scholarly journals Equations of motion for isolated bodies with relativistic corrections including the radiation reaction force

1986 ◽  
Vol 114 ◽  
pp. 19-34 ◽  
Author(s):  
L. P. Grishchuk ◽  
S. M. Kopejkin
Keyword(s):  
Equations Of Motion ◽  
Reaction Force ◽  
Slow Motion ◽  
Major Axis ◽  
Radiation Reaction ◽  
Secular Change ◽  
Semi Major Axis ◽  
Relativistic Corrections ◽  
Relativistic Mass ◽  
Osculating Elements

We have derived in an explicit form the equations of motion for two spherically-symmetric non rotating bodies in the slow motion approximation. The equations include relativistic corrections of order (v/c)2, (v/c)4 and (v/c)5 to the newtonian equations of motion. It is shown that the equations depend on the only parameter characterizing each body, namely on its relativistic mass, regardless of its internal structure and degree of compactness. This means that the equations can also be applied to bodies with a strong internal gravity, such as neutron stars and black holes. It is shown that in the (v/c)2 and (v/c)4 approximations the equations can be derived from a Lagrangian. The Lagrangian is given in an exact form. The integration of the equations of motion is performed by the method of osculating elements. The formulae for secular change of the semi-major axis and eccentricity coincide precisely with the standard ones whose derivation is based on a calculation of the energy flux in the outgoing gravitational waves.

The two-body problem: an effective-one-body approach

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Body Problem ◽  
Equations Of Motion ◽  
Reaction Force ◽  
Kerr Black Hole ◽  
Radiation Reaction ◽  
Spherically Symmetric ◽  
Geodesic Motion ◽  
Two Body Problem ◽  
Symmetric Spacetime ◽  
Radiation Reaction Force

This chapter presents the basics of the ‘effective-one-body’ approach to the two-body problem in general relativity. It also shows that the 2PN equations of motion can be mapped. This can be done by means of an appropriate canonical transformation, to a geodesic motion in a static, spherically symmetric spacetime, thus considerably simplifying the dynamics. Then, including the 2.5PN radiation reaction force in the (resummed) equations of motion, this chapter provides the waveform during the inspiral, merger, and ringdown phases of the coalescence of two non-spinning black holes into a final Kerr black hole. The chapter also comments on the current developments of this approach, which is instrumental in building the libraries of waveform templates that are needed to analyze the data collected by the current gravitational wave detectors.

scholarly journals Elliptical Tracks: Evidence for Superluminal Electrons?

2019 ◽  
Author(s):  
Keith Fredericks
Keyword(s):  
Nuclear Reactions ◽  
Structure Constant ◽  
Major Axis ◽  
Magnetic Monopoles ◽  
Quantization Condition ◽  
Fine Structure Constant ◽  
Semi Major Axis ◽  
Relativistic Mass ◽  
Charge Quantization ◽  
Particle Tracks

In the literature of Low-Energy Nuclear Reactions (LENR), particle tracks in photographic emulsions (and other materials) associated with certain electrical discharges have been reported. Some Russian and French researchers have considered these particles to be magnetic monopoles. These tracks correspond directly to tracks created with a simple uniform exposure to photons without an electrical discharge source. This simpler method of producing tracks supports a comprehensive exploration of particle track properties. Out of 750 exposures with this method, elliptical particle tracks were detected, 22 of which were compared to Bohr-Sommerfeld electron orbits. Ellipses fitted to the tracks were found to have quantized semi-major axis sizes with ratios of ≈n2/α2 to corresponding Bohr-Sommerfeld hydrogen ellipses. This prompts inquiry relevant to magnetic monopoles due to the n2/α2 force difference between magnetic charge and electric charge using the Schwinger quantization condition. A model using analogy with the electron indicates that the elliptical tracks could be created by a bound magnetically charged particle with mass mm = 1.45 × 10-3 eV/c2, yet with superluminal velocities. Using a modified extended relativity model, mm becomes the relativistic mass of a superluminal electron, with m0 = 5.11 × 10-3 eV/c2, the fine structure constant becomes a mass ratio and charge quantization is the result of two states of the electron.

