Gravitational Fields and Gravitational Waves

The relative velocity between objects with finite velocity affects the reaction between them. This effect is known as general Doppler effect. The Laser Interferometer Gravitational-Wave Observatory (LIGO) discovered gravitational waves and found their speed to be equal to the speed of light c. Gravitational waves are generated following a disturbance in the gravitational field; they affect the gravitational force on an object. Just as light waves are subject to the Doppler effect, so are gravitational waves. This article explores the following research questions concerning gravitational waves: What is the spatial distribution of gravitational waves? Can the speed of a gravitational wave represent the speed of the gravitational field (the speed of the action of the gravitational field upon the object)? What is the speed of the gravitational field? Do gravitational waves caused by the revolution of the Sun affect planetary precession? Can we modify Newton’s gravitational equation through the influence of gravitational waves?

On the Relativistic Harmonic Oscillator

In view of interest in relativistic harmonic oscillations in media, through which the speed of light is orders of magnitude smaller than in vacuum, the solution of the equation of motion is analyzed in the extreme- and weak-relativistic limits. Using scaled variables, it is shown rigorously how the equation of motion exhibits the characteristics of a boundary-layer problem in the extreme-relativistic limit: The solution differs from a sharp asymptotic pattern only around the turning points of oscillations over a vanishingly small fraction of the period. The sharp asymptotic pattern of the solution is a saw-tooth composed of linear segments. The velocity profile tends to a periodic step function and the phase-space plot tends to a rectangle. An expansion of the solution in terms of a small parameter that measures the proximity to the limit (v/c) → 1 yields an excellent approximation for the solution throughout the whole period of oscillations. In the weak-relativistic limit the same approach yields an approximation to the solution that is significantly better than in traditional asymptotic expansion procedures.

Gravitational Fields and Gravitational Waves

The relative velocity between objects with finite velocity affects the reaction between them. This effect is known as general Doppler effect. The Laser Interferometer Gravitational-Wave Observatory (LIGO) discovered gravitational waves and found their speed to be equal to the speed of light c. Gravitational waves are generated following a disturbance in the gravitational field; they affect the gravitational force on an object. Just as light waves are subject to the Doppler effect, so are gravitational waves. This article explores the following research questions concerning gravitational waves: What is the spatial distribution of gravitational waves? Can the speed of a gravitational wave represent the speed of the gravitational field (the speed of the action of the gravitational field upon the object)? What is the speed of the gravitational field? Do gravitational waves caused by the revolution of the Sun affect planetary precession? Can we modify Newton’s gravitational equation through the influence of gravitational waves?

Uniform Scaling: Relativistic Energy-Momentum Relationships

A number of the most often cited results of relativity theory deal with the relationships between energy, momentum and inertial mass. The history of how Einstein and Planck came to these conclusions is reviewed. It is pointed out that considerations of how the speed of light is affected by the motion of the Earth played a determining role in these developments. After the Michelson-Morley null-interference result became available, Voigt introduced a new space-time transformation by amending the classical Galilean transformation so that the speed of light in free space has the same value of c regardless of the state of motion of both the light source and the observer. This led to the Lorentz transformation which has been the cornerstone of relativity theory for the past century. A thought experiment is presented which proves, however, that there are many situations for which the measured speed of light is NOT equal to c. Furthermore, it is pointed out that the rate of an inertial clock cannot change spontaneously, which result is perfectly compatible with Newton’s First Law of Kinetics (Law of Inertia). This result contradicts the space-time mixing characteristic of the Lorentz transformation and leads to the conclusion that events which are spontaneous for one inertial frame will also be so for every other one. The uniform scaling procedure is a generalization of this result for all other physical properties than elapsed times. Its application shows that the commonly accepted relationships between energy and momentum are only special cases in which it is assumed that the observer is stationary in the rest frame in which force has been applied to cause the object’s acceleration

