PROPOSED FOR THE REALIZATION OF A
EXPERIMENT THAT SERVE TO MEASURE THE
SPEED OF PROPAGATION OF THE
GRAVITATION ACCORDING TIDES
By Alfonso León Guillén Gómez
Santafé of Bogotá, September of 1993
WORKS OF THE AUTHOR:
was registered like “PROPOSED FOR THE REALIZATION OF A EXPERIMENT THAT SERVE TO
MEASURE THE SPEED OF PROPAGACION OF THE GRAVITATION” in the Special
Administrative Unit, National Direction of the Right of author, Office of
adventure of the discovery of
Nowadays, the physicists and astronomers have the possibility to carry out one of the most spectacular measurements, as is the speed with which the gravity spreads, so much by introducing an important experimental reference to theory about the gravity that without her seeks refuge in the speculation  as by permitting, crucially, to confront the theory of the Relativity, with respect to its explanation, of the phenomenon, of the constancy of the speed of light, relating to any system of reference, and that, according to that theory, not greater speeds should exist that speed of light, since would break with the law of the causality because would be possible to send messages to past time .
In the context of the previous theory, the majority of the physicists reckon that the speed of gravity is the same as speed of light, that is to say, in the vacuum of 300 thousand Km/s , but, also, the possibility exists that be greater, as is inferred of the formulation that did, the own Albert Einstein, of the dependence of speed of light of the gravity field, that according physical M. Abraham, is the bankruptcy of the theory of the Special Relativity, with its hypothesis of the constancy of the speed of light.
In the theory of the quantum gravity it is expected that in the distances of Planck, regions from 10-30 centimeter, greater speeds appear that speed of light .
On the other hand, in astronomy, so much in the theory of the stationary Universe  as in the estimation of the speed with which themselves separate some quasars and the radio sources that accompany them , the possibility of the greater existence of speeds has been considered that the speed of light although subsequently have been ruled out.
In the year of 1969 I proposed that the speed of gravity is greater that the speed of light, basing in the book "The Cosmos and its seven states", Moscow, 1967, of the Russian physicists M, Vasiliev and K. Staniukovich where they published that the gravity could be a state more of the matter than it expresses under the aspects of the gravitational graviton-wave of the field gravitational, able to transmute itself in the electromagnetic field or any other material state and in the paper that public in 1968 the Russian scientist Andrei Saharov in that he said that the gravity could come from changes that the presence of the matter in the Universe causes in zero point of the energy of the vacuum and, consequently, that the gravitation would be able to be a purely quantum phenomenon  and in another interpretation of the phenomenon of the independence of the speed of light, with respect to inertial systems of reference where the speed be measured, I conceived like the general situation of the speeds limits, that correspond about change in the forms of existence of the substance and the energy, that is to say, among the different material states; in these points, the transformation of the speeds of mobile, among different systems of reference, does not correspond to transformation of Galilei, but to transformations of the type of that of Lorentz , since in such "worlds", To different states, limit speeds exist for the communication of signs, as are the own speeds of each state or material form, that play equal role to speed of light in our universe .
In this work a proposal is presented to measure, experimentally, the speed of gravity or, at least, comparing it with that of light, based on the tides that the Sun causes in the Land.
The presentation that is done of the theory, that enables the execution of the experiment, is always in terms of simplifications, about how the phenomena occur that are treaties, but, valid as approximation to a scientific theory.
The development of the proposed solution here has like framework the following premises:
- Existence of the natural phenomenon of the tides caused by the action of the gravity of the Moon and of the Sun 
- Possibility to study such phenomenon under conditions of variation of the action of the gravity.
- The supposition that the gravity possesses a speed of propagation .
- The possibility to measure the delay with which communicates the variation of the gravity according phenomenon of the tides.