The Kepler problem

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Kepler Problem ◽  
Equations Of Motion ◽  
Major Axis ◽  
Radius Vector ◽  
Lagrangian Formalism ◽  
The Sun ◽  
Semi Major Axis ◽  
Johannes Kepler ◽  
Reduced Equations ◽  
Central Forces

This chapter considers Newton’s 1665 explanations of the dynamics in the laws governing the motion of a planet around the Sun, which were established by Johannes Kepler in 1618. The first law states that the motion is planar and the trajectories are ellipses. The second states that the area swept out by the radius vector per unit time is constant. Finally, the cube of the semi-major axis a is proportional to the square of the period P, a3 = (const)P2. The chapter begins with the reduced equations of motion before turning to the ellipses of Kepler. It then illustrates the Kepler problem in the Lagrangian formalism, as well as central forces.

The two-body problem and radiative losses

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Mechanical Energy ◽  
Equations Of Motion ◽  
Reaction Force ◽  
Radiation Reaction ◽  
Compact Objects ◽  
Einstein Equations ◽  
Two Body Problem ◽  
System P ◽  
Radiative Losses ◽  
Radiation Reaction Force

This chapter begins by finding the field created by compact objects in the post-linear approximation of general relativity. The second quadrupole formula is then completely proven. Next, the chapter finds the equations of motion of the bodies in the field which they create to second order in the perturbations, assuming that their velocities are small. It shows that, to correctly describe the radiation reaction at 2.5 PN order, it will prove necessary to iterate Einstein equations a third time. This leads the discussion to the equations of motion, which generalize to order 1/c5 the EIH equations of order 1/c⁲. Finally, the chapter studies the effect of the radiation reaction force on the sources, and shows that there is an energy balance at 2.5 PN order between the energy radiated to infinity and the mechanical energy lost by the system.

scholarly journals Dynamical evolution of asteroid pairs in the vicinity of resonances

2021 ◽  
Author(s):  
A. E. Potoskuev ◽  
◽  
E. D. Kuznetsov ◽  
Keyword(s):  
Equations Of Motion ◽  
Dynamical Evolution ◽  
Major Axis ◽  
Time Interval ◽  
Orbital Elements ◽  
Semi Major Axis ◽  
Mean Motion Resonances ◽  
Mean Motion ◽  
Yarkovsky Effect ◽  
Numerical Integrations

Dynamical evolution of asteroid pairs in close orbits near Jovian mean motion resonances (3 : 1, 4 : 1, 5 : 2, 7 : 3) has been researched by means of numerical integrations of the equations of motion over 1 Myr time interval in the future. Initial orbital elements’ uncertainty and semi-major axis drift due to the Yarkovsky effect significantly affect orbit modification with time, especially for objects originally situated in the vicinity of resonances. Passing through a resonance generally leads to orbital distance growth.

scholarly journals Elliptical Tracks: Evidence for Superluminal Electrons?

2019 ◽  
Author(s):  
Keith Fredericks
Keyword(s):  
Nuclear Reactions ◽  
Structure Constant ◽  
Major Axis ◽  
Magnetic Monopoles ◽  
Quantization Condition ◽  
Fine Structure Constant ◽  
Semi Major Axis ◽  
Relativistic Mass ◽  
Charge Quantization ◽  
Particle Tracks

In the literature of Low-Energy Nuclear Reactions (LENR), particle tracks in photographic emulsions (and other materials) associated with certain electrical discharges have been reported. Some Russian and French researchers have considered these particles to be magnetic monopoles. These tracks correspond directly to tracks created with a simple uniform exposure to photons without an electrical discharge source. This simpler method of producing tracks supports a comprehensive exploration of particle track properties. Out of 750 exposures with this method, elliptical particle tracks were detected, 22 of which were compared to Bohr-Sommerfeld electron orbits. Ellipses fitted to the tracks were found to have quantized semi-major axis sizes with ratios of ≈n2/α2 to corresponding Bohr-Sommerfeld hydrogen ellipses. This prompts inquiry relevant to magnetic monopoles due to the n2/α2 force difference between magnetic charge and electric charge using the Schwinger quantization condition. A model using analogy with the electron indicates that the elliptical tracks could be created by a bound magnetically charged particle with mass mm = 1.45 × 10-3 eV/c2, yet with superluminal velocities. Using a modified extended relativity model, mm becomes the relativistic mass of a superluminal electron, with m0 = 5.11 × 10-3 eV/c2, the fine structure constant becomes a mass ratio and charge quantization is the result of two states of the electron.

