On the cosmological and Hubble constants

In this work we use the results found in Ferreira [1] to explore the dark matter with a simpli ied model of the Milky Way. The exploration shows that, for the ratio dark matter / bright matter existing in a distance less than the distance from the center of the Milky Way to the Sun is equal to 89% and a quantity of negative mass equal to -3.53×10-47 kg can be converted into the dark matter for R0 = 8.50 kpc, V0 = 220 km s -1 and 1 = 160 L v km s , where R0 is the distance from the center of the Milky Way to the Sun, V0 the speed of the Sun around the center of the galaxy and L v the velocity of the Sun around the center of the galaxy when only the luminous matter is considered. The main contribution for this negative mass is


Introduction
In this work we use the results found in Ferreira [1] to explore the dark matter with a simpli ied model of the Milky Way. The exploration shows that, for the ratio dark matter / bright matter existing in a distance less than the distance from the center of the Milky Way to the Sun is equal to 89% and a quantity of negative mass equal to -3.53×10 -47 kg can be converted into the dark matter for R 0 = 8.
which depends only on the space. This suggests that for r equal to c t 0 , where t 0 is the age of the universe, we obtain the contribution of the vacuum energy to the ield equation. Using the value of the vacuum energy found in Ferreira [2] the aproximated value of the cosmological constant L is determined as well as the value of H O .

The u sed transformation
Let S′ be a reference system moving with respect to the reference system S with constant speed u in the direction x+. The y′-axis and the z′ -axis are parallel to axis-y and z-axis, respectively. Let us suppose that the zero of t′ coincides with the zero of t and the origin of x′, y′, z′ coincides with x, y, z when t = o. The Lorentz transformation 2 1/ 2 2

=
(1 ) x ut x u c -¢ - is substituted in this work by the following transformation found in Ferreira [1]: -- and On the dark ma tter that exists in the distance of the center of the Milk Way smaller than R 0 Let a space probe be in circular orbit in the plane of the Milky Way, being at the same distance from the center of the galaxy in which the Sun is. The probe is in a region where the gravitational attraction is basically due to the existing matter in the galaxy at a distance from its center smaller than the distance from the Sun to the Milk Way center. In the Figure 1 the probe is represented by a blue cicle and its velocity around the center of galaxy, denoted by ν, is indicated by the red arrow. The center of the galaxy is at rest with respect to the inertial frame S. In the Figure the probe is at the origin of the inertial frame S′. The axis x′ is colinear with the axis x, the plane xy and the plane x′ y′ are in the Milk Way plane.
Let M be the mass of the galaxy existing at a distance from its center smaller than the distance from the Sun to the Milk Way center, r is the distance of the probe to the galaxy center and G is the gravitational constant for the inertial frame S. For the inertial frame S′ the mass M′ is the existing mass in the galaxy at a distance from its center smaller than the distance from the Sun to the Milk Way center, r′ is the distance of the probe to the galaxy center and G′ is the gravitational parameter. The force exerted on the probe of mass ḿÂ ¢ is the orbital period is Using the equation obtained in Ferreira [1] the force at the position of the probe shown in Figure 1 is and the radius The unity of G is With (17) in this case we have g pratically equal to 1 and Let us consider that practically all mass is concentrated in the plane de ined by the xand y-axis; the z-axis is directed to the north galactic pole. The Figure 2 shows the xy -plane.
Let ∆ ν be the difference between the velocities in r + ∆r and r in the frame system S.
In the system S′ the difference becomes Let R 0 be the distance of the Sun to the center of the Milky Way and V 0 the measured   [7].
Let V L be the estimated velocity of the Sun around the center of the galaxy when only the luminous matter is considered. From the Figure 3 of [8] we have that V L varies from 152 ± 2 km / s to 179 ± 2 km / s -1 for 8.0 mpc < R 0 < 8.5 mpc. For two results used in the Figure 3 of [8] the value is 172 ± 2 km s -1 .
Let us assume that In [2] we found that the contribution of the vacuum energy to the ield equation is where H O is the Hubble constant, l planck is Planck's length and ∆e the vacuum energy. Using where t 0 is the age of the universe and (40), we have the Casimir result [10] for the force between perfectly conducting parallel plates was used and the result is The adopted age of the universe is equal to 1.380000×10 10 year (13.800 0.024 ×