In [3], a solution is proposed to explain the dark matter, compliant with gen- eral relativity. This explanation leads to the assumption that we are embedded in a relatively uniform **gravitational** **field** generated by larger structures than galax- ies (likely the clusters). Just like the **Earth** **gravitational** **field** can be measured, this hypothetical embedding **gravitational** **field** could be measured by its preces- sion effect (Lense-Thirring effect). Such a measure will be a direct measure of the “dark matter”. We are going to calculate the magnitude of this measure. This value is consistent with its non-detection until now. But it seems accessible to the next generation of experiments. In the most advantageous case, the accuracy of 1% (as expected in GINGER experiment) could be enough to detect it.

Since the launch of the European Space Agency spacecraft Hipparcos (high precision parallax collecting satellite) in 1989, the deflection of light at total solar eclipses has been consigned to a quaint part of history. The 29 cm aperture telescope on board has measured the position of 118 200 stars to a precision of 3" x 10 -3 for the magnitudes 8 - 9. Any effect on the deflection of starlight by the Sun can now be measured by checking the distance between pairs of stars over time. The advantages inherent in this system were that there was no need for a total solar eclipse, bending by the solar corona could be eliminated, measurements could take place over large angular distances from the Sun and the same instrument was used well calibrated over the entire sky for 37 months. Data were collected on a set of stars chosen within 47 - 133° of the Sun. As an example, the relativistic prediction is that at 90° from the Sun the deflection would be 4".07 x 10 -3 . As a number of theories incorporate some predictions similar to general relativity, nine so called parameterised post-Newtonian parameters have been introduced. Radiation deflected by the **gravitational** **field** of the Sun and entering a telescope on **Earth** is expressed as an amount equal to

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The theoretical model depicted herein, encompasses a model where the third quantum number, is a central prop- erty in governing the occurrence of Low and High pressure systems. Upon high pressure, the **gravitational** **field** has the projection intensified in the direction of the centre of the High pressure system (Figure 2). During Low pressure system, the projection of the **gravitational** fields is reduced in the direction of the Low-pressure system, and the **gravitational** intensity on the local air masses yields a lower pressure, by the reduced **gravitational** pull. Figure 2 illustrates this simple rationale. This pattern can also be viewed in the general occurrence of localized bands of high and low pressure systems across the northern and southern hemisphere, as recently seen in a series of images captured during the year 2013 by the European Organisation for the Exploitation of Meteorological Satellites [15]. As seen in the satellite data at the EUMETSTAT Institute, the bands occur at specific bands be- tween the tropics and the higher latitudes of the globe, on the Southern ( −) and the Northern (+) projections. The nature of the high and low pressure system can also itself be well explained by quantum mechanical operators, as reported recently in a parallel study [16], and the relationship between the behaviour of atmospheric compo- nents and the gravity can therefore find a putative formulation in the relationships as reported in herein and in context with the expression provided recently [16].

The correspondent of **gravitational** gauge transformation in classical mechanics is the transformation of a local reference. According to Equation (17), when the state of mo- tion of a local reference is changed, the **gravitational** gauge **field** in that local reference will be changed accordingly. In other words, the **gravitational** gauge **field** in different local reference will be different, and the corresponding **gravitational** force on a mass point will also be different. The real **gravitational** force on a mass point depends on the state of motion of a reference. For example, an object which is at rest on the **earth** will feel the **gravitational** force of the **earth**. But if it is in a local inertial reference, it cannot feel any **gravitational** force, for the **gravitational** force of the **earth** and the vacuum gra- vitational force cancel each other out. This conclusion is the same as that in general re- lativity.

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Current theories [3] explain the absence of the **gravitational** slowing of the GPS clocks by the solar **field** in terms of the principle of equivalence. Accor- dingly, the local Lorentz frame (LF) of **earth** is a local proper LF in which the or- biting **earth** as well as the GPS clocks, moving with it, are stationary. It is alleged that these clocks are free-falling with **earth** in the solar **field** and that this orbital motion cancels locally all the effects of the solar **gravitational** **field**. According to Einstein, in a free-falling elevator the effects of gravity are locally canceled and the conditions of a proper reference are locally restored. However, consider ele- vators falling from all different altitudes, at velocities from zero to the local es- cape velocity. How can all these mutually moving elevators at a same given point be proper references? Moreover, according to this view, if the free-fall of the ref- erences is stopped, all clocks in them begin to run slow according to Equation (3) and the path of light becomes bent. The upward force, stopping the free-fall, seems to be the cause of the **gravitational** slowing. However, Muon decay in Cyclotrons [4] demonstrates that accelerations up to 10 19 m/sec 2 do not give rise

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12. The escape velocity of a particle on **Earth** is the minimum velocity re- quired at Earth’s surface in order that that particle can escape from Earth’s **gravitational** **field**. Neglecting the resistance of the atmosphere, the system is conservative. From the conservation theorme for potential plus kinetic energy show that the escape veolcity for **Earth**, ingnoring the presence of the Moon, is 11.2 km/s.

