THEORETICAL PROCEDURE

Transcription

1 1 UNIVERSAL GRAVITATIONAL CONSTANT: ITS EXACT VALUE INTERNATIONAL SYSTEM OF UNITS G = x N m kg G = x m 3 kg 1 s UNIVERSAL GRAVITATIONAL CONSTANT: ITS EXACT VALUE RELATIVISTIC QUANTUM MECHANICS G = x 10-8 cm/s This value of the universal gravitational constant is exact. THEORETICAL PROCEDURE UNIVERSAL GRAVITATIONAL CONSTAN: ITS EXACT VALUE How to determine the exact value of the universal gravitational constant ( G ) The procedure is mathematical theory. The mathematical calculation is so accurate and clear that no practical procedure is required: mathematics is an exact science. Theoretically, it consists of accelerating the particle from a velocity v o = 0 until the particle reaches the velocity vn, and due to the change in the quantum energy state the particle experiences, the exact value of the gravitational constant (G) can be mathematically determined. To obtain the theoretically accurate value of the gravitational constan (G), the relativistic quantum law of universal gravitation, the energy of formation or disintegration of the graviton, the variation of mass with velocity and Newton's law of universal gravitation are considered. The mathematical expressions are: ( G / K' ) = ( 1 / c ) (1) o bien G. c = K' () Equations (1) and () are the mathematical expressions of the relativistic quantum law of universal gravitation. In these equations (1) and (), we know only the exact value of the speed of light; but not the units it should be measured in. The value and

2 measurement units of G are not known, and it is known only that K' takes the units of G and c. The mathematical expression for the energy of formation or disintegration of the graviton is: E g = m g c = r g c (3) Equation (3) states that the graviton mass m g is equal to its radius squared, i.e. ( m g = r g ). The graviton is contracted accelerated 3-dimensional space ( space-time, pure energy). When any particle of mass m o changes its speed from v o to a higher value, the particle increases its mass from m o to m according to its velocity. The mathematical expression known to all that relates mass with velocity is: where, m o, mass of the particle at rest. m = m o / ( 1 - (v / c ) ) 1/ (4) m, mass of the particle when moving with velocity v. v, velocity at which the particle moves. c, velocity of light. The mathematical expression of Newton's law of universal gravitation to establish equivalences between systems of units is: where, F, force of attraction between two masses. G, the universal gravitational constant. M, m, masses of the particles considered. G M m F = (5) R R, distance between two particles, measured from the respective centres of gravity. The mathematical expression of Newton's law of universal gravitation in

3 3 relativistic quantum mechanics is as follows: K' m 1 m F = (6) c R where, F, force of attraction between two masses. K', relativistic quantum constan. c, speed of light. m 1, m, masses of the particles considered. R, distance between two particles, measured from the respective centres of gravity. The Units of measurement corresponding to equation (5), expressed in space-time Units, the CGS System of Units and the International System of Units are as follows: Units, space-time: Gue-t x 1cm x 1cm Gue-t x 1cm x 1cm Gue-t x 1cm = = = 1 (7) 1cm 3 /s x (1cm) 1cm x 1cm/s x (1cm) 1cm/s x (1cm) where, Gue-t, universal gravitational constant expressed in space-time Units. 1cm 3 /s, Units of force, expressed in space-time Units. Units, CGS system: Gcgs x 1g x 1g Gcgs x 1g x 1g Gcgs x 1g = = = 1 (8) 1dyne x (1 cm) 1g x 1 cm/s x (1 cm) 1 cm/s x (1 cm) where, Gcgs, universal gravitational constan expressed in CGS Units. 1 dyne, Unit of force, expressed in CGS Units. 1dyne = 1g x 1 cm/s.

4 4 Units, International System: GSI x 1kg x 1kg GSI x 1kg x 1kg GSI x 1kg = = = 1 (9) 1N x (1m) 1kg x 1m/s x (1m) 1m/s x (1m) where, GSI, universal gravitational constan expressed in International System Units. 1N, Unit of force, expressed in International System Units 1N = 1Newton = 1kg x 1m/s. The equivalente ratio between space-time Units, CGS System Units and the International System of Units is: GSI x 1 kg Gue-t x 1,000 cm Gcgs x 1,000 g = = = 1 m/s x (1 m) 100 cm/s x (100 cm) 100 cm/s x (100 cm) Gue-t Gcgs = = (10) 1,000 cm/s 1,000 cm/s Gue-t = Gcgs = 1,000 cm/s x GSI (11) Gcgs Gue-t GSI = = (1) 1,000 cm/s 1,000 cm/s The mathematical expressions, equations (1), (), (3), (4) and (6), are evident mathematical equations related to the speed of light which, in turn, is related to mass and energy. Gravity and all entities in the universe are the result of a particular state in which energy is found, they are energy and are transmitted and interact through energy; that is, through accelerated 3-dimensional space (they are their own energy in a given state), and are caused by free or forced accelerate 3-dimensional space (by energy). Determination of space-time Units, in which the speed of light (c) should be measured in equations (1) and (), relativistic quantum mechanics. Suppose a particle of mass m g (corresponds to the mass of the graviton), whose

