INTRODUCTION TO MASS INCREASES BY     
           GRAVITATIONAL RELATIVITY         
                                            




     The following proposes that steady state relativistic effects
     can be understood to occur pursuent to gravitational fields.

     The wider range of distortions in space embraced by the GENERAL
     THEORY OF RELATIVITY are put aside and certain specific effects
     are studied in detail. These specific effects are understood to
     come under the heading of GRAVITATIONAL RELATIVISTIC EFFECTS.



                               R. S. Livingstone
                               Ottawa, Canada, June, 1990.




      GRAVITATIONAL RELATIVITY THEORY      
     CONNECTS CERTAIN SOLAR PLANET MASSES.                



           ALSO, GRAVITATIONAL AND SPECIAL RELATIVITY THEORIES         
                        ARE INTRINSICALLY RELATED                      




      By assuming a mass and spacial effect in general relativity, a
      proposed gravitation relativity is evident, in which there is a
      direct tie-in between effects seen in Special Relativity and in
      Gravitational Relativity. In fact, properties commonly factored
      for a star or black hole in Gravitational Relativity, can also
      be factored in Special Relativity, and visa versa. This suggests
      not necessarily a unified field theory, but definately a connection
      betweeen certain properties in gravity, and in electro-magnetism.



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º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º
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º ABSTRACT      º
ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ

                    Several facets are to be discussed in the following.


  (Part 1)  Arguments demonstrating an increase in mass by the
  effects of gravitational relativity are shown through events
  which occur in the solar system.

  (Part 2)  Effects for gravitational and special relativity are shown
  to be synonymous for a given mass. Critical limits are uncovered in
  the behaviors of both relativities. In specific situations, mass is
  locked to a ceiling which is less than, but is determined from, black
  hole mass equivalents. In this, it is found that the maximum original
  mass which can be gathered before gravitational relativistic effects
  are maximized, is that of a black hole's mass divided by a factor
  of 1.618034 (a number constant known as the Golden Harmonic Ratio).
  The maximum velocity attainable by this mass when moving in special
  relativity, is the speed of light divided by the Golden Harmonic Ratio.


  (Part 3)  It is found that for any visible mass, there is a
  maximum special relativistic limit on the mass. This limit can be
  known in advance by knowing the maximum velocity the moving mass can
  attain and still remain visible in the normal sense, when observed by
  a stationary observer. The maximum effect is a derivative of the speed
  of light reduced by the relativistic effect of the mass's gravity.
  This is shown to define an upper limit velocity at which any given
  mass can appear in the same state of the universe as the stationary
  observer. Any rest mass reaches this barrier at a plateau that is
  predictable, and so the mass cannot visibly expand to infinity.


  (Part 4)  Innuendos of a unified field theory are harking loudly,
  popping out of the framework of relativistic physic. There is a
  universality in obvious behaviors working directly between the
  one field's venues (gravity) and the other field's venues
  (electromagnetism). As to whether these equalities can constitute
  segments of a full fledged unified field theory is not to be
  addressed at this time, in the scope of the following disclosures.




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º  part 1  ±±±±±±±±±±±±±±±±  GRAVITATIONAL RELATIVITY  ±±±±±±±±±±±±±±±± º
ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ

      A little known (entirely unknown) fact is that certain solar
      planetary masses can be connected as a direct consequence of
      gravitational relativity. This is shown to be true when it is
      surmised that relativistic effects of gravity may include an
      intrinsic increase in the mass comprising the source of the
      gravity.

      The relativistic increase for the Sun mass is very small compared
      to the mass of the Sun itself. Even though the increase in mass
      is small at roughly 4.23 x 10 to the power 27 grms, the increase
      is nevertheless nearly 7 times the mass of Mars, and is marginally
      less than the mass of Venus.

      Such an increase in the Sun mass, when calculated to advanced
      accuracy, is found to be exactly equal to the mass difference
      between Venus and Mars. Another discrete relativistic potential
      includes 1/2 the mass of Jupiter added to the mass of the Sun.
      The existence of states makes it possible to infer a more
      accurate estimate for the existing mass of the Sun.


      The radius of the Sun is considered to be a constant for various
      manifestations, shown to correspond to parameters which operate
      between solar mass equivalents up to the masses of black holes.
      In this, a link between gravitational and special relativity
      is shown. The link is the subject of part 2.


ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ»
º  part 2  ±±±±±±±±±±±±±±±±±±±±  SPECIAL RELATIVITY  ±±±±±±±±±±±±±±±±±± º
ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ

      It can be easily demonstrated that a visible mass moving at
      velocities nearing the speed of light, can never grow to infinite
      quantities and remain visible in the normal sense, and so can never
      achieve a velocity equal to the speed of light, in the normal sense.

      This is because gravitational relativistic effects have to be
      considered for a moving mass, if it is assumed that gravitational
      relativity includes an effect that increases the original state of
      the mass which is the source of the gravity's relativistic effect.
      It is readily shown that such gravity effect has significance to
      special relativity.

      There is a boxed in limit, where the moving mass (bumped in
      value in special relativity) assumes a value equivalent to the
      mass of a black hole, when the original rest mass is expanded by
      the effect of special relativity, in direct accord with the mass's
      radius contracted by the effect of special relativity.

          When assuming the mass of a black hole equivalent, the
          moving mass effectively drops from sight in the normal
          physical view as seen by a stationary observer.

          (See Appendix A at the end of this document, for a related
          discussion involving elementary particles such as the proton).

      One of the finite limits to which a mass can be accelerated
      in special relativity, and to which a mass can be accumulated
      in gravitational relativity, can be explicitly expressed for
      both modes of relativity as factors of a number constant known
      as the Golden Harmonic Ratio, 1.61803398875 .

      In this, the Golden Ratio's significance is to the existence of
      black holes. Specifically, a black hole's mass includes both an
      original mass and an augmentive portion from the relativistic
      effect of gravity, to comprise the total mass involved. The
      relationship between original, gained, and final black hole
      mass aggregations, can be expressed in exact terms of the
      Golden Harmonic ratio.

      In particular, however, in the dynamic behaviors of both
      relativities, important boundaries are reached at a certain
      critical limit whose mathematical significance is the Golden
      Harmonic Ratio. The parameters here include a black hole's
      mass aggregate and event horizon.



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º  part 3  ±±±±±±±±±±±±±±±  THE GOLDEN HARMONIC RATIO  ±±±±±±±±±±±±±±±± º
ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ

      The effects of gravitational relativity can be generally related
      to the effects of special relativity, to the extent that relativity
      effects of gravity and of special relativity can be shown to be
      equated through a single common factor.

      The maximum velocity attainable by a visible moving mass, is
      the speed of light reduced by the proportionate effect of the
      gravitational relativistic effect in the mass being accelerated.


      The critical limit (maximum velocity) possible, is restricted
      by bounds achieved in special relativistic effect when the rest
      mass has increased, and radius has contracted, to a point where
      the moving entity reaches a state where it forms a black hole and
      effectively disappears from view, relative to a stationary observer.

      The barrier limit is easy to calculate and to mathematically
      confirm, when given the original rest mass and radius.

      It becomes clear that, generally a visible mass accelerated to
      relativistic velocities cannot theoretically achieve an infinite
      mass, and the velocity can never theoretically equal the speed of
      light. The traditional interpreted statements in special relativity
      which say any visible mass continues to expand toward infinity,
      and the velocity continues to the speed of light, are in error
      about such things.







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º ±±±±±±±±±±±±±      GRAVITATIONAL RELATIVITY THEORY      ±±±±±±±±±±±±± º
º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º
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º ±±±±±±  GENERAL INTRODUCTION   for part 1   The Solar System  ±±±±±±± º
ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ


           In the following, the existing orbits of planets are not
           considered as terms, and all of the events are shown to
           occur as within a constant confinement radius which is
           the existing radius of the sun.


 A general relativistic equation is in common use for gravitational
 effects. Such an equation has been around in physics since 1916.
 Variations of the equation are also in common use. Given a known mass
 for instance, a Schwarzschild radius for that mass confined as a black
 hole can be immediately calculated.


 Conversely, given a radius, how much mass would be needed to be
 confined within that radius as a black hole can also be calculated.

      Such effects are a steady state system. It is the amount of
      mass within a specified radius which counts. The effects are
      constant per given mass and radius, since no outside velocity
      or acceleration is involved with the masses sitting stationary.

      The same is true for mass aggregates which are not a black hole,
      but which have mass sufficiently large, and a radius sufficiently
      small, for gravitational relativistic effects to be discernible.

