The virial theorem and planetary atmospheres

We derive a version of the virial theorem that is applicable to diatomic planetary atmospheres that are in approximate thermal equilibrium at moderate temperatures and pressures and are sufficiently thin such that the gravitational acceleration can be considered constant. We contrast a pedagogically inclined theoretical presentation with the actual measured properties of air.Comment: 5 pages. Accepted for publication in Id\H{o}j\'ar\'as - Quarterly Journal of the Hungarian Meteorological Service (HMS

Study of the Pioneer Anomaly: A scientific detective story

NASA's first two deep space missions, Pioneers 10 and 11, have been travelling through the outer solar system for three decades. A slight deviation from their calculated trajectories presents an as yet unsolved scientific mystery. The use of recently recovered Doppler and telemetry data may help us develop a better understanding of this anomaly, and decide whether or not it is due to a force of on-board origin.Comment: 4 pages, 1 figure. Invited articl

Accelerating classical charges and the equivalence principle

We compare the behavior of a charged particle in a gravitational field and empty space. We resolve the apparent conflict between the Lorentz-Dirac equation and Larmor's formula of radiation by noting that the former describes an electron that is itself accelerated by an electromagnetic field. If instead, a hypothetical particle is considered that is accelerated by a non-electromagnetic force, Larmor's formula is found to be consistent with the accelerating particle's equation of motion. We consider the consequences concerning the equivalence principle and find that it is indeed violated if one demands that the same electromagnetic field be present in both the gravitational and accelerating cases; however, if one allows for the external electromagnetic fields to be different, the validity of the equivalence principle is restored. In either case, the basic idea behind the equivalence principle, which leads to a geometrized theory of gravity, remains unaffected.Comment: 3 page

Sparse Representations of Clifford and Tensor algebras in Maxima

Clifford algebras have broad applications in science and engineering. The use of Clifford algebras can be further promoted in these fields by availability of computational tools that automate tedious routine calculations. We offer an extensive demonstration of the applications of Clifford algebras in electromagnetism using the geometric algebra G3 = Cl(3,0) as a computational model in the Maxima computer algebra system. We compare the geometric algebra-based approach with conventional symbolic tensor calculations supported by Maxima, based on the itensor package. The Clifford algebra functionality of Maxima is distributed as two new packages called clifford - for basic simplification of Clifford products, outer products, scalar products and inverses; and cliffordan - for applications of geometric calculus.Comment: 23 pages, 2 figures; accepted for publication in Advances in Applied Clifford Algebras, special issue AGACSE 201

Diffraction of electromagnetic waves in the gravitational field of the Sun

We consider the propagation of electromagnetic (EM) waves in the gravitational field of the Sun within the first post-Newtonian approximation of the general theory of relativity. We solve Maxwell's equations for the EM field propagating on the background of a static mass monopole and find an exact closed form solution for the Debye potentials, which, in turn, yield a solution to the problem of diffraction of EM waves in the gravitational field of the Sun. The solution is given in terms of the confluent hypergeometric function and, as such, it is valid for all distances and angles. Using this solution, we develop a wave-theoretical description of the solar gravitational lens (SGL) and derive expressions for the EM field and energy flux in the immediate vicinity of the focal line of the SGL. Aiming at the potential practical applications of the SGL, we study its optical properties and discuss its suitability for direct high-resolution imaging of a distant exoplanet.Comment: 43 pages, 9 figures, updated to match published versio

Wave-optical treatment of the shadow cast by a large sphere

We study the electromagnetic (EM) field in the shadow cast by a large opaque sphere. For this, we consider the scattering of a high frequency monochromatic EM wave by the large sphere and develop a Mie theory that accounts for the presence of this obscuration. Applying fully absorbing boundary conditions, we find a solution for the Debye potentials, which we use to determine the EM field in the shadow in the wave zone at large distances from the sphere. We use the standard tools available from the nuclear scattering theory to develop the wave-optical treatment of the problem. Based on this treatment, we demonstrate that there is no EM field deep in the shadow, except for the field that is diffracted into the shadow by the edges of the sphere, as anticipated.Comment: 11 pages, 1 figur