The gravity attraction of the Moon, the Sun, and the Land gives for result the forces that cause the tides. These forces are the difference among the gravity forces exercised by the Sun and the Moon on the Land and the centripetal forces that in the Land are originated in its orbit movements with respect to these stars (to see graphic 1).
The effect on the surface of the sea is that assume a configuration of double bulge, one in direction to Moon and the other bulge in opposition to this (to see graphic 2), that corresponds to a gravity field efficient, which consists of the gravity field Moon-Sun-Land more the modification by the dynamic effects of translation of the Land before referred , and by the rotation around Its own axis, these movements produce effects of inertia, such as the force of Coriolis, if intervene accelerations, that are communiqués to masses of water .
The horizontal component (to see graphic 3), of the resultant force, is the only force that produces the tides because it causes the horizontal displacement of water that is the wave of tide which has the same period of this resultant force  and its most maximum value is only the nine millionth splits of the gravity terrestrial force . The effect of the vertical component is to change, very slightly, the magnitude of the terrestrial gravity.
The phenomenon of the tides is basically the movement of a fluid submitted to a gravity field and to different astronomical movements that, besides, is modified by the size and form of the maritime basin, as well as, by its depth, frictions  and the atmospheric phenomena.
The effect of the gravity forces of the other stars in the tides is despicable, still the effect of Venus in which although reaches to produce very weak tides , only comes to represent, approximately, the .00006 of the force exercised by the Moon, in the Venus New, when more next phase of Venus is found to Land.
The main influence, in the phenomenon of the tides, is that of the Moon due to its proximity to our planet. Nevertheless, it is not the best option to measure the speed of gravity since if is equal to speed of light only will spend a little more than one second in travelling through the 382000 kilometers that, on the average, exist among the Land and the Moon.
The adequate experiment, for to measure the speed of gravity, would must base it on the effect of the Sun in the tides since is a little less than the half from that of the Moon, approximately .46 of the force exercised by this  and, on the other hand, is found to 150 million kilometers of the Land, delaying its light, approximately, 8 minutes and 31 seconds in arriving us.
The effect of the sun in the tides is found always mixed with the effect of the Moon, from the gravity force exercised by two bodies on a third, in any point, is the sum vectorial of the forces exercised individually by the two first . Such hypothesis is bases on the effects observations absence that permit to think, that some type of capture of the gravity of a star can be produced by another .
The main effects of the Sun in the tides are known as S2, solar semidiurnal effect that possesses a periodicity of 12 hours, and K1, lunisolar diurnal effect with periodicity of 23 hours, 56 minutes and 4 seconds (sidereal day) .
As a result of the movement of rotation of the Land, around their own axis, a same point on the Equator will pass first through an bulge of water and later through the other (to see graphic 2), and two tides will be produced for day, of magnitude more or less equal, that will reach the maximum height, since passes for the highest part of each bulge. On the other hand, a point something more to north or to south of the Equator will cross only a part of the bulge, that will have a smaller amplitude in the height of the tide .
The elliptic orbit of the Moon around the Land produces a variation of the gravity effect as result change of the distance among the perigee that is, approximately, of 357 thousand kilometers and the apogee, when its distance is close to 407 thousand kilometers (to see graphic 4). The period since a perigee to following one, known as anomalistic month, is of 27.55 days .
Likewise, the part of the generating forces of the tides produced by the Sun various from it is affected for the orbit elliptic of the Land around this (to see graphic 5). The periodicity corresponding is named anomalistic year, slightly greater that the year sidereal, because the line that unites the Land and the Sun, in the perigee, advances around the orbit of the Land 11 seconds of arch per year as average. The anomalistic year is of 365.26 days .
The forces that produce the tides, also, vary on account of effects of sicigias and quadrature, which are produced by the variation of the relative positions among the Sun and the Moon, what occurs with a periodicity, approximate, of 15 days  and are known as the result of the action combined of the solar and lunar tides .