      For stars the size of the Sun, for instance, there are discernible
      effects, even though they appear to be very slight at first sight.
      In a closer look, however, the slight effects can reveal many major
      properties in the fundamental relativistic behavior of gravity.







  ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
ÛÄ´     GRAVITATIONAL RELATIVISTIC EFFECT     ³
  ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

 In principle, gravitational relativistic effects are calculated via
 the standard equation, for varying mass and radius, until a meeting
 point is reached at which the mass and radius correspond to the
 formal parameters of a black hole.

      In the standard equation, a term for the relativistic effect
      results, which has been mainly used to determine the slowing
      of time in closer vrs more distant proximities to the field
      generating the effect.

      The same term can be used to find out how much a gravitational
      mass's radius can further contract relativistically per given
      increase in mass, when assuming that gravity relativistically
      contracts its own confinement radius. The same term can be used
      to calculate the gravity's relativistic effect on its own mass.

      This term can be called E (for effect). The value of term E
      suddenly nose dives toward 0 when the mass is sufficiently large,
      due to a sudden relativistic upsurge in pull in the greater power
      of the gravity itself, at which point the existing mass becomes
      a so called black hole and the existing mass's radius no longer
      appears to contract, rather, it will begin to increase given
      further increases in mass.

      This mass and radius stabilization is considered a physical
      boundary called the Schwarzschild radius, or event horizon.

          The stabilization is discussed in 'A Comparison Between
          Gravitational And Special Relativity' (found directly
          under the 'General Introduction for Relativity' Part 2',
          below), and is formally described in Equations 3 to 5
          in APPENDIX B at the end of this document.



  ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
ÛÄ´     GENERAL MASS QUANTA EFFECT      ³
  ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

      In variations of the equations, when a quantity of mass is given
      and the radius containing it is also known, then a simple solution
      using term E can denote how much of a mass increase may occur in
      the mass, due to a relativistic augmentation by the mass's gravity.

          The augmentation can be conjectured to occur in two ways.
          Either a measured mass is naked (original with no relativistic
          augmentation), or is augmented (the measured mass includes
          the augmentation).

          Hence the augmentation can be conjectured to be in two
          modes; either a decrease upon the originating mass, or
          an increase.

          In keeping with special relativity effects, a mass increase
          in gravitational relativistic augmentation can be presumed
          with no difficulties.

          For instance the Sun (given its mass and radius) is surmised
          to have a visible radius which is marginally reduced by
          relativistic augmentation (shrunk), and so the Sun's apparent
          mass is also surmised to be marginally augmented (expanded) in
          a mass increase by an equivalent relative proportion.

          The problem is that such a conjecture (relativistic augment-
          ation in mass) is hard to prove, since it is not possible to
          actually separate a given mass from its gravity and so observe
          any change in the apparent mass, when the mass is compared with
          vrs without the relativity of the gravity.

          In which case, any evident mass augmentation will have to
          be learned by some secondary means.

          In this solar system such a means is provided mechanically,
          by the fact that the amount of solar mass augmentation is a
          meaningful quantity in company with the existing mass of some
          of the planets.

          The mass augmentation has a value which is in a quantum
          correspondence to the existing masses of Venus and Mars.
          This makes the mass augmentation clearly visible. The fact
          that the relativistic mass is involved with these planets
          (in relationship with small particles external from the Sun)
          is very curious.


     ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
     ³     GRAVITATIONAL RELATIVISTIC EFFECTS     ³
     ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

      The standard equation for gravitational relativistic effect
      is described as follows:


 EQUATION A

              ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
              ³         2G (Mass)
       E  =   ³  1  Ä   ÄÄÄÄÄÄÄ
             \³           Cý R

          The square root of ((1  -  the product of 2 times the
          gravitational constant G, times a mass), divided by the
          radius of that mass times the speed of light squared),
          yields a gravitational relativistic effect factor, termed E.












 
 EQUATION B

          The radius of the mass times the reciprocal of the
          E factor, gives the originating radius of the mass,
          ie., before contraction of the radius by the mass's
          gravitational relativistic effect.

