be expanding as a whole. Wegener’s inability to provide an adequate explanation of the forces and energy source responsible for continental drift and the prevailing belief that the Earth was a rigid solid body resulted in the acrimonious dismissal of his theories. Today, that the continents are generally receding from each other is no longer a point of debate but a sacrosanct pillar of modern geology and geophysics. What is debatable is the energy source driving this phenomenon. Herein, we hold that continental drift is a result of the Earth undergoing a secular radial expansion. An expanding Earth hypothesis is currently an idea that is not accepted on a general consensus level. Be thatas it may, we show herein that the law of conservation of angular momentum and energy entail that the Earth must not only expand as a consequence of the secular recession of the Earth-Moon system from the Sun, but invariably, that the Moon must contract as well. As a result, the much sort for energy source driving plate tectonics can (hypothetically) be identified with the energy transfers occurring between the orbital and rotational kinetic energy of the Earth. If our calculations are to be believed—as we do;then, the Earth must be expanding radially at a paltry rate of about +1.50 mm/yr while the Moon is contracting radially at a relatively high rate of about -410 mm/yr.

New upper limits on deviation from the inverse-square law of gravity in the solar system:a Yukawa parameterization

New physics beyond the standard model of particles might cause deviation from the inverse-square law of gravity. In many theoretical models of modified gravity, it is parameterized by the Yukawa correction to the Newtonian gravitational force in terms of two parameters α and λ. Here α is a dimensionless strength parameter and A is a length scale. Using the supplementary advances in perihelia provided by INPOP10a and EPM2011 ephemerides, we obtain new upper limits on the deviation from the inverse-square law when the uncertainty of the Sun＇s quadrupole moment is taken into account. We find that INPOP10a yields the upper limits as α =- 3.1× 10-11 and λ= 0.15 au, and EPM2011 gives α = 5.2 × 10-11 and λ=- 0.21 au. In both of them, α is at least 10 times less than the previous results.

Detecting the errors in solar system ephemeris by pulsar timing

Pulsar timing uses planetary ephemerides to convert the measured pulse arrival time at an obser- vatory to the arrival time at the Solar System barycenter （SSB）. Since these planetary ephemerides cannot be perfect, a method of detecting the associated errors based on a pulsar timing array is developed. By using observations made by an array of 18 millisecond pulsars from the Parkes Pulsar Timing Array, we estimated the vector uncertainty from the Earth to the SSB of JPL DE421, which reflects the offset of the ephemeris origin with respect to the ideal SSB, in different piecewise intervals of pulsar timing data, and found consistent results. To investigate the stability and reliability of our method, we divided all the pulsars into two groups. Both groups yield largely consistent results, and the uncertainty of the Earth-SSB vector is several hundred meters, which is consistent with the accuracy of JPL DE421. As an improvement in the observational accuracy, pulsar timing will be helpful to improve the solar system ephemeris in the future.

Updating the orbital ephemeris of the dipping source XB 1254–690 and the distance to the source

XB 1254-690 is a dipping low mass X-ray binary system hosting a neutron star and showing type I X-ray bursts. We aim at obtaining a more accurate orbital ephemeris and at constraining the orbital period derivative of the system for the first time. In addition, we want to better constrain the distance to the source in order to locate the system in a well defined evolutive scenario. We apply, for the first time, an orbital timing technique to XB 1254-690, using the arrival times of the dips present in the light curves that have been collected during 26 yr of X-ray pointed observations acquired from different space missions. We estimate the dip arrival times using a statistical method that weights the count-rate inside the dip with respect to the level of persistent emission outside the dip. We fit the obtained delays as a function of the orbital cycles both with a linear and a quadratic function. We infer the orbital ephemeris of XB 1254-690, improving the accuracy of the orbital period with respect to previous estimates. We infer a mass of M2 = 0.42 ± 0.04 M for the donor star, in agreement with estimations already present in literature, assuming that the star is in thermal equilibrium while it transfers part of its mass via the inner Lagrangian point, and assuming a neutron star mass of 1.4 Mo. Using these assumptions, we also constrain the distance to the source, finding a value of 7.6±0.8 kpc. Finally, we discuss the evolution of the system, suggesting that it is compatible with a conservative mass transfer driven by magnetic braking.

Guidelines for measuring solar radius with Baily beads analysis

By inspection of central eclipses videorecords, data of Baily beads timings are retrievable. Knowing the lunar limb profile at the moment of the eclipse we evaluate the excess or defect of solar limb when the Sun is assumed at its standard radius. Two procedures of data analysis are here presented: one based on limb heights and the other on times. While these methods are based upon Occult 4 software, they can be used with other ephemerides and new lunar profiles. The example of 2006 total eclipse data, with its remarkably negative value of ΔR= - 0.41"± 0.04", is presented.

Kinematics in Randers-Finsler geometry and secular increase of the astronomical unit

Kinematics in Finsler space is investigated. It is shown that the result based on the kinematics with a special Finsler structure is in good agreement with the reported value of the secular trend in the astronomical unit, dAU/dt = 15 ±4[m/century]. The space deformation parameter A in this special structure is very small, with a scale of 10^-6, and should be a constant. This is consistent with the reported value of an anomalous secular eccentricity variation of the Moon＇s orbit.