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**Gravitational**-wave astronomy is complementary to electromagnetic astronomy, in part, because GWs penetrate the shrouds of dust and gas that typically obscure the most energetic parts of the universe. Yet, GWs may still be scattered indirectly, by the influence of matter or energy on the curvature of spacetime. In principle, the scattering of GWs provides information on the strong-**field** geometry of compact objects (i.e. black holes, neutron stars and white dwarfs), or hypothetical exotic alternatives (e.g. boson stars [12,13], ‘hairy’ black holes [14,15], or wormholes [16,17]). The time-independent scattering of planar GWs (and other fundamental fields) by black holes has been the subject of numerous works since 1968 [18 – 38]. By comparison, the time-independent scattering of GWs by compact bodies such as neutron stars has received little attention (though for related work see e.g. [39–41]).

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Tables 3 and 4 also confirm that the upward wave in various oblique magnetic fields is always characterized by a larger wave number than that of downward wave and this is consistent with numerical results presented in figures 6 and 7. Note from equation (14) that the magnitude of the non-dimensional magnetic **field** is proportional to parameter N, which is inversely proportional to the pyromagnetic coefficient that characterizes fluid magnetization, and thus the large value of non- dimensional magnetic **field** corresponds to weaker fluid magnetization and vice versa. Perturbation patterns in a stronger magnetized fluid in oblique magnetic **field** are characterized by larger wave numbers and ba- sic flow is less stable there than in a weaker magnetized fluid. The upward propagating wave remains the most dangerous as follows from corresponding data presented in Tables 3 and 4 (compare data for He = 100 in even-numbered and He = 10 in odd-numbered lines).

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Abstract―This paper investigates the influence that a non- uniform **gravitational** **field** has on the dynamics of a space robot. This is accomplished by obtaining the differential equations of motion of the space robot using three **gravitational** **field** potential approximations: a uniform **field** approximation, a zeroth-order Taylor series expansion of the **field** about the center of mass of each body, and a second-order binomial series expansion of the **gravitational** **field**. The three models are then simulated in a free-fall from identical initial conditions. The results indicate that a zeroth-order series expansion of the **gravitational** **field** about the center of mass of each body provides a sufficiently high degree of accuracy without resulting in a significant computational burden.

Tables 3 and 4 also confirm that the upward wave in various oblique magnetic fields is always characterized by a larger wave number than that of downward wave and this is consistent with numerical results presented in figures 6 and 7. Note from equation (14) that the magnitude of the non-dimensional magnetic **field** is proportional to parameter N, which is inversely proportional to the pyromagnetic coefficient that characterizes fluid magnetization, and thus the large value of non- dimensional magnetic **field** corresponds to weaker fluid magnetization and vice versa. Perturbation patterns in a stronger magnetized fluid in oblique magnetic **field** are characterized by larger wave numbers and ba- sic flow is less stable there than in a weaker magnetized fluid. The upward propagating wave remains the most dangerous as follows from corresponding data presented in Tables 3 and 4 (compare data for He = 100 in even-numbered and He = 10 in odd-numbered lines).

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According to legend, Newton noticed an apple drop from a tree. He is said to have been struck with a sudden inspiration: If gravity acts at the tops of trees, and even at the tops of mountains, then perhaps it acts all the way to the Moon! With this idea that it is the Earth’s gravity that holds the Moon in its orbit, Newton developed his great theory of gravitation. But there was controversy at the time. Many thinkers had trouble accepting the idea of a force “acting at a distance.” Typical forces act through contact — your hand pushes a cart and pulls a wagon, a bat hits a ball, and so on. But gravity acts without contact, said Newton: the **Earth** exerts a force on a falling apple and on the Moon, even though there is no contact, and the two objects may even be very far apart. †

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DOI: 10.4236/am.2018.912089 1361 Applied Mathematics of the latter are bar spiral galaxies (such as the Milky Way), the rings of Saturn, viewed as disks with a large central hole, and protoplanetary disks, consisting of dense gas and dust surrounding a newly formed star that add mass to the star [1]. Thus, the **gravitational** fields of such structures have been studied, and we hope that the work presented here on various aspects of the **gravitational** fields of uniform disks, albeit a geometric simplification, will augment previous work and be of general interest as a problem in physics.

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Their relative strength may vary relative to each other but directions up to flipping don't seem within their reach. For present established results, please refer, NASA's Feature, 'Earth's Inconstant Magnetic **Field** dt. 29/03/ 12. The variation of magnetic **field** strength is dependent on the electric charge caught by **Earth** during Sun's flares. However, Earth's magnetic depletion is bound to happen microscopically due to reasons innovatively revealed in this research paper. In magnetic polar region the magnetic dip varies very much; at times it reverses and comes back during its day today observations. It can happen due to magnetic fields of ionosphere's +ve ions layer and the magnetic **field** of electrons beyond it. The ionosphere electrically charged particles are of earth's atmosphere and due to thermal air currents and Sun's flares, the ionosphere densities vary much day to day. And main thing is that the magnetic fields of +ve ionic sphere and 0f -ve electron sphere, both opposite to each other meet at poles, peculiarly in the same direction as explained above; therefore, the resultant direction of the magnetic **field** changes their frequently so that, the dip measuring free needle of the meter practically dances what so ever manner.