The alive tides or sicigias are produced with intervals of 15 days during the full moon (opposition) and the novilunio (conjunction), when the Sun, the Moon and the Land are in straight line (to see graphics 6 and 7) and the generating forces of the tides reach a maximum, which causes at two o'clock high higher tides that occur daily , being especially observables in the Bay of Fundv to east of Canada . In said phases the Moon appears when the Sun does it, that is to say, at local time and this in the meridian of the observer in medium day and itself hidden, approximately, at 6 o'clock p.m. .In reality, due to effects done not yet you consider the tides of sicigias are something delayed with regard to moments of conjunction and opposition 
Also, each 15 days the Sun and the Moon are in quadrature (to see graphic 8) and due to that the generating forces of the tides operate in straight angles among itself, that is to say, that are 90 degrees out of phase, the dead tides are produced or tides of quadrature in which the amplitude of the tides is minimum .
When the Moon is in intermediate position among the quadrature and the conjunction or opposition, the crests of the tide is formed behind or ahead of the Moon (to see graphic 9 ), which causes that in the Land be seen before or after the passage from the Moon the high tide. They are named delayed tides .
The forces that produce the tides, also, vary on account of the declines of the flat defined by the paths of the Land when it is moved around the Sun, the plan of the orbit, of the Moon around the Land and the equatorial terrestrial flat. These are three different plans in the space.
The axis of the Land has an inclination such that the equatorial flat forms an angle of 23.5 degrees with the plan of the terrestrial orbit. Besides, the plan of the orbit of the Moon forms an angle of 5 degrees with the orbit of the Land .
The terrestrial axis conserves a constant direction in the space, inclined in an angle of 23.5 degrees regarding a designed line perpendicularly to flat of the terrestrial orbit. The equatorial terrestrial flat passes through the Sun in the positions of the equinoxes of spring and autumn (21 of March and 21 of September). But, in the positions of the solstice of summer (21 of June) its inclination is of 23.5 north degrees of latitude and in the solstice of winter (21 of December) its inclination is of 23.5 south degrees of latitude (to see graphic 10). Therefore, the line of the center of the forces of the solar tides varies 47 degrees on the terrestrial surface to extent that elapses the year .
In turn, the axis of the plan of the Moon moves 10 degrees among the north and the south, respect to equatorial terrestrial flat, during the month in a similar way to as it does the Sun during the year .
Other two effects of decline exist although are produced in more extensive interim.
One of them it is the lunar retrograde nodes which owes to that the intersection of the plan of the lunar orbit with the plan of the terrestrial orbit revolves with a period of 18.6 years, what causes two phases: in a the decline of the Moon reaches 28.5 degrees and in the other 18.5 degrees (23.5 degrees more or less 5 degrees). These phases happen each 9.3 years. The effect in the generating force of the lunar tide is that, in the first phase, various 57 degrees to north and to south on the terrestrial surface during the month. In the second phase, 9.3 years later, the north-south monthly variation is only of 37 degrees .
The other effect of decline is that of the precession of equinoxes to see graphic (11) that must itself to change lentissimo of the direction of the axis of rotation of the Land, which outline a cone whose angle measures 23.5 degrees and delay 26.000 years in giving a complete revolution (37).
The consequences of the declines are that two successive tides do not have the same amplitude, what is named diurnal inequality. So much the Sun as the Moon contribute, to this inequality, due displacement from the Equator toward the south and north hemispheres. The maximum amplitude semidiurnal of the tide will be produced when the Moon is in the Equator, the minimum when the Moon has the maximum decline (to see graphic 12). This variation is named biweekly lunar tide, since the oscillation of the decline complies in a tropic month of 27.32 days (a month tropic is the time among two successive passages from the Moon through the equatorial terrestrial flat) and the period of decline of the tide is the half, that is to say 13.66 days. For the Sun, the corresponding effect is the solar semi-annual tide .