5 5 geometrical shape is considered spherical and r g is the distance between its centre of gravity and any of the infinite points forming the spherical particle surface. The intensity of the gravitational field at a PA located on the spherical surface of the particle is: g AVo = g AVo g = ( m g / c r g ) (13) where, g AVo, the gravitational field intensity caused by the particle at the point considered as PA when the particle is at rest with respect to the chosen coordinate system, that is, v o = 0. g AVo g, the gravitational field intensity caused by the graviton at the point considered as PA located on the spherical surface of the graviton. g AVo g = ( G / K' ) = ( 1 / c ), the gravitational field of attraction units caused by the graviton, which causes or leads to the acceleration g AVo g. m g, mass of the graviton. r g, radius of the graviton. c, speed of light. If the particle is at rest, its velocity (with respect to a chosen coordinate system) is zero, i.e. v o = 0. For this velocity, v o, the gravitational field strength caused by the particle at point PA is: g AVo = g AVo g m g / [ r g ( 1 - ( v o / c ) ) 1/ ] (14) Because the velocity v o = 0, equation (14) becomes: g AVo = g AVo g = ( m g / c r g ) (15) If the particle is at rest with respect to the chosen coordinate system, the velocity v o is zero and, according to the relativistic quantum universal gravitation law g AVo = g AVo g = ( G / K' ) = ( 1 / c ).

6 6 speed vn. By a mechanical process, the particle of mass m g is accelerated up to the If a constant force Fn is applied to the particle of mass, m g, let us suppose it moves at a constant velocity of vn. The gravitational field created by the particle at point PA is: g AVn = g AVo g m g / [ r g ( 1 - ( vn / c ) ) 1/ ] (16) where, g AVn is the gravitational field strength caused by the particle when it moves with speed vn. No variation in the radius r g of the particle at velocity has been assumed, as this is not necessary. It is assumed that the distance from the centre of gravity of the particle to the point considered PA remains constant, whatever speed the particle moves. Equations (14) and (16) become: g AVo g c = [( r g 4 g AVo c ) / m g ] - [( r g 4 g AVo v o ) / m g ] (17) g AVo g c = [( r g 4 g AVn c ) / m g ] - [( r g 4 g AVn vn ) / m g ] (18) Considering that the energy of formation or disintegration of the graviton is: E g = m g c = r g c In equations (17) and (18), ( r 4 g / m g ) = 1. Simplifying and ordering the terms, equations (17) and (18) become: g AVo g c = g AVo g AVo g c = g AVn ( c - v o ) (19) ( c - vn ) (0) Equation (0) calculates the velocity vn via the theoretical mechanical efficiency equations, h. Dividing the two sides of equations (19) and (0) by squared gives: c, and extracting the

7 7 g AVo g = g AVo ( 1 - ( v o / c ) ) 1/ = g AVo sin α o (1) g AVo g = g AVn ( 1 - ( vn / c ) ) 1/ = g AVn sin α n () Using the theoretical mechanical efficiency, h, equation () mathematically reveals the natural Units the speed of light in relativistic quantum mechanics should be measured in. The theoretical mechanical efficiency, h, is the relationship between the gravitational field strength g AVn caused by the particle at point PA when it moves with velocity vn, and the gravitational field strength g AVo caused by the particle at point PA when it is at rest, v o = 0. The theoretical mechanical efficiency, h, can also be defined as the relationship between the quantum energy state when the particle moves velocity vn, and the quantum energy state when the particle is at rest, v o = 0. For a variable speed between minimum and maximum speed and a minimum speed other than zero, the theoretical mechanical performance, h, is defined as the relationship between the final and initial space-times (energies), when undergoing a complete cycle; considering the states of contraction and expansion of space and time (space-time) in the realization of the complete cycle. h = ( g AVn / g AVo ) = ( g AVn / g AVo g ) (3) Substituting g AVo and g AVn in equation (3) by their respective values (equations 15 and 16), the theoretical mechanical efficiency, h, is: h = ( g AVn / g AVo ) = ( g AVn / g AVo g ) = = [ m g / ( ( c r g ) (1 - ( vn / c ) ) 1/ )] / [ m g / ( c r g )] = = [ 1 / (1 - (vn / c ) ) 1/ ] = ( 1 / sin α n ) (4) Therefore,: g AVo = g AVo g = g AVn sin α n (5)

