

	Pavlov – Gigliotti theory of gravitation Fancy abstract mathematical exercises, for the larger part, are meaningless. Thoughtful experiments and careful observations and measurements are of main value. The standard model of gravity describes it in terms of force of attraction between two or more masses at a non-zero distance from each other to infinity. The association between masses is viewed as direct linear interaction, or interaction along a warped curvature of space. The courses on the subject of gravitational interaction between masses delicately skirt the theory of special relativity, which claims that nothing can move faster than the speed of light in a vacuum, and profess that all gravitational interactions between masses are instantaneous. Thus we calculate all orbits using the assumption of instantaneous interaction. Introducing a delay into gravitational interactions is disastrous because conservation of angular momentum is destroyed then. Although the idea of instantaneous interaction between masses is correct (observations and calculations support the assumption), its interpretation is totally in error. Aberration is the angle between the present and the past positions of a moving mass as viewed from one frame. To measure the speed of propagation of any entity (particle, or wave, or dual) is to measure its transit delay, or, in this case, the angle of aberration. Gravity has no aberration! But how could that be? We will come to that subject later. Meanwhile, we will introduce a *new galactic spherical gravity constant k (k = 1.5410-14) and galactic variables like distance (radius) to the center of our galaxy containing a supermassive black hole. The supermassive black hole (sbh) at the center of our galaxy is the body that holds our galaxy together. Our Solar system is within the gravitational force field of that black hole. Therefore, it is subject to the black hole’s influence. To the best of my knowledge, there are no equations which take that into account. Ours do. The equations which follow are computer-generated -- the simplest possible. Mercury's precession of perihelion ---------------------------------------------- Before we introduce the main equations, we will establish a base. We will start with the old problem of Mercury’s unaccounted perihelion advance. There are several factors which cause Mercury’s precession of perihelion. They are Table 1 -------- Arcseconds / century Cause -------------------------------------------------------------------------------------------- 5025.6 Precession of equinoxes 531.4 Gravitational tugs of the other planets 0.0254 Oblateness of the Sun 43 Predicted by the GR 5600 Total 5599.7 Observed There are two errors in this summation. The first error is the number assigned to gravitational tugs of the other planets. Gravitational force fields of Mars, Uranus, and Neptune cannot reach Mercury (see Tables 2 and 3). After subtracting points assigned to these three planets, we have the total of 529.1 instead of 531.4 Table 2 --------- Distance from Distance from Gravity Mass (kg) from Sun (m) Mercury (m) limit (m) ---------------------------------------------------------------------------------------------- *Sun 1.991030 *Mercury 3.302210*23 5.790910*10 5.0854109 *Venus 4.868510*24 1.082110*11 5.030110*10 7.49751010 *Earth 5.973610*24 1.496010*11 9.169110*10 9.19931010 *Mars 6.418510*23 2.279410*11 1.700310*11 9.8845109 *Jupiter 1.898610*27 7.785510*11 7.206410*11 2.92381013 *Saturn 5.684610*26 1.433510*12 1.375610*12 8.75431012 *Uranus 8.681010*25 2.876710*12 2.818810*12 1.33691012 Neptune *1.024310*26 4.503410*12 4.445510*12 1.57741012 Table 3 -------- (Interaction between Mercury and the other planets) Force Force (pct) Points ------------------------------------------------------------------------------------------------ *Venus 4.24091016 29.069 154.47 *Earth 1.56601016 10.734 57.04 *Mars 4.89321014 0.3354 1.78 *Jupiter 8.05772016 55.2313 293.45 *Saturn 6.62101015 4.54 24.13 *Uranus 1.65701013 0.0114 0.06 Neptune *1.14231014 0.078 0.4145 Total: 531.4 The second error is major. Einstein’s computations are based on erroneous assumptions. Space does not curve, gravity does. Also, Einstein did not take into account the tug by the sbh at the center of our galaxy. The actual precession advance is 45 arcseconds per century. Table 4 -------- Arcseconds / century Cause -------------------------------------------------------------------------------------------- 5025.6 Precession of equinoxes 529.1 Gravitational tugs of the other planets 0.0254 Oblateness of the Sun 45 Predicted by the GS theory 5599.7 Total 5599.7 Observed Our