The tide, from the perspective of its astronomical causes, comprises the combination of a certain partial or harmonic number of waves of the tide, classified as forced, by being constantly submitted to astronomical forces that generate them . These forces are related, as was seen previously, with:
- Changes in the distance of the Sun and the Moon
- Changes in the relative position of the Sun and the Moon
- Changes in the decline of the Sun and the Moon
Other waves exist of periodicity fixed although its contribution is small and can be omitted [40)
Those waves and its behavior in the time can be calculated with great precision. Nevertheless, the tide neither nor when is produced nor its amplitude generally coincide with the prediction based on its astronomical causes. This it is due to that is necessary to add the own real dynamic conditions of the movement of a fluid, modified by the maritime topology, by: the friction, by geostrophic effects originated by the rotation of the Land and by the atmospheric phenomena.
Nevertheless, for a locality given the hour of the high tide due to a determined partial tide will be produced in a definite and invariable number of hours before or after the passage of the Moon. Besides the ascent or descent degree will be always the same degree. Therefore the tide can be predicted for any instant, being basing on two constant: the degree of ascent and descent and the interval among the passage of the Moon and the high tide. To obtain these constant depends on the place of observation during a long time, and the real tide should be registered there perhaps 20 years in order that the long period tides remain included and the changes caused by chance, for example, the weather effects, they can average and eliminate. The real tide will be obtained, for each place, adding the partial tides that compose it .
The problem of prediction is simplified if the phenomenon of the terrestrial tides is considered which is simple, since the particles that form the Land only can vibrate like a sphere and the theory of such vibrations is acquaintance for a very long time and is known that the fundamental period of oscillation is of around 54 minutes, which eliminates the resonances and the complications that bring, since that the periods of the astronomical forces generators of the tides are superiors .
Therefore, the astronomical theory of the tides, named theory of the equilibrium, is more adequate to terrestrial tides that to tides on the sea. Although, not fully sufficient since in the terrestrial tides, also, some factors of distortion exist such the diurnal solar fluctuation east-west due to a differential warming-up of the Land by the Sun that causes an expansion-contraction and the inclination of the earth´s crust caused by the variations of the weight of the water that seem related to maritime tides in the coasts and neighboring places, especially if long geological failures exist as happens in great part of the territory of the Japan .
The terrestrial tides are declared in the variation in the intensity of the gravity and in the vertical direction, phenomenon fully established and about which there is not doubts some . Also, it is expectable that a real deformation of the Land as a result of the tensions to that is submitted.
The effect of the terrestrial tide if the Land went completely stiff would correspond only to forces of the tide that can be predicted through the theory of the equilibrium . Nevertheless, the Land possesses some level of elasticity that introduces uncertainty in the measurement.
terrestrial tides have been studied mainly in the
analysis, of the data of the experiment carried out in
In another experiment carried out in Marburgo, Germany, was measured the changes in magnitude and direction of the lunar semidiurnal tide, using two horizontal pendulums placed in straight angle, that can measure changes infinitesimals in the vertical one. The graphic 13 show the registration of such changes to extent that elapses the time
The exterior ellipse is a representation of 105 values calculated from the theory for a stiff Land, that is to say, with base only in the astronomical harmonics of origin. The experimental values represented in the interior ellipse are everywhere smaller, which indicates certain degree of elasticity of the Land. The numbers that appear in the ellipses represent lunar hours. As it can be observed a difference exists of near half an hour among the experimental value and the theoretical prediction.
So the difference of phase as the deflexion can vary enough with the place. Neither the axes of the ellipses coincide always so well as here .
The diverse experiments carried out, in the world about so maritime tides as terrestrial tides, never have had the purpose to measure the speed with which spreads the gravitation, but have sought to throw greater knowledge about the tides, fundamentally with the purpose of prediction. Also, some of the relating to solid tides there are satisfied objectives of geophysicists and geologists to gathered information about the configuration in the interior of the Land, as well as about their elasticity.