Detection and Characterization of earth-like Planets

1997 ◽  
Vol 161 ◽  
pp. 299-311 ◽  
Author(s):  
Jean Marie Mariotti ◽  
Alain Léger ◽  
Bertrand Mennesson ◽  
Marc Ollivier
Keyword(s):  
Direct Detection ◽  
Contrast Ratio ◽  
Angular Size ◽  
Physical Nature ◽  
Major Axis ◽  
Infrared Emission ◽  
Space Technology ◽  
Semi Major Axis ◽  
Earth Like Planets ◽  
Visible Wavelengths

AbstractIndirect methods of detection of exo-planets (by radial velocity, astrometry, occultations,...) have revealed recently the first cases of exo-planets, and will in the near future expand our knowledge of these systems. They will provide statistical informations on the dynamical parameters: semi-major axis, eccentricities, inclinations,... But the physical nature of these planets will remain mostly unknown. Only for the larger ones (exo-Jupiters), an estimate of the mass will be accessible. To characterize in more details Earth-like exo-planets, direct detection (i.e., direct observation of photons from the planet) is required. This is a much more challenging observational program. The exo-planets are extremely faint with respect to their star: the contrast ratio is about 10−10at visible wavelengths. Also the angular size of the apparent orbit is small, typically 0.1 second of arc. While the first point calls for observations in the infrared (where the contrast goes up to 10−7) and with a coronograph, the latter implies using an interferometer. Several space projects combining these techniques have been recently proposed. They aim at surveying a few hundreds of nearby single solar-like stars in search for Earth-like planets, and at performing a low resolution spectroscopic analysis of their infrared emission in order to reveal the presence in the atmosphere of the planet of CO H2O and O3. The latter is a good tracer of the presence of oxygen which could be, like on our Earth, released by biological activity. Although extremely ambitious, these projects could be realized using space technology either already available or in development for others missions. They could be built and launched during the first decades on the next century.

Radiation-reaction force on a moving mirror

1993 ◽  
Vol 3 (11) ◽  
pp. 2151-2159 ◽  
Author(s):  
Claudia Eberlein
Keyword(s):  
Reaction Force ◽  
Radiation Reaction ◽  
Radiation Reaction Force

Incompleteness of General Relativity, Einstein's Errors, and Related Experiments-- American Physical Society March meeting, Z23 5, 2015 --

2015 ◽  
Vol 8 (2) ◽  
pp. 2135-2147 ◽  
Author(s):  
C. Y. Lo
Keyword(s):  
General Relativity ◽  
Einstein Equation ◽  
Reaction Force ◽  
Radiation Reaction ◽  
Gravitational Energy ◽  
Energy Conditions ◽  
Experimental Investigations ◽  
Positive Mass Theorem ◽  
Wave Source ◽  
Photonic Energy

General relativity is incomplete since it does not include the gravitational radiation reaction force and the interaction of gravitation with charged particles. General relativity is confusing because Einstein's covariance principle is invalid in physics. Moreover, there is no bounded dynamic solution for the Einstein equation. Thus, Gullstrand is right and the 1993 Nobel Prize for Physics press release is incorrect. Moreover, awards to Christodoulou reflect the blind faith toward Einstein and accumulated errors in mathematics. Note that the Einstein equation with an electromagnetic wave source has no valid solution unless a photonic energy-stress tensor with an anti-gravitational coupling is added. Thus, the photonic energy includes gravitational energy. The existence of anti-gravity coupling implies that the energy conditions in space-time singularity theorems of Hawking and Penrose cannot be satisfied, and thus are irrelevant. Also, the positive mass theorem of Yau and Schoen is misleading, though considered as an achievement by the Fields Medal. E = mc2 is invalid for the electromagnetic energy alone. The discovery of the charge-mass interaction establishes the need for unification of electromagnetism and gravitation and would explain many puzzles. Experimental investigations for further results are important.

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