Technology of determining the Earth’s gravitational field parameters using gradiometric measurements Part 6. Calculation the components of the gravitational potential tensor in the earth’s spatial rectangular coordinate system

This is the sixth one in a series of articles describing the technology of determining the Earth’s gravitational field parameters through gradiometric measurements performed with an onboard satellite electrostatic gradiometer. It provides formulas for calculating the components of the gravitational potential tensor in a geocentric spatial rectangular earth coordinate system in order to convert them into a gradiometric one and obtain a free term for the equations of correcting gradiometric measurements when determining the parameters of the Earth’s gravitational field. The components of the gravitational gradient tensor are functions of test masses accelerations measured by accelerometers and relate to the gradiometer coordinate system, while the desired parameters of the Earth’s gravitational field model relate to the Earth’s coordinate one. The components of the gravitational gradient tensor are the second derivatives of the gravitational potential in rectangular coordinates. The calculated values of the gravitational potential tensor components in the earth’s spatial rectangular coordinate system are obtained through double differentiation of the gravitational potential formula. Basing on the obtained formulas, an algorithm and a program in the Fortran algorithmic language were developed. Using this program, experimental calculations were performed, the results of which were compared with the data of the EGG_TRF_2 product.

The Metric of Space-Time Curvature in a Weak Gravitational Field and it’s Consequence in Newtonian Approximation

In Newtonian mechanics, space and time are separate but in General, Relativity is unified. It is considered that the space in the weak-field approximation is quasi-static and it arises from a perfect field whose particles have very small velocity in comparison to light velocity in this coordinate system and the metric is a gravitational potential tensor of rank two which implies the field of empty space. If each point of an area in N-dimensional space there existed a corresponding definite tensor, where the components of the tensor are the function of space and space acts as the strong or weak gravitational field.

Generalization of the Particle Spin as it Ensues from the Ether Theory

In previous papers we generalized the ether waves associated to photons, to waves generally denoted , associated to Par(m,e)s, (particles of mass m and electric charge e), and demonstrated that a Par(m,e)s is a superposition of such waves that forms a small globule moving with the velocity of this . That, at a point near to a moving , the ether velocity , i.e., the magnetic field H, is of the same form as that of a point of a rotating solid. This is the spin of the Par(m,e)s, in particular, of the electron. Then, we considered the case where e=0 and showed that the perturbation caused by the motion of a Par(m,e)s is also propagated in the ether, and is a propagating gravitational field such that the Newton approximation (NA) is a tensor Guobtained by applying the Lorenz transformation for Vm,o on the NA of the static gravitational potential of forces Gu,s. It appeared that Gu is also of the form of a Lienard-Wiechert potential tensor Au created by an electric charge.<br />In the present paper, we generalized the above results regarding the spin by showing that the ether elasticity theory implies also that like the electron, the massive neutral particle possesses a spin but much smaller than that of the electron, and that the photon can possess also a spin, when for example it is circularly polarized. In fact, we show that the spin associated to a particle is a vortex in ether which in closed trajectories will take only quantized values.<br /><br />