The tides are studied, by means of a technical mathematics, breaking down in their harmonics that, as was seen, are simple movements due to different astronomical causes and to other phenomenas, that permit, once known these harmonics, to reconstruct the tides for any date and hour .
According to the theory of the equilibrium the fundamental short period harmonics are four following:
- M2, lunar semidiurnal period of 12 hours, 25 minutes, 14 seconds.
- 01, diurnal lunar period of 25 hours, 49 minutes, 10 seconds.
- S2, solar period semidiurnal of 12 hours.
- K1, period lunisolar diurnal of 23 hours, 56 minutes, 4 seconds (sidereal day).
Considering, only, the astronomical effects can be calculated the amplitudes of all the previous harmonics for any latitude.
The vertical components vary with the latitude as is shown in the graphic 14. The diurnal forces of the tide do not have vertical component in the Equator while the semidiurnals reach there the maximum. As it can be concluded, to study the periodicities the optimum thing is to carry out the observations for the diurnal harmonics, O1 and K1, to 45 degrees of latitude and for the semidiurnals, M2 and S2 near the Equator .
The horizontal components differ in their north-south effects and east-west effects.
The graphic 15 show the variations of the north-south horizontal components with the latitude. The diurnal forces of the tide have their most negative and positive maximums in the Equator and in the poles; the semidiurnals are zero .
The Graphic 16 show the variations of the horizontal components east-west with the latitude. Again the two periodicities are opposite. M2 is the harmonic main in all the latitude, except in the high .
The variations of the vertical components are measured with the gravimeter. The most maximum effect of the harmonic M2, in the Equator, corresponds to an acceleration of the gravity of 7.3*10-5 centimeters by second2 .
The variations of the horizontal components are measured with an instrument as the horizontal pendulum that serves to establish inclinations, that is to say, variations in the direction of the plumb line. The most maximum value for the north-south components is that of the harmonic K1 and represents an inclination of around + or - 0.01 second. For the component east-west,M2, reaches a maximum of 0.016 second. If two pendulums are used, in straight angles among S1, the effects due to north-south components and east-west components can be detected and to be measured .
The main effects that can exercise the forces of the tide on the solid part of the Land are two:
- A change in the effective magnitude of the gravity terrestrial force that can be translated in a vertical displacement of the surface of the Land.
- A variation in the apparent direction of the terrestrial gravity force can also produce deformation.
Some of the physical consequences observables are:
- Reduction of the amplitude of the maritime tides by the protuberance in the fund of the sea caused by the solid tides.
- Periodic deviations in the readings of the gravimeter.
- Inclination of the earth´s crust with regard to elastic distortions of the crust, medibles with the horizontal pendulum. They can take the form of tensions and expansions and contractions of its volume .
One of the long period harmonics is the semi-annual solar period that is consequence of the elliptic orbit of the Land around the Sun (to see graphic 5), which is represented by L2 and its extreme values correspond to perihelion, when the Land is near 147.1 million kilometers of the Sun (31 of December) and to aphelion when the Land is more distant of the Sun, near 152.1 million kilometers (1 Of July) .
The periodicity is the anomalistic year during which the gravity force of the Sun, generating of the tide L2, various and can have effects observables, since the changes in the distance affect the forces of the tides according to law of the inverse bucket .
The change produced in the acceleration of the gravity, among the perihelion and the aphelion in the Equator, is of 3 millionths of centimeters by second2, that is to say, 24.3 smaller times to it caused by the vertical harmonic component M2, is the one that has the most maximum effect.
Nevertheless, the so negligible effect of the variation caused by the vertical component of the harmonic L2, in the acceleration of the gravity, can be measured by the gravimeter given the extraordinary sensibility of this, which toward 1988 permitted to register variations of the gravity terrestrial field of, at least, a part in thousand million that is to say, from 10-9 parts of g (980 centimeters by second2) .