8 8 Equation (4) is resolved: When the particle reaches the speed vn, the gravitational field strength created by the particle at the supposed point PA is g AVn = 1 and g AVo = g AVo g = sin α n ; since g AVo g = ( 1 / c ), and equal to sin α n, and g AVn = 1, substituting these values in equation (0) gives: 1 = 1 ( c - vn ) (6) where, From equation (6): vn = ( c - 1 ) (7) vn = ( c - 1 ) 1/ (8) Equation (8) allows the value of the speed vn to be calculated. Velocity vn is the minimum speed at which the accelerate 3-dimensional space behaves like a material particle, causing a gravitational field attraction of value ( G / K' ) = ( 1 / c ). Let's consider the same particle of mass m g which has been accelerated up to the speed vn. Looking at equation (4), the theoretical mechanical performance equation, and that: cos α n + sin α n = 1 (9) From equation (9): sin α n = 1 - cos α n (30) Figure 1 represents the ETG (particle) moving with velocity vn. ( G / K' ) = ( 1 / c ) c sin α n a α n vn c b ETG cos α n figure 1

9 9 Considering the mathematical expression of the relativistic quantum law of universal gravitation, the triangle abc (figure 1) shows: G 1 = = sin α n (31) K' c vn cos α n = (3) c From triangle abc (figure 1), it is deduced that: cos α n = ( vn / c ) (33) sin α n = ( G / K' ) = ( 1 / c ) (34) ( vn / c ) + ( G / K' ) = 1 (35) or ( vn / c ) + ( 1 / c ) = 1 (36) From equation () we know: sin α n = (1 - (vn / c )) 1/. For a constant speed vn, the angle α n is constant, regardless of the Unit of measure taken for vn and c. According to equation () for the angle α n, g AVn = 1, and g AVo = g AVo g, the units of the gravitational field of attraction or quantum energy state of the graviton, i.e. = ( G / K' ) = ( 1 / c ). sin α n = (1 - (vn / c ) ) 1/ = constant (37) Substituting the value vn obtained (equation 7) in equation (37) and performing the operation, its exact value is known due to the speed of light (c). sin α n = (1 - (vn / c )) 1/ = [1 - (( c - 1) / c ) ] 1/ = constant cos α n = ( vn / c ) = (( c - 1) / c ) = sin α n = (1 - (vn / c )) 1/ = ( ) 1/ = = ( ) 1/ = x 10 11, from

10 10 where the angle α n is: α n = arc sin ( x ) = x This angle α n is constant, regardless of the Unit of measurement taken for vn and c. It is the same if vn and c are expressed in centimeters, meters, kilometers or any other multiples or divisors of these. Knowing that g AVo g = ( 1 / c ), expressing the speed of light ( c ) in centimeters per second via the equation (5), where g AVo = g AVo g = g AVn sin α n, gives the following after substitution: ( 1 / ccm/s ) = sin α n = x = constant (38) Only ( 1 / ccm/s ), expressing the speed of light in centimeters per second (cm/s), gives x Therefore, in relativistic quantum mechanics, speed of light is measured in centimeters per second (cm/s), and the centimeter and second are the natural physical measurement Units (space-time Units). In equations (1) and (), the speed of light ( c ) is expressed in centimeters per second (cm/s). Considering the mathematical expression of the universal gravitation relativistic quantum law and knowing the speed of light is expressed in centimeters ( ccm/s ), the following is true: G 1 = (39) K' ccm/s Equation (39) is a general equation for all System of Units. It does not mean in this equation that G and K' correspond to a particular System of Units. G 1 1 = = = x s/cm (40) K' ccm/s 9,979,45,800 cm/s ( G / K' ) = ( 1 / ccm/s ) are units of the gravitational field of attraction or quantum energy state which causes the graviton. The units of the gravitational field of attraction are those causing the acceleration. The quantum energy state of the graviton is equal to the amount of energy of formation or disintegration of the graviton.