Gravitational Fields and Gravitational Waves

The relative velocity between objects with finite velocity affects the reaction between them. This effect is known as general Doppler effect. The Laser Interferometer Gravitational-Wave Observatory (LIGO) discovered gravitational waves and found their speed to be equal to the speed of light c. Gravitational waves are generated following a disturbance in the gravitational field; they affect the gravitational force on an object. Just as light waves are subject to the Doppler effect, so are gravitational waves. This article explores the following research questions concerning gravitational waves: What is the spatial distribution of gravitational waves? Can the speed of a gravitational wave represent the speed of the gravitational field (the speed of the action of the gravitational field upon the object)? What is the speed of the gravitational field? Do gravitational waves caused by the revolution of the Sun affect planetary precession? Can we modify Newton’s gravitational equation through the influence of gravitational waves?

Gravitational Energy Levels: Part Two: مستويات طاقة الجاذبية: الجزء الثاني

We present here a model that explains in a simple, easy and summarized manner, the values, meaning and reasons for the force of gravity, using simple physical tools. According to this model, a gravitational field actually creates different energy levels, similar to the atom, around the center of mass of the gravitational source, and a transition between the energy levels results in the creation of the force of weight acting on each small body which is in the gravitational field. As the body approaches a gravitational field, its energy value decreases to a value of m0u2(R), proportional to the distance R between the centers of the masses, when u(R) is the magnitude of the self-speed of light vector (the progression in the time axis) of the small body, and its value decreases as it approaches the center of the origin of the field. This change in the energy levels is the cause of the force of gravity. A formula is obtained for the concept of potential gravitational energy and the variables on which it depends, and for the time differences between two frames that are in the gravitational field, taking into account the motion and location of each frame. It is obtained from this model that the speed of light is also a variable value as a result of the effect of the gravitational field.

Gravitational Fields and Gravitational Waves

The relative velocity between objects with finite velocity affects the reaction between them. This effect is known as general Doppler effect. The Laser Interferometer Gravitational-Wave Observatory (LIGO) discovered gravitational waves and found their speed to be equal to the speed of light c. Gravitational waves are generated following a disturbance in the gravitational field; they affect the gravitational force on an object. Just as light waves are subject to the Doppler effect, so are gravitational waves. This article explores the following research questions concerning gravitational waves: What is the spatial distribution of gravitational waves? Can the speed of a gravitational wave represent the speed of the gravitational field (the speed of the action of the gravitational field upon the object)? What is the speed of the gravitational field? Do gravitational waves caused by the revolution of the Sun affect planetary precession? Can we modify Newton’s gravitational equation through the influence of gravitational waves?

Gravitational Fields and Gravitational Waves

The relative velocity between objects with finite velocity affects the reaction between them. This effect is known as general Doppler effect. The Laser Interferometer Gravitational-Wave Observatory (LIGO) discovered gravitational waves and found their speed to be equal to the speed of light c. Gravitational waves are generated following a disturbance in the gravitational field; they affect the gravitational force on an object. Just as light waves are subject to the Doppler effect, so are gravitational waves. This article explores the following research questions concerning gravitational waves: What is the spatial distribution of gravitational waves? Can the speed of a gravitational wave represent the speed of the gravitational field (the speed of the action of the gravitational field upon the object)? What is the speed of the gravitational field? Do gravitational waves caused by the revolution of the Sun affect planetary precession? Can we modify Newton’s gravitational equation through the influence of gravitational waves?

The Mathematical Model of Space – Time and Gravity

This model predicts the details of Origination (the Big Bang), Expansion, Contraction, Termination (the Big Crunch) and Repetition (the Big Loop) of Space – Time.It represents time as internally related to the system determined by the gravity. It gives the relationship between the speed of light and Gravitational constant.Further, Schwarzschild radius can be represented independently either of speed of light or Gravitational constant.The Gravitational Constant is directly proportional to Planck’s Length and inversely proportional to Planck’s Mass.It predicts the existence of the Multiverse or regions within the Universe.