The Gravitational Fish Tank (página 2)

1. 

   Fig. Gravitational Fish Tank

2. RESULTS

1. THE UNIVERSAL GRAVITATION CONSTANT

2. Up to now the numeric value of the universal gravitation constant (G) is equal to:

     (2)

   There is a consideration in the Cavendish balance experiment, where an (L) long strip was used to equal the force between the masses M and m from Newton (1) with the torsional force produced by on strip L. There is no doubt that when the (L) long strip is twisted the distance L is shortened by L minus the L differential; it means that up to date it has been neglected that the mass M must produce a net work against the gravitation field of the earth on the mass m and this very small gravitational force component introduces an error if it is not considered.

   As a matter of fact, the Newton force (1) must be considered as the force resulting from the sum of torsional force plus the gravitational force component on m.

   If we consider the result of these two vectors we find that:

     (3)

   This experiment showed that:

   m21 R01 = m22 R02 = Constant (4)

   The experiment results to be equivalent to the solar system; therefore, since we know that:

   R0E = 1.496 x 1011 m (distance between the earth and the sun)

   mE = 5.976 x 1024 Kg (mass of the earth)

   we get:

   m2E R0E = 5.3426 x 1060 mKg2 = ß (5)

   and generalized:

   m2n R0N = ß (6)

3. THE MASSES OF THE PLANETS
4. THE ANGULAR MOMENTUM

It is known that the angular momentum (L) for each planet with a distance (R ) from the sun and a speed (V) is a constant defined by:

If we use the hypothesis that:

1. The trajectories of the planets are very close to be circumferential and that
2. The angular momentum (Lo) is in fact a universal planetary constant;

We can write:

  (7)

And based on the third Law from Newton we obtain:

  (8)

Or for variable (v):

Finally:

With M = 1.989 x 1030 Kg for the mass of the sun.

For our planet:

L0 = mE R0E vE

Where:

VE = 2.9813 x 104 m/s

We get:

L0 = 2.6653 x 1040 Kgm2 / s

By this, through (9) we can also calculate the mass of each one of the planets.

Table I shows that the numeric values for the masses of the planets of our solar system do not defer between the calculations made with the formulas (6) and (9).

The other data are those the NASA provides for the universities.

1. CONCLUSIONS

The gravitational fish tank model represents in fact a planet-sun system for the laboratory of Physics.

It was possible to find a gravitational repulsion area, a point of zero interaction and a region of gravitational attraction.

Although we didn’t dispose of the necessary equipment to determine the numeric value of the forces, we observed that the behavior of m1 and m2 confirms from a qualitative perspective the existence of a gravitational well obtained from the product of the Newton force (1) with the ratio R/R0 base ten logarithm, where R0 is the distance from the planet to the sun.

Therefore, although the Newton force is not equal to zero Newtons, the logarithm of R = R0 makes the force to be cancelled.

Also, when R < R0 there exists a gravitational repulsion, but when R > R0 there exists gravitational attraction.

From the result (6) of this experiment we achieved to obtain a numeric value for the mass of each planet identical to the one based on the supposition that the angular momentum is a planetary constant of the solar system.

The calculations obtained through the experimental result (6) and the theoretical result (9) make us trusting more in them than in the data reported by the NASA. Further, the planets of higher masses are located at smaller distances from the sun than planets of a smaller mass, and this is exactly what we observed in the laboratory of Physics.

REFERENCES

Adelaido Flores Montejano. Gravitación. Revista Tecámatl del ITT. Vol. 8, No. 7.

Nueva Época. Tijuana, B.C., September 2000.

Arthur F. Kip. Fundamentos de Electricidad y Magnetismo

Mc. Graw-Hill. Mexico 1982.

Grant R Fowles. Analytical Mechanics Second Edition.

Holt Rinehart Winston. USA. 1978

Adelaido Flores M:

Amado Nervo 602, Edif. B-103 Col. San Nicolás Tolentino; CP 13220.

Tlahuac; México, D.F.