The variation, due to eccentricity of the terrestrial orbit, of the gravity force exercised by the Sun, on the Land can be drawn in a map , during where the two following periods will be represented:
- T1 in which during the interim covers among July 1 (aphelion) and December 31 (perihelion) the distance of the Land respect Sun diminishes in 5 million kilometers and, therefore, the generating force of the tide L2 is increased continuously until reaching, for the vertical component in the latitude of the Equator, its most maximum value of approximately, 3.3*10-5 centimeter by second2 and, also, the most maximum value for the horizontal component, that in the latitude of 45 degrees is of 2.5*10-5 centimeter by second 2.
- T2 in which during the interim covers among December 31 (perihelion) and July 1 (aphelion) the distance of the Land respect Sun enlarges in 5 million kilometers and the generating force of the tide L2 diminishes continuously until reaching its most minimum values which, approximately, are: for the vertical component, in the latitude of the Equator, 3*10-5 centimeter by second2 and for the horizontal component, in the latitude of 45 degrees, of 2.3*10-5 centimeter2.
In the phase T1 enlarges + 3, in the vertical axis, and + 2,In the horizontal axis, millionths of centimeter by second2 while in the phase T2 diminishes said quantities.
The previous data were calculated with base in the following formulae:
-Force by unit of mass according to vertical axis = G Mr * (cos2 z -1) / d3
- It Forces by unit of mass according to horizontal axis = G (-3Mr) sin 2Z / 2d3
G is the constant gravitation.
M is the mass of the star that causes the generational force of the tide
d is the distance of its center to Land.
Z is the geocentric zenithal distance.
R is the distance of the unit of mass respect central of the Land.
In the graphic 17 the variation of the terrestrial gravity is shown, in the Equator, and of the force, exactly, of the tide, to 45 degrees of latitude, during the periods T1 and T2.
Extensively it is admitted and verified that the wave of tide is not produced instantly, consistent fact physically in the difference of phase among the generating forces of the tides and the harmonics because in the formulae of prediction of the tides is represented for the value of delay K  and that was indicated before, when the experiment was presented carried out in Marburqo about the lunar semidiurnal tide M2 (to see graphic 13), where there is an half an hour phase difference.
The delay K owes to structures of the Land and of the oceans and its various values with the place, as a result of the differences of such structures. Nevertheless, it is omitted and ignores the existence of the other type of delay that is the attributable delay to speed of gravity, that I will name K0, not significant in the harmonics of periodicity short, that are the ones that have been studied especially, but if in the solar semi-annual tide, L2, since the generational force, of this tide, has to travel through the 150 million kilometers, that average, exist among the Sun and the Land.
The delay, K0, has, also, to be declared like a difference of phase in time among the phase predicted theoretically based on the terrestrial orbit around the Sun, and the phase experimentally obtained for the harmonic L2. Such difference is the interim that delays in being transmitted the variation of the gravity, caused by the change of distance among the perihelion and the aphelion, and which should correspond to, approximately, 8 minutes and 31 seconds that is the time that the gravity of the Sun would delay in arriving us if this spreads with a speed equal than speed of light, according to belief of the majority of physicists. If, on the other hand, as the theoreticians and experimental studious of the tides have done to ignore K0, that is the same thing that to suppose it with value closed to zero, the gravity would spread among the Sun and the Land instantly as prerelativists physicists believed. It is the key, that exists in the solar tides, for to find the speed of gravity, and that up to now has remained hidden.
An experiment can be carried out of the type of that of Marburgo, although for to register the variations of the generational force of the terrestrial solar tide of semi-annual periodicity L2.
The reason for to elect the terrestrial harmonic L2 and not the maritime L2 is that this has one closed behavior to predicted by the theory of the equilibrium.