11 11 From relativistic quantum mechanics, the energy of formation or disintegration of a graviton is expressed in Units of space-time in equation (3): ( cm cm /s ) = ( cm cm cm/s ) = cm 3 cm/s (41) Energy is accelerated three-dimensional space (space-time). Accelerated 3-dimensional spaces (energy, space-time) cause accelerations; thus, accelerated 3-dimensional space is energy (space-time). Accelerations caused by accelerated 3-dimensional space when they interact, whether free or bound, may be treated algebraically: added, subtracted, partially or entirely canceled and give rise to one or other accelerated 3-dimensional spaces of similar or different properties. Determining the relative value of the relativistic quantum constant K' : Consider particles of masses, m g and m g ' ( gravitons); the value of the mass or their distance from each other do not matter. The units of the gravitational field of attraction caused by the particle of mass m g cause the acceleration of the particle of mass m g ', and the units of the gravitational field of attraction caused by the particle of mass m g ' cause the acceleration of the particle of mass m g. The acceleration caused by both particles is the sum of the acceleration or the units of gravitational field of attraction caused by both particles, namely: G G G + = (4) K' K' K' = (43) ccm/s ccm/s ccm/s The numerical and relative values of the relativistic quantum constant K' deduced from equations (4) and (43): are Relative numerical value of K' = (44) In equations (39) and (40), the speed of light ( c ) is an absolute value; we know the value and the Units it is measured in, and the values of the unknowns G and K' are

12 1 relative. Thus, the value and measurement Units of G and K' need to be solved, so their values are absolute. The relativistic quantum constant K' takes the Units of G and c; therefore, the numerical and relative value of the relativistic quantum constant K' is as follows from the calculation: Numerical and relative value K' = cm/s (45) Because equation (3) expresses the speed of light in centimeters per second, it can only accept the gram as a unit of mass, or squared centimeters, in place of the gram. The radius of a graviton is a function of the speed of light, r g = m g = ( E g / c ) = ( 1 / c 3 ). These natural Units of measurement in centimeters, seconds and square centimeters ( cm = g ) are space-time Units and are identical to those used in the CGS system of Units. For any system of Units we want to adopt or conceive, we only have to transform the adopted or devised system Units to space-time Units. If we want to express the gravitational constant (G) Units in those corresponding to the International System, we only need to know the Units of mass, space and time and establish the equivalence relationship with natural system or CGS system of Units, for equivalent equations (10), (11) and (1). In equation (39), we must consider that the sped of light has to be measurable in other Units or multiples or divisors of the centimeter. If we say that a signal or body is moving with a speed of 1 cm/second, we can also say that the signal or body is travelling at a speed of 10 mm/second or 0.01 meters/second. The signal or body moves with the same speed and travels through equal spaces in equal times, and the speed of the signal or body is expressed in the Units we want to express them in. Therefore: G 1 1 = = (46) K' ccm/s 100 x cm/s Equation (46) includes the values the equivalence of G and K' (equation 1). After substitution:

13 13 K' K' Gue-t Gcgs GSI = = = = (47) ccm/s 100 x cm/s 1,000 cm/s 1,000 cm/s In equation (47), the value corresponding to K' is the relative value (equation 45). K' acquires the absolute value with the measurement Units of G and c which they have to be expressed in. cm/s cm/s Gue-t Gcgs GSI = = = = (48) ccm/s 100 x cm/s 1,000 cm/s 1,000 cm/s The absolute value of the relativistic quantum constants and the universal gravitational constant G are deduced from equation (48) which correspond to the system of Units: space-time, CGS and International system of Units. Absolute value of the relativistic quantum constant: space-time Units The absolute value of the relativistic quantum constant K' expressed in space-time Units is: K' = Kue-t = Gue-t x ccm/s = (1,000 cm/s x cm/s ) =,000 cm /s 3 Absolute value of the relativistic quantum constant: CGS Units The absolute value of the relativistic quantum constant K' expressed in CGS Units and space-time Units is: dyne x cm dyne x cm 3 K' = Kcgs = Gcgs x ccm/s = 1,000 x cm/s =,000 = g g x s = (1,000 cm/s x cm/s ) =,000 cm /s 3 Absolute value of the relativistic quantum constant: International System Units The absolute value of the relativistic quantum constant K' expressed in International System Units and space-time Units is:

14 14 m 3 m 4 K' = KSI = GSI x cm/s = 0.0 x m/s = 0.0 =,000 cm /s 3 s x kg s 3 x kg RELATIVISTIC QUANTUM MECHANICS, ABSOLUTE VALUE OF UNIVERSAL GRAVITATION CONSTANT G. In relativistic quantum mechanics, if the speed of light (c) is expressed in centimeters per second, ccm/s = 9,979,45,800 cm/s, the universal gravitational constant, Gue-t, is: Kue-t G = Gue-t = = [ (1,000 cm/s x cm/s ) / ccm/s ] = ccm/s = [(,000 cm /s 3 ) / (9,979,45,800 cm/s )] = = x 10-8 cm/s CGS SYSTEM OF UNITS: ABSOLUTE VALUE OF GRAVITATIONAL CONSTANT G. In the CGS system of Units, if the speed of light (c) is expressed in centimeters per second, ccm/s = 9,979,45,800 cm/s, the universal gravitational constant, Gcgs, is: Kcgs G = Gcgs = = [(,000 dyne cm 3 g s 1 ) / (9,979,45,800 cm/s)] = ccm/s = x 10-8 dyne cm g If the Units, dyne cm g, which correspond to the CGS system of Units are equivalent in space-time Units to cm/s, the universal gravitational constant, ( G = Gcgs ), is: G = Gcgs = ( Kcgs / ccm/s ) = [(,000 dyne cm 3 g s 1 ) / (9,979,45,800 cm/s)] =

15 15 = [(1,000 cm/s x cm/s ) / (9,979,45,800 cm/s)] = = [(,000 cm /s 3 ) / (9,979,45,800 cm/s )] = = x 10-8 cm/s INTERNATIONAL SYSTEM OF UNITS: GRAVITATIONAL CONSTANT G. ABSOLUTE VALUE OF In the International System of Units, if the speed of light (c) is expressed in meters per second, cm/s = 99,79,458 m/s, the universal gravitational constant GSI, is: KSI G = GSI = = [( 0.0 m 4 kg 1 s 3 ) / ( 99,79,458 m/s )] = cm/s = x m 3 kg 1 s If the Units m 3 kg 1 s, which correspond to the International System of Units are equivalent in space-time Units to 1,000 cm/s, the universal gravitational constant, ( G = GSI ), is: G = GSI = x 10-8 cm/s The universal gravitational constant, G, is an acceleration for all systems of Units in the universe and is expressed in centimeters per second square (cm/s ), the natural space-time Units corresponding to acceleration. UNITS FOR GRAVITATIONAL FIELD OF ATTRACTION The units for the gravitational field of attraction or quantum energy state is a constant, with the natural measurement Units for this constant being all existing Unit System in the universe, the second per centimeter (s/cm). For all Units Systems, the Units for gravitational field of attraction or quantum energy state are a constant, and are unique, unchanging and irreplaceable. The Units of the gravitational field of attraction or quantum energy state are measured in natural space-time Units, which are seconds per centimeter (s/cm).

16 16 Units for gravitational field of attraction, or quantum energy state, relativistic quantum mechanics ( G / K' ) = ( 1 / ccm/s ): Measurement Units, seconds per centimeter (s/cm). ( G / K' ) = ( Gue-t / Kue-t ) = ( 1 / ccm/s ) = = ( x 10 8 cm/s ) / ( 1,000 cm/s x cm/s ) = = x s/cm Units for gravitational field of attraction, or quantum energy state, CGS System ( G / K' ) = ( Gcgs / Kcgs ) = ( 1 / ccm/s ): Measurement Units, seconds per centimeter (s/cm). ( G / K' ) = ( Gcgs / Kcgs ) = ( 1 / ccm/s ) = x 10 8 dyne cm g = =,000 dyne cm 3 g s 1 = x s/cm Units for gravitational field of attraction, or quantum energy state, International System ( G / K' ) = ( GSI / KSI ) = ( 1 / ccm/s ): Measurement Units, seconds per centimeter (s/cm). ( G / K' ) = ( GSI / KSI ) = ( 1 / ccm/s ) = = [( x m 3 kg 1 s ) / ( ( cm/s ) ( m 3 kg 1 s )) ] = = x s/cm These values obtained for the universal gravitational constant are mathematically exact. Thus, equations (1), (), (3), (4) and (5) from which they were obtained, are demonstrable theoretical mathematical expressions and require no proof or practical experimentation.