computations follow. The galactic equation to compute the precession advance for all planets. P = k (pi) R M / 10 d r Where: k - gravity sphere galactic constant (in m/kg) (pi) - constant (in radians) (pi times 1 rad) R - Radius of the Sun (in m) M - Mass of the Sun (in kg) d - Solar system distance from the center of galaxy (in m) r - radius of planetary orbit (in m) Compute: *P = 1.5410*-14 x 3.14159 x 6.9610*8 x 1.9910*30 / 10 x 2.21020 x *5.79091010 *= 5.2610-7 radians per orbit Mercury spins 415.0139 orbits per century. *P = 5.2610*-7 x 415.0139 = 2.18310-4 rads. *1 arcsec = 4.848195 10-6 rads. *P = 2.18310*-4 / 4.84819510-6 = 45.03 arcsec. Using the galactic equation to compute the unaccounted perihelion advance for the other planets, we have: Venus = 9.39, Earth = 4.2, Mars = 1.46, Jupiter = 0.068, Saturn = 0.0148, Uranus = 0.0026, Neptune = 0.00084 arcseconds per century. The inclusion of galactic constants and variables in gravity equations is important because the influence of the central black hole in our galaxy and on our Solar system is undeniable. For example, let’s say that our Solar system was located twice as close to the black hole instead of being on the outskirts of the galaxy. When we compute the precession advance of the Earth at that distance, we come up with the value of 8.4 arcsec per century, which seems small, but the increased precession would drastically change the climate on our planet. Gravitational density and orbital decay --------------------------------------------------- Observations of the decrease in orbital period of the binary pulsar PSR B1913+16 made by Hulse and Taylor and of the most recently discovered pulsar system PSR J0737-3039 are valid though their interpretaion is not. The loss of energy and the orbital decay in these systems is not due to generated gravitational waves, but due to mutually obstructing strong gravitational fields. The density of gravitational fields creates a dragging force (the "molasses effect"), which causes both pulsars to spiral down towards each other. In neutron binaries, with strong gravitational fields, the effect is more pronounced and can reach 3.5 meters per year or more. The Earth is subjected to the same effect though on a much more subtle scale. It spirals down towards the Sun 8.9410-10 meters per year. I don't think we should worry about falling into the Sun. The Sun will explode long before we could fall into it. The calculations follow. Let's concentrate on the decrease of semi-major axis (the decrease of orbital period comes with it)* PSR B1913+16 *Companion-1 mass = 2.86761030 kg *Companion-2 mass = 2.76001030 kg *Separation = 1.95109 m Observed decrease of distance = 3.5 m per year Final inspiral = 300,000,000 years F = G m1 m2 / r2 = 6.6742810-11 x 2.867610*30 x 2.76001030 / *(1.95109)2 = 1.391032 newtons* *1 N = 3.5 / 1.3910*32 = 2.52 10-32 m per year Earth: *Sun's mass = 1.991030 kg *Earth's mass = 5.97361024 kg *Separation = 1.4961011 m F = G m1 m2 / r2 = 6.6742810-11 x 1.9910*30 x 5.97361024 / *(1.4961011)2 = 3.5451022 newtons* *Decrease of semi-major axis = 2.5210*-32 x 3.5451022 *= 8.9410-10 m per year And that brings us to the point of defining gravitational density. Gravitational density is a "viscosity" of gravity. Gravitational density's magnitude is directly proportional to the mass and inversely proportional to the distance from the mass. It is also directly proportional to gravitational acceleration, which is very convenient in our case. We equate 1 m/s2 of acceleration to 1 gilotti of gravitational density. Thus at the Earth's surface, the gravitational density is 9.83 gi. When a mass enters the gravitational force field of another mass (or orbits it), the viscosity of the field causes friction between the entering mass and the field. What happens is that the mass loses some of its kinetic energy. That energy is converted into thermal energy. The amount of loss is minimal on the planetary scale because the gravitational force field of the Sun is not dense and distances are great. But for neutron binaries the picture is different. The distance between companions is short and their gravitational force fields are incredibly dense and strong. The loss of kinetic energy for both companions is significant and easily measurable. Thus, the companions spiral into each other. The generated heat dissipates into the outer space. No gravitational waves are produced. To find the quantity of dissipated energy in the form of heat by the binary, we sum up its kinetic energy first. K = m v2 / 2 *Companion-1: k1 = (2.867610*30 x (2.8105)2) / 2 = 1.1241041 joules* *Companion-2: k2 = (2.7610*30 x (2.8105)2) / 2 = 1.0821041 joules* *System: K = k1 + k2 = 1.12410*41 + 1.0821041 *= 2.21041 joules Now we can compute the energy loss. *Semi-major axis = 1.95109 m Decrease of semi-major axis = 3.5 m/yr *Percent of decrease = 1.794910-7 *Loss of kinetic energy = (2.210*41 / 100) x 1.794910-7 *= 3.9491032 joules/yr This energy is converted to thermal energy and is dissipated in the form of radiation. Gravitational time dilation ----------------------------------- Neither of the relativities took into account an important natural phenomenon: gravitational density. Gravity has density, and that density slows down ALL natural processes including atomic interactions. Thus, atomic clocks run slower in stronger gravitational fields. Time does not slow down, atomic clocks do. Clocks on the GPS system satellites, for example, run faster than clocks on the Earth's surface. Guys at the GPS facilities update the satellite clocks by about 38 microseconds per day synchronizing them with the surface clocks. We will use that number to compute the gravity viscosity coefficient for our future calculations. Gravitational density is directly proportional to gravitational acceleration. That allows us to borrow the Newtonian equation. a = G m / r2 where: a - gravitational acceleration G - gravitational constant m - Earth's mass r - orbital radius Above, we defined gravitational density in terms of gilottis. From the previous equation, we can redefine it in terms of acceleration. At the Earth's surface, the gravitational acceleration equals 9.83 m/s2. Thus, the gravitational density at the Earth's surface is 9.83 gi. Gravitational density at the GPS satellites' distance: D = G m / r2 = (6.6742810-11 x 5.973610*24) / 2.6562107)2 = 0.5651 The orbital velocity of the GPS satellites: v = sqrt(G m / r) = sqrt(6.6742810-11 x 5.973610*24) / 2.6562107 *= 3.873103 = 3873 m/s The factors which influence the rate of satellite clocks are gravitational density and orbital velocity. We add the distance that clocks cover in one day. The GPS satellites' orbit radius is 2.6562107 m, velocity 3.87310*3 m/s, and orbital distance per day 3.337108 m. To find the gravity viscosity coefficient, we construct an equation. C = D d f / v where: C - clocks' rate increase (in seconds) D - gravitational density (in gi fractions) d - orbital distance per day (in m) f - the coefficient v - satellite velocity (in m/s) f = C v / D d = (0.000038 x 3.873103) / (0.5651 x 3.337108) *= 7.80610-10 The GPS satellites' clocks update of 38 microseconds per day (actually, the clocks are already preset to run slower) has three components: + 7.2 microseconds for velocity + 0.7 microseconds for solar and galactic influence - 45.9 microseconds for gravitational density -------- - 38 microseconds total Orbital velocity slows down the atomic clocks. When moving, the clocks encounter more of the gravitational substance per unit of time. That is equivalent to a greater gravitational density. The faster clocks travel, the more gravitational density per unit of time they encounter and the slower they "tick". The galactic influence is the influence of gravitational force field of the Sun and the distant supermassive black hole at the center of our galaxy. Both slow the clocks a bit. And the final component is the main one -- gravitational density. Gravitational density at the distance from the Earth is lower. The atomic clocks run faster. Gravitational redshift ----------------------------- Electromagnetic radiation coming from a body through its gravitational force field loses energy, becomes lower in frequency and longer in wavelength. This phenomenon is called gravitational redshift. z = (lambda-out - lambda-in) / lambda-in where: z - gravitational redshift lambda-in - wavelength of radiation at the source of emission lambda-out - wavelength of radiation exiting a gravitational field Let's test it on the Earth. z = 3 D d f / c where: z - gravitational redshift (in sec) D - integral of gravitational density within the body's gravitational limit (in gi) d - distance of gravitational limit (in m) f - gravitational viscosity coefficient found with gravitational dilation c - speed of light (in m/sec) D = integral (a dx) between 0 and 9.83 (acceleration) where f(x) = a and F(x) = a2 / 2 = F(9.83) - F(0) = (9.83)2 / 2 - 0 = 48.32 *d = 9.19931010 *f = 7.80610-10 *c = 2.9979108 *z = 3 x 48.32 x 9.199310*10 x 7.80610*-10 / 2.9979108 = 0.0000347 sec = 34.7 microseconds (not the end) (Proceed to "The math 2" page for continuation…)

The Gravity Spheres theory opens up a wide field of exploration in many sciences.

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