The Gravitational Fish Tank (página 2)

2.  

   The arrangement of our experiment is shown on Figure 1: Gravitational Fish Tank. It consists of a 16 m long, 40 cm high and 38 cm wide fish tank Three disks of the following masses M = 3.269 Kg; m2 = 0.923 Kg and m1 = 0.495 Kg were produced out from three one-inch wide wrought iron strips formed to a ring by welding of a perimeter of 30, 15 and 10 inches.

   A one inch wide wrought iron support was then placed perpendicularly on the inner face of each ring. An orifice was then drilled on each one of these structures and a 3/8" nut welded on it. Finally, each structure was covered with mortar by taking care not to obstruct the thread of the nut at the inner face of each disk.

   Also, a metallic base made of a ½" thick wrought iron plate of 12 x 6" with a strip at the center of the square made also out of a ½" wide wrought iron.

   Finally, a screw of two inches in length and 3/8 inch thread was welded to the center of said base, where masses m1 and m2 may be screwed onto individually. A styrofoam floating body was included with and eighteen by seven inch base and three inches in thickness.

   The metal base was placed on this floating body; first with m1 and then m2. Along the exact center of the fish tank, a metal support was included on which M was suspended with an inextensible thread tied to M from a two inch screw. Mass M was suspended above the tank’s water level (which was 12 cm deep), taking care that the center of mass of m1 and m2 coincide with that of M.

   Finally, a tape with centimeter graduation was adhered to the external face of the fish tank.

3. DESIGN

   When mass m1 approached mass M (from either side), gravitational repulsion occurred, such that the floating body experienced an acceleration that decreased steadily until it reached 2.54 meters; this was the point of zero interaction for m1.

   The floating body was then moved away and gravitational attraction was observed; again up to exactly R01=2.54 meters.

   Mass m2 was then experimented on, such that when this body was approached to M, gravitational repulsion was observed, similarly to the effect on m1, except that the acceleration effect was less apparent, reaching 0.73 meters as the point of zero interaction of m2.

   The floating body was then moved away and gravitational attraction was observed; until again it reached R02=0.73 meters.

   

   Fig.1 Gravitational Fish Tank

4. EXPERIMENT
5. RESULTS

1. 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)

2. THE UNIVERSAL GRAVITATION CONSTANT

   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 distance on the third Law of Kepler

The extrapolation of our results to the solar system conduced us to a information about masses of planets(6 ) identical to (9) based on the supposition that the angular momentum is a maximun planetary constant of the solar system .

There exist a second theoretical alternative to explain the results for the masses of the planets: That the ratio mass/velocity of every planet or satellite is a constant for our solar system.

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

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
• The gravitational well make us to be thusting more in their real existance than the Newton theory.
• True the gravitational well we can demostrate the three Laws of Kepler vality.

Adelaido Flores Montejano

Universidad Autónoma de Baja California

Tlahuac; México, D.F.