17 17 The mathematical calculation is so accurate that it does not require a practical procedure. The method is useful for gravitons and any particles made up of gravitons that can be accelerated. Except the graviton itself, everything we know today as material particles are formed by gravitons. Newton's law F = m a is always true. SUMMARY UNIVERSAL GRAVITATIONAL CONSTANT: ITS EXACT VALUE RELATIVISTIC QUANTUM MECHANICS G = x 10-8 cm/s In relativistic quantum mechanics, everything is expressed and measured in space-time units; as all entities existing in the space-time universe in either of their two main states, or in their two major states, energy and matter accelerated 3-dimensional space and contracted accelerated 3-dimensional space. Accelerated 3-dimensional space is energy in its kinetic state, and contracted accelerated 3-dimensional space is energy in its potential state (matter). In relativistic quantum mechanics, the universal gravitational constant, ( G ), is an acceleration; a consequence of the nd postulate of relativistic quantum mechanics, and is expressed in space-time units, with correspond to the theory called relativistic quantum mechanics. In relativistic quantum mechanics, the universal gravitational constant, ( G ), is: G = x 10-8 cm/s This value for the universal gravitational constant is exact, and is the equivalent in energy to the particular state the energy is fund in. It can be obtained theoretically, with no margin for error, by means of general universal gravitational relativistic quantum law. This establishes and expresses all gravitational 3-dimensional space when it is accelerated and reaches or exceeds the speed, vn, which causes a constant gravitational field of attraction equal ( G / K' ) = ( 1 / c ), while the 3-dimensional space remains accelerated and with a velocity greater than or equal to vn. The

18 18 velocity vn is the minimum velocity at which the accelerated 3-dimensional space behaves as a material particle. Universal gravitation relativistic quantum law this state the energy is found in states: all material particles or sets of material particles in the universe cause constant gravitational fields of attraction equal to ( G / K' ) = ( 1 / c ); regardless of the mass or geometric shape of the material particle or set of material particles in the universe. ( G / K' ) = ( 1 / c ) (1) or even G. c = K' () Equations (1) and () are the mathematical expression of the universal gravitation relativistic quantum law, where: G, Universal gravitational constant: The units for this constant in relativistic quantum mechanics are centimeters per square second (cm/s ). c, Speed of light: The units for this constant in relativistic quantum mechanics are centimeters per second (cm/s). K', Relativistic quantum constant: The units for this constant in relativistic quantum mechanics are centimeters squared per cubic second (cm /s 3 ). The relativistic quantum constant K' in relativistic quantum mechanics is: K' =,000 cm /s 3 The exact value of the speed of light, c, in relativistic quantum mechanics is: c = 9,979,45,800 cm/s The accelerated gravitational 3-dimensional space that reaches the velocity vn, has the condition of appearing to be matter (it is matter); as it originates from the gravitational attraction field of value ( G / K' ) = ( 1 / c ). For this state of accelerated 3-dimensional space causing the gravitational field of attraction of value ( G / K' ) = ( 1 / c ), the velocity, vn, is: vn = 9,979,45, cm/s This velocity vn is a constant. In relativistic quantum mechanics, the units for the gravitational field of attraction

19 19 or quantum energy state for the velocity vn is: ( G / K' ) = (1 / c ) = x s/cm UNIVERSAL GRAVITATIONAL CONSTANT: ITS EXACT VALUE INTERNATIONAL SYSTEM OF UNITS G = x N m kg G = x m 3 kg 1 s This value of the universal gravitational constant is exact. The mathematical expression of the universal gravitation relativistic quantum law corresponding to the International System of Units has the following mathematical form: G. c = KSI (SI) Equation (SI) is the mathematical expression of the universal gravitation relativistic quantum law for the International System of Units, where: G, universal gravitational constant: The units for this constant in the International System of Units are Newtons meter squared per kilogram squared ( N m kg ). It can also be expressed in the International System fundamental Units, which are meters cubed per kilogram per second squared ( m 3 kg 1 s ). c, speed of light: the units for this constant in the International System of Units are meters per second (m/s). KSI, relativistic quantum constant: The units for this constant in the International System of Units are meters to the fourth per kilogram per cubic second (m 4 kg 1 s 3 ). The exact value of the relativistic quantum constant ( KSI ) in the International System of Units is: KSI = 0.0 m 4 kg 1 s 3 The exact value of the speed of light, c, in the International System of Units is: c = 99,79,458 m/s The units of the gravitational field of attraction or energy quantum state for the velocity, vn, in the International System of Units are:

20 0 ( 1 /ccm/s ) = x s/cm ccm/s corresponds to the speed of light expressed in centimeters per second. NOTE: see the authentic version in Spanish CONSTANTE DE GRAVITACIÓN UNIVERSAL, SU VALOR EXACTO.