Testing modified gravity with motion of satellites around galaxies

A modified gravity (MOG) theory, that has been successfully fitted to galaxy rotational velocity data, cluster data, the Bullet Cluster 1E0657-56 and cosmological observations, is shown to be in good agreement with the motion of satellite galaxies around host galaxies at distances 50-400 kpc.Comment: 4 pages, 2 figures; substantial revision with independent data analysi

The running of coupling constants and unitarity in a finite electroweak model

We investigate the properties of a Finite Electroweak (FEW) Theory first proposed in 1991. The theory predicts a running of the electroweak coupling constants and a suppression of tree level amplitudes, ensuring unitarity without a Higgs particle. We demonstrate this explicitly by calculating W_L^+W_L^- -> W_L^+W_L^- and e+e- -> W_L^+W_L^- in both the electroweak Standard Model and the FEW model.Comment: 14 pages, 4 figures, corrections in response to referee comment

Physics Engineering in the Study of the Pioneer Anomaly

The Pioneer 10/11 spacecraft yielded the most precise navigation in deep space to date. However, their radio-metric tracking data received from the distances between 20--70 astronomical units from the Sun has consistently indicated the presence of a small, anomalous, Doppler frequency drift. The drift is a blue frequency shift that can be interpreted as a sunward acceleration of a_P = (8.74 +/- 1.33) x 10^{-10} m/s^2 for each particular spacecraft. This signal has become known as the Pioneer anomaly; the nature of this anomaly remains unexplained. Recently new Pioneer 10 and 11 radio-metric Doppler and flight telemetry data became available. The newly available Doppler data set is significantly enlarged when compared to the data used in previous investigations and is expected to be the primary source for the investigation of the anomaly. In addition, the flight telemetry files, original project documentation, and newly developed software tools are now used to reconstruct the engineering history of both spacecraft. With the help of this information, a thermal model of the Pioneer vehicles is being developed to study possible contribution of thermal recoil force acting on the two spacecraft. The ultimate goal of these physics engineering efforts is to evaluate the effect of on-board systems on the spacecrafts' trajectories.Comment: 6 pages, 5 figures, invited talk at the "IV Physics Engineering International Meeting," Mexico City, Mexico, 15-19 October 200

Diffraction of light by the gravitational field of the Sun and the solar corona

We study the optical properties of the solar gravitational lens (SGL) under the combined influence of the static spherically symmetric gravitational field of the Sun---modeled within the first post-Newtonian approximation of the general theory of relativity---and of the solar corona---modeled as a generic, steady-state, spherically symmetric free electron plasma. For this, we consider the propagation of monochromatic electromagnetic (EM) waves near the Sun and develop a Mie theory that accounts for the refractive properties of the gravitational field of the Sun and that of the free electron plasma in the extended solar system. We establish a compact, closed-form solution to the boundary value problem, which extends previously known results into the new regime where gravity and plasma are both present. Relying on the wave-optical approach, we consider three different regions of practical importance for the SGL, including the shadow region directly behind the Sun, the region of geometrical optics and the interference region. We demonstrate that the presence of the solar plasma affects all characteristics of an incident unpolarized light, including the direction of the EM wave propagation, its amplitude and its phase. We show that the presence of the solar plasma leads to a reduction of the light amplification of the SGL and to a broadening of its point spread function. We also show that the wavelength-dependent plasma effect is important at radio frequencies, where it drastically reduces both the amplification factor of the SGL and also its angular resolution. However, for optical and shorter wavelengths, the plasma's contribution to the EM wave is negligibly small, leaving the plasma-free optical properties of the SGL practically unaffected.Comment: 54 pages, 3 figures. arXiv admin note: substantial text overlap with arXiv:1805.0039