The cosmic membrane theory was proposed by the author to find a direct and physical way to Newton’s law of gravitation [8]. The indroduction of a space filling stuff led necessarily to a special relativity [7]. The 3-d cosmic membrane expands like a ballon in an etherfilled 4-d space (Fig. 1). One can derivate geometrically or differentially the ordinary differential equation (ODE) of curvature. In the case of the sun the approximative solution is w(r)=-W_oR/r (R radius of sun, r distance to the centre of the sun, W_o the depth of space at the edge of sun). From W_o follows the membrane tension F_o= MA_E/(4pW_oR) with ether acceleration A_E= gM/(W_oR). (M mass of sun, g gravitational constant) [8].

We compare Feynman’s radius of excess [3] of the sun r_Ex=a/3=491[m] (2a is the Schwarzschild radius) with the geometrical path lengthening dS_R from the edge of sun to its centre. The exact density distribution r(r) inside the sun is unknown. Therefore we take the mean value of some arbitrary unimodal curves as a model of the unknown density curve r(r). Now, with a difference equation [9] using only r(r) and a supposed value of F_o, we may calculate w‘(r) and then the path lengthening dS_R. Varying F_o and fitting so the value of dS_R to the radius r_Ex=491 [m] we get W_o = 0,942´10⁶ [m], A_e= 2.071´10⁵ [m/s²] and F_o= 5.001´10¹⁹ [N/m²].

The speed of light is not a constant, but follows c(r)=c_o(1-2a/r) [2,9]. c_o is the speed of light in the vacuum for r®¥. The Shapiro effect of signal retardation is caused essentially by the decrease of speed of light in the gravitational funnel and delivers the same value dt= (2a/c) ln( (X_e+R_e) (X_r+R_r) /y²) as the General Relativity (GR). X_e, R_e, X_r, R_r are distances in the system earth-sun-reflector [9]. y is the nearest distance of trajectory and centre of sun.

W_o is not deriveable from the effects of first order. We consider effects of higher order in 1/y. The first (positive) higher effect is given by the path lengthening caused by the curvature of space (see fig. 2). Simulation calculations yielded dr/r=(1+w’²)^1/2 for a central radial stretching of the membrane, causing a decrease of the density, and thus by the Dispersion Equation [9] an increase of the speed of light according to dc/c=1 + w’²/2. The caused time-effect is negative. The sum of both effects (path lengthening and sun-near acceleration of speed of light) is dt_W= -3pW_o²R² / (16cy³). The experimental data of Shapiro [6] show a small tendency of reduction of the retardation in cases of sun-near trajectories of radar signals. A regression analysis yields W_o=(1.204 ± 0,869) ´10⁶ [m] [9].

The main effect f(y)= -4a/y of the solar gravitational deflection of light is caused by the common gravitation together with the effect of eq. c(r)=c_o(1-2a/r) [9]. This result is the same as in the GR. f is the angle of deflection. Additionally, we find three effects of the order 1/y⁴. All 5 effects of light deflection are:

- The B-effect means that a photon is braked when it is entering the gravitational funnel. Additionally, the x-component of gravitation acts. The sum of both accelerations A_bx=c²ax/r³ is negative at the entrance to the funnel (x<0), but positive at the exit. G- and B-effect yield together f=-4a/y.

P-effect and A-effect cancel one another. The only remaining effect of higher order is the C-effect f_C= -3pW_o²R² / (16y⁴). Measurements of light bending are given by Schmutzer [5]. We get a weighted mean deflection angle Df= 2.093±0.193". The GR predicts f=4a/R=1.75" for trajectories grazing the sun. From the difference (0.342 ±0.193)" and the C-effect we get another estimate of W_o=(1.168 ± 0.659)´10⁶ [m].

The author already delt with the perihelion advance dy in [8]. Unfortunately, this part contained an error. So the author gives here a corrected version. The perihelion advance is caused by an additional relativistic acceleration -kgMa/r³ with k=6 added to the common gravitational acceleration -gM/r² ( r is the distance sun-planet). The direct integration of the equations of motion can be done numerically for one revolution with sufficient accuracy to prove the formula. In [9] a derivation is given of the constant k=6 starting with Einstein’s formula for the perihelion advance. We find k= (12p/T)(r³/(gM))^1/2. T is the time of one revolution. Using Earth data or Venus data we get k=6, indeed. In the case of Mercury with its great eccentricity we get k=5.64. But the numerical integration yields the true value of the perihelion advance only with the original value of k=6, too.

To explanate the factor k=6, we start with the expression for the square of energy e²= (m_ooc_o²)² + (pc)². m_oo is the mass of a body at infinite distance and velocity v=0. c_o is the speed of light at infinite distance. Differentiation of energy e yields the acceleration forces. Hereby we use c(r)= c_o(1-2a/r), m(r)» m_oo(1+Ka/r), v_f²= 2gM/r, dc/dr=c_o2a/r², dm/dr= -m_ooKa/r², dv_f/dr= -gM/(v_fr²). v_f is the pure falling speed from infinite distance in direction of the sun. The still unknown constant K determines the dependence on speed v and on distance r of the mass m. All forces are caused by the effect of the ether wind -gmM/r²= -gm_oo (1+Ka/r) M/r² on the mass m. Comparing this force with the forces gotten by the derivation of e, we find [9] an additional acceleration (-3K+9)gMa/r³. Following Einstein as well as the numerical integration of the orbit, we put -3K+9=6, giving the amount of K=5, and we find m(r) =m_oo(1+5a/r). Comparing this eq. with c(r)=c_o(1-2a/r), we find with c(r)²=c_o² (1-4a/r) and m_o(r)= m_oo (1+4a/r) the new constant m_oc². Here m_o is the mass at velocity v=0, but within a gravitational field. The constant m_oc² replaces the constancy of c.

The membrane allows transversal and longitudinal waves with speed c. The GR calculates a power flow of 195 [W] caused by the orbiting earth. The membrane theory yields nearly the same value with a deviation of -0.56% (the difference between factor 9/Ö2 and 32/5, [9]).

A simple model of an electron [7] as whirlpool of two rotating auges yields together with the density of the membrane r= F_o/c²= 0,556´10³ [Kg/m³] a wavelength l_A= 2.445´10 ^-12 [m]. The value meets the compton wavelength of the electron l_C=2.426´10 ^-12 [m] with an error of 0.8% [9].

90% of all gravitation in the cosmos is caused by dark matter. The ether wind acts on the slope of the membrane in the gravitational funnel and causes a thickening of the membrane [9]. We find two additional members in the ODE of curvature. Simulation experiments with models of galaxies gave dark matter coefficients of d=4 (80% dark matter). With F_o and r and an estimation R_U of the radius of the universe one gets an estimation of the Cosmological Constant L not far from the value found by [1].

Link back to the index: Home:

http://www.fh-furtwangen.de/~webers/index.htm