In this study, we performed local N -body simulations in- cluding the mutual **gravitational** force between ring particles as well as the direct (inelastic) collision with identical (up to N 40000) particles. Salo (1995) showed that the spatial structures (wake and clumps) arise spontaneously in a dense, self-gravitating, and collisionally dumping particle system due to **gravitational** instability. He also showed that as the wake forms, the radial velocity dispersion increases with the relation Q ∼ 2, where Q is Toomre’s non-dimensional pa- rameter. We reconfirmed his results (Subsection 3.1). Fur- thermore, our simulations showed a regular oscillatory pat- tern in the velocity dispersion which was not found in Salo (1995). We analyzed the motion of particles in the wake structure in detail and clarified that the intrinsic physics of the regular oscillation is coherent “pseudo”-Keplerian motion in- duced by self-**gravitational** instability (Subsection 3.2).

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It has been shown that a **gravitational** **field** can be generated by the oscillation of a quark in a paper written by author Eli Peter Manor published in 2016 in the Journal of Modern physics [1]. While oscillating, the quark would achieve velocities that near the speed of light; the inertial mass of the particle would increase resultantly generating a **gravitational** **field** [1]. The aim of this paper is to show that a **gravitational** **field** can also be pro- duced as the inertial mass of a charged particle increases when accelerated to the verge of the speed of light via an electromagnetic **field** (as in a particle accelerators). Moreover, a description of the space-time curve asso- ciated with the **gravitational** **field** generated will be mathematically formulated.

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Measurements of the MFE are made only with the help of dipole—a magnetic pointer. A dipole responds to the dipole component of the **field**. Its energy of in- teraction with multi-poles of any order other than a dipole is zero, therefore, the information acquired concerns only the dipole component of the MFE. That means that the coefficients in the expansion of the MFE applying the Legendre polynomials are purely abstract values having no physical sense, and they cannot be compared with existing multi-poles, whose values have not been measured. They cannot give information on the real structure of the MFE. To measure the quadrupole component of the MFE, it is necessary to use the magnetic quadru- pole as a sensor, however, I am not aware of such measurements. The same is true for the multi-poles of a higher order. It is necessary to measure them to un- derstand the real structure of the MFE, since the dependence of the interaction energy of multi-poles differs from that of dipoles. Therefore, by measuring it one can get information on the depth of the magnets’ position, their orientation and distribution through the **Earth** volume, etc. At the moment there is no such in- formation.

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Janos (2011) explained Ibnsina’s outer space kinematics which is an important aspect of the cosmology. He has given basic feature of some of cosmological view and then differentiated between different celestial theories and intellects. It was concluded in the study by explaining the role of outer space souls in causing celestial activity. Elkins (2008) explained through the research has been done that how human being view forms of art. Six forms of art have been taken for this study, image (work of art), photography, astrophysics, microscopy and physics and has created stories of perception around them. He then tested how each form of art influences its viewer who is both experienced and inexperienced in this **field**. It was concluded about study of unique structure on how it is viewed and perceived with its relation to the universe.

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impedance of free space is known to be 377 ohms. This characteristic impedance is a function of the ratio of the magnetic and electric **field** thought to be produced by the Sun and planets. Historically we have thought that this was an intrinsic impedance and not a physical impedance. However, the actual density of hydrogen as it exists in interstellar space is on the average of about 1 atom per cubic centimeter. In the extremes, as low as 0.1 atom per cubic centimeter has been found in the space between the spiral arms and as high as 1000 atoms per cubic centimeter are known to exist near the galactic core. The interstellar medium also contains cosmic dust which are much larger than hydrogen. When combined the resistance value of space becomes a network of parallel resistance paths all of which may combine to 377 ohms. The Fibonacci Sequence is known to be a mathematical model for spiral formation and the highly efficient transfer of information. H 377 and characteristic impedance might be

Attempts to solve a problem of the **gravitational** waves quantization with the help of 5-dimensional space-time use [7] can hardly lead to success. Apparently, the theory of 5-dimensional space-time now has only a historical value. By comparison of distance from the source of **gravitational** waves calculated by the attenuation of experimentally registered **gravitational** waves and by the red dis- placement of electromagnetic radiation it has been established [8] that dimen- sion of our space-time is equal ~ 4 0.1 ± . Thus our space-time is described by four coordinates: time and three spatial coordinates.

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rates of **gravitational** and internal energy loss are calculated for the new models in Section 4. The results depend on the assumed cooling rate, and this also affects the rapidity with which the SIC accretes mass through freezing of the overlying ﬂuid. The concomitant release and ascent of light constituents of core mix is an important source of gravita- tional power to drive motions in the ﬂuid outer core (FOC). This source is included in the present models and is found to be roughly 30% as large as the **gravitational** energy re- lease in the cooling and contraction of the entire **Earth**. Its evaluation and the related question of the entropy budget for the **Earth** are however topics of subsidiary interest in the present paper, which is only aimed at assessing the global energy budget.