Such variations can be observed and registered during the periods T1 and T2, although, only during the instants in which the variations in the generational force of the tide are produced that the present instruments of measurement, gravimeter, and horizontal pendulum can register. It excludes the options to carry out experiments based on observations of interim, exactly as that of Marburqo since these observations have to be punctual and restricted only to said moments.
The experiments to measure the variations in the vertical component of L2, that are measured with the gravimeter (to see graphic 18); they should be performed in stations situated on the Equator. If it opts for the horizontal component of L2 that is measured with two pendulums placed in straight angle (to see graphics 19 and 20), the experiments should be should carry out in stations situated to 45 degrees of latitude. This with the objective to count on the most maximum values that reach said components (to see graphic 21).
To carry out the experiments, in agreement to state of the art and the technology that there was to height of 1988, counts on gravimeters that permit to register variations of the gravity field from 10-9 parts of g and with pendulums that register inclinations of the vertical axis of 0.0008 seconds .
To select the observations, that they will be taken register in the experiments, the calendar of the moments should be built in which the observations about the variations of the generational harmonic force can be performed, according to the capacity of measurement. For it, the exact calculation of the positions should be performed, of the Land according to their elliptic orbit around the Sun, discriminated in units during the day, hour, minute and second, of those moments in which the variations occur that can be measured. In the Table 1, an example of a calendar, aforesaid in days is presented, of the moments in which the variations are produced that are medibles of the vertical harmonic component L2, with base an in thick calculation of the dates in which said variations occur.
30 August...30 October...31 December..1 March......30 April.....1 July
30 to 31........31 to 32.......32 to 33...........33 to 32......32 to 31....31 to 30
In the upper row, of the table, the dates appear. In the second row the values of the force by unit of mass according to vertical generational force of L2, aforesaid in millionths of centimeter by second2. And in the lowest row the value of the variation, which is of one millionth of centimeter by second2 that, in the terms of the terrestrial force of gravity, represents one thousand millionth splits of this, value that is, exactly, the most minimum value that can detect the gravimeter.
For to register an observation the instrument of measurement should be found operating in the station with a sufficient advance such that cover the period inside which the variation occurs. In the example, if the observation selected is that of August 30 the gravimeter should be in the station since July 1.
It is convenient to observe that in the interim among the moments in which are performed the observations, in the instrument of measurement is maintained constant the value of the component, of the generational force of L2, holds to the experiment (to see graphic 22). Thus, in the example among July 1 and August 30 the gravimeter registers the value of 30 millionths of centimeter by second2. Only it will pass to value of 31 millionths to when be completed the variation of a millionth, which occurs 30 of August.
The experiment should be carried out based on several observations taken in diverse years, in order to eliminate, by means of averages, the spurious effects.
Prior, to the execution of an experiment it should be to know for the places, where the stations be located, the values of the delay K, due to terrestrial structure of the place.
That is to say, those places should be preferred for which an estimation exists of K; otherwise, additionally and before, will be required to carry out experiments of the type M2 to calculate K.
It is maybe to apply the following procedure:
- To estimate the values of the component, vertical or horizontal of the harmonic L2, chosen according to experiment that be going to carry out, under the supposition that the Land is totally stiff, that is to say, according to theory of the equilibrium that only considers the astronomical causes of the tides. Such estimation should be done during the periods T1 or T2, for those moments that, in agreement to calendar, they have been selected to observe.
In the example of the Table 1, the values of the vertical component are the following;
30 August...30 October...31 December..1 March......30 April.....1 July
30 to 31........31 to 32.......32 to 33...........33 to 32......32 to 31....31 to 30
- To register the dates, of the observations that intervene in the experiment, in which the values expected were produced specified in hours, minutes and second. In the example, the date will be August 30 at 15 o'clock hours, 38 minutes, 31 seconds, under the supposition that in a gravimeter, placed in an experimental station in Marburgo, was registered, in such moment, the value expected, for August 30, of the 31 millionths of centimeter by second2, of the vertical component of the generational force of L2.
- To calculate the difference horary among the experimental date and that of the theoretical prediction, according to calendar, for each one of the observations carried out. For example, under the supposition that in the calendar the value of the 31 millionths of centimeter by second2, of the vertical component of L2, it is expected that occur August 30 at 15 o'clock hours, or minutes the difference horary is 38 minutes and 31 seconds.
- To estimate the delay K0 = difference horary obtained in the previous step - K. In the example, K0 is 8 minutes and 31 seconds, since, in Marburgo, K is equal to 30 minutes, according to experiment carried out there with M2.
- To calculate the speed of the gravity = distance among the Land and the Sun / K0. In the example, that speed is equal that speed of light.
Without place to doubts, another option for to reckon the speed of gravity is that of establishing, experimentally, the evolution of the lunisolar sinodic harmonic of semi month period, Msf, pertaining to tides of sicigias and quadrature, that during the month occurs, and result of the changes in the relative position among the Moon and the Sun (to see graphics 6 to 8). The lunar sinodic revolution is the lapse between two equal relative consecutive positions of the Sun-Land-Moon system. The sinodic revolution governs the lunar phases and the eclipses.
If in a specific place the Moon passes for the meridian to noon will occupy, in new Moon, the relative position k0 and the high tide will be in c0 and c4 that coincide with them produced by the Sun, the same thing will happen when the Moon this in k4, full Moon, these are the tides of sicigias, the two highest tides than occur during the lunar month. The contrary thing occurs when the Moon is found in k2, first quart, or k6, last quart, then, the crests of the lunar wave are formed in c2 or c6 and the breasts in c0 or c4, exactly it opposed of what occurs with the solar wave, consequently, the tides of quadrature are produced that it is two more intense low tides of the lunar month (graphic 23).
The extreme values of Msf are produced among the high tide of sicigia, most maximum value, when is equal to sum of the effects of the two stars, that is, of the harmonic M2, lunar main, and S2, solar main, and the low tide of quadrature, most minimum value, when is equal than S2 - M2. Consequently, the generational force of the harmonic Msf various, among the high tide and the low tide in the vertical component, cerca 14.4*10-5 of centimeter by second2, and in the horizontal component, near 10.8*10-5 of centimeter by second2. Also, the values of Msf are maximums in the Equator for the vertical component and to 45 degrees of latitude for the horizontal component (to see graphics 24 and 25).
The complete evolution during the month of Msf presents four periods the first period, T1, is the high tide of new Moon. The second period, T2, a week occurs then and is the low tide of first quart. The third period, T3, a week occurs later and is the high tide of full Moon. The fourth period, T4, occurs in the last week and is the low tide of the last quart (to see graphic 26). In consequence, to observe the effect of the variation of Msf, the most minimum interim is of a week.
It is important to notify that the generational force of Msf has during the sicigias or the quadrature another type of variation, which is of daily period and the movement of the Land around its own axis causes it (to see graphic 27). Such variation does not interest the experiment to measure the speed of gravity, since the distances in which occurs are despicable by being confined to only 12.7 thousand kilometers that is the length of the diameter of the Land. But it is very important considers in order to determine that the values expected of the moments in which occurs Msf, valid to carry out the true experiment, they should coincide when the Moon passes, exactly, by the meridian of the observer.
Due to that the weekly variation of Msf represents, approximately, ten millionth splits of the force of gravity easily can measure and, therefore, constitutes a good option to carry out an experiment of the type M2 of Marburgo. But, it has the disadvantage that the difference of phase among the theoretical layout and the experimental layout, caused by the delay K0, will be only a little more than one second that is the time that delays the lunar gravity in arriving to Land, if this spreads with the speed of light.
The graphics, except the 5, 17 AND 21 to 27, they were taken of Clancy Edward, The tides press of the Land. The graphics 23 and 27 originate of the General Encyclopaedia of the sea. Volume 5.
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