Abstracts Details

Kepler?s second law is calculated for 18 planets and asteroids. It is shown that equal areas are swept in equal intervals of time only near the perihelion (P) and the aphelion (A). A highly significant relation between the ratio of the area swept at the average of P and A to the area swept at semimajor (S) in the same interval of time and the eccentricity is presented. The equation is ratio = a⋅eb+c with a = −0.617, b = 2, and c = 1.00. The correlation coefficient is 0.9975. The ratio is equal to , which is equal to sin θ, where θ is the smaller angle between the two vectors v and r. Angular momentum is a vector perpendicular to the plane formed by v and r and is conserved, indicating that there is no torque in the direction vertical to the plane of the orbits.

Kepler's second law is calculated for 18 planets and asteroids. It is shown that equal areas are swept in equal intervals of time only near the perihelion (P) and the aphelion (A). A highly significant relation between the ratio of the area swept at the average of P and A to the area swept at semimajor (S) in the same interval of time and the eccentricity is presented. The equation is ratio = a⋅eb+c with a = −0.617, b = 2, and c = 1.00. The correlation coefficient is 0.9975. The ratio is equal to (1 - e^2)^1/2 , which is equal to sin θ, where θ is the smaller angle between the two vectors v and r. Angular momentum is a vector perpendicular to the plane formed by v and r and is conserved, indicating that there is no torque in the direction vertical to the plane of the orbits.

The gravitational force of the sun, based on observations, is derived as the product of acceleration times area. This quantity is constant for all planets, asteroids, and artificial satellites; it is independent of the mass of the attracted body. The equation for the sequential mean distance of the planets from the center of the sun is derived as d = A*B^{n}, where A and B are constants and n is the sequential number of the bodies. The correlation coefficient is 0.997. It is concluded that gravitation is quantized. When the gravitational force is calculated by this new equation (Fs = a*A), there is a highly significant correlation between the magnitude of perturbative forces and the eccentricity of the orbit of the planets and the asteroids. A graph of the maximum inclination of the orbit of each planet to the equatorial plane of the sun shows no correlation between the inclination and the eccentricity of the orbit. Thus, General Relativity cannot explain the eccentricities. The residual advance of the perihelion of the planet Mercury of about 0.1" per revolution is explained by the fact that the direction of the advance coincides with the direction of the movement of the solar system in space, as detected recently by measurements of anisotropy in the cosmic microwave background radiation.