           ÚÄ                 Ä¿
           ³        ÚÄ     Ä¿  ³                     Where Re is the
           ³        ³   1   ³  ³                     amount of space
           ³  R  x  ³  ÄÄÄ  ³  ³   -  R  =  Re       by which the Sun's
           ³        ³   E   ³  ³                     radius is contracted
           ³        ÀÄ     ÄÙ  ³                     by the relativity
           ÀÄ                 ÄÙ                     in the Sun's mass


           ÚÄ                 Ä¿                Ro is the original
           ÀÄ        Ro       ÄÙ                radius before effect.

                                       R is the existing radius
                                       (the radius we see) which
                                       includes effect (Ro + Re)


      These (Equations A and B) are well known and nothing new
      has been so far stated.

          The relativistic collapse in the Sun's radius
          is very slight, hardly 1« kilometers.

          This is learned as the difference between the originating Sun 
          radius Ro, minus the existing (augmented) radius R. The difference 
          seems to be a remarkably close approximation of « the Schwarzschild 
          radius needed for the Sun mass to be a black hole. However this is 
          not surprising, in that the smaller the mass and/or the larger the 
          radius, the closer the radius augmentation is to « the Schwarzschild 
          radius. The 1/2 approximation grows closer, the less the mass
          aggregate is a black hole.

          In principle, with little mass and a large radius, there is 
          very little augmentation. Conversely, a very small radius for 
          the small mass is needed as the event horizon for the small mass 
          to become a black hole.

          The point intended is that as the mass to radius ratio
          approaches the primes of a black hole, the rates of
          change due to gravitational relativistic effects climbs
          up a steepening gradient.

      At solar quantities, the effects are so slight as to be
      normally thought of as negligible. But this is not so.

          If for instance 1/2 the mass of JUPITER is added to that of
          the Sun, and this enhanced mass sum is regarded as being within
          the confines of the existing Sun radius, the relativistic mass
          augmentation effect when applied to the mass of the Sun minus
          1/2 the mass of Jupiter, equals the previously noted congress
          involving Venus and Mars masses, (at the end of 'General Mass
          Quanta Effect', above).

          Such state arrays reveal a previously unsuspected property,
          of relativistic mass quantal arrangements displaced at long
          distance from the source generating the relativistic mass
          effect. A first suspicion is that:

             'THERE IS AN INCOMPATIBILITY BETWEEN A GRAVITATIONAL
              FIELD AND THE RELATIVISTIC EFFECT IT GENERATES'.

          The appearance is that some aspect of the relativistic mass
          effect generated in a field of gravity, does not stay within
          the field generating it.

          In supposition, it appears that some relativistic component
          is expunged (externalized) from the originating field of
          gravity. In the case of our solar system's example, the
          masses of Venus and Mars, along with Jupiter, are external
          and yet relativistically tied to the Sun mass.


  ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
ÛÄ´     ESTIMATED ACCURACY OF SOLAR MASSES     ³
  ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

      Masses in the solar system are traditionally published in two
      ways. A mass for each planet is given as a ratio between it and
      the mass of the Sun. Since comparative ratios can be inferred to
      considerable accuracy, the Sun to planet mass ratios for most of
      the planets are well known.

      On the other hand estimating the actual mass of a planet or
      the Sun in terms of (say) gram units, is not so easy, since
      there is no way of actually sitting a planet on a scale. For
      that matter, estimating the real mass of the Sun (in say grams)
      is also difficult since the Sun cannot be weighed on a scale.

      The problem is compounded in that in order to know a real
      weight (in grams) requires that the universal gravitational
      constant (G) be known to high accuracy, which it is not.
      Whereas determining the mass influences of one body on another,
      as a ratio, is easier since (G) is not a critical factor for
      the accuracy.

          For these reasons the real mass of (for instance) the
          Sun (in say grams) cannot be stated with great accuracy
          by ordinary measuring methods.

      The Sun's mass is currently given as somewhere between
      1.989 x 10 to 33 grms, and 1.991 x 10 to 33 grms. Whereas
      planet masses are currently given in gram figures accurate
      to between 4 and 5 significant figures. The greater accuracy
      for planet masses is assisted by the fact that the planets
      tend to subtlety bounce each other around in orbit, and their
      bouncing can be closely watched. Whereas the Sun is hardly
      bounced by the less hardy influence of the planets.

      The Earth - Moon combination gives the best look at bouncing.
      But rigorous real weight analysis for the Earth is not so easy
      when tried, because both the Earth and Moon also subtlety bounce
      around as a unit.

      If the gram weight of the Earth  (5.976 ñ .004 x 10 to 27 grms)
      is multiplied by the Sun to Earth mass ratio  (332,995.9 ñ .4),
      then the Sun's gram weight results as (1.9899834 x 10 to 33 grms).

      This value is actually deemed low to a very minor degree for the
      equations which follow below. In the following, a Sun mass in the
      vicinity of  (1.990993 x 10 to 33 grms)  is explicitly inferred.

      Another problem in any advanced accuracy is inherent in the weak
      solar gravitational relativistic effects per se. Because the effect
      for solar mass quantities is so slight, there is a loss of some
      accuracy due to inherent truncation in doing the calculations.

      In the equations which follow, accuracy has been maintained
      to 13 significant digits, but inherent truncation results at
      the 7th significant digit of certain of the terms.

      Such truncation is diminished when dealing with larger
      masses confined within small radii. The truncation disappears
      completely when dealing right at the range of black hole masses.

      Hence, black hole limits can provide a tool for comparing
      calculations, to determine which calculations produce
      exactitudes and which produce close approximations only.
      This is actually more straightforward than it sounds.


  ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
ÛÄ´     BASIC CONVENTIONS     ³
  ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

      In the following, the existing orbits of planets are not
      considered as terms. All of the events are shown to occur
      as within a constant confinement radius, which is the
      existing radius of the sun.

          For the sake of convenience, the mass of the
          Sun is shown as a standard term labeled (MM).

      In the following, the calculations are accomplished at
      an accuracy of 10 to the 13 significant digits. Zeros are
      used to fill gaps between available digits and the 13th
      significant digit. As already mentioned, some of the terms
      are accurate only to the 7th significant digit. In fact,
      some terms cut off at the 7th digit. For this reason, the
      highest maintained accuracy possible is very important.

         For the universal gravitational constant G, a recent
         revision having a digital value of 6.6720 x 10 to -8
         is used.

         The speed of light C of the following value is used:
         2.99792458 x 10 to 10 cms/sec.

         The radius of the Sun is used as a constant R, having
         the value 6.96265 x 10 to 10 cms.


       ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
       ³      MASS CONVENTIONS     ³
       ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

     The following mass aggregates have been adopted as standards for
     the involved quantities. The high accuracy given them has been
     by the adjusting of repeated pure math experimental results until
     a semblance of coherency in the mass standards looked viable.

         The term 'aggregate mass' is used for denoting a mass (such as
         the Sun, plus or minus another mass (such as 1/2 the mass of
         Jupiter). 'Aggregate mass' is also used to denote any apparent
         mass, since the mass is assumed to include relativistic
         augmentation due to gravity. Hence, the original mass before
         augmentation is termed 'original mass', or 'originating mass'.

         K has been adopted as a term to explicitly denote the
         relativistic mass augmentation in the Sun's mass due
         to the Sun's gravity.

     In determining aggregate mass values, the value of MM for the
     Sun's apparent mass was first determined, based on an assumed
     equality that a so called K augmentation factor for the Sun mass
     is indeed the mass difference between planets Venus and Mars.

         Without doubt the real values for the mass aggregates (given
         in grms for instance) will marginally change depending on
         future adjustments of the universal gravitational constant,
         and perhaps sharper astronomy techniques.

             (For that matter, mass MM may not be the true real
             mass of the Sun. It may turn out that MM is the mass
             of the Sun ñ something else).

         It is anticipated that any such changes would nevertheless
         prove to continue to be coherent within the realms of the
         gravitational relativistic state equations which involve them.

         Several tables and basic equations follow. Following these,
         a discussion begins on how a mass of MM was inferred for the
         Sun, via gravitational relativistic effects.

         Table 1 which follows, lists important mass aggregations,
         and the highest resolved real mass values possible as used
         to explore their relativistic highlights.




ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ»
º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º
ÌÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍËÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ
º  INFERRING A GRAVITIONAL RELATIVISTIC  º
º  AUGMENTED MASS VALUE FOR THE SUN      º
ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ






 
 TABLE 1        INFERRED VALUES

  ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
  ³                                                          ³
  ³      MM    =   Existing Sun mass, presumed to include    ³
  ³                original mass plus mass augmentation K    ³
  ³                                                          ³
  ³            =   1.9909930      x 10 to 33 grms            ³
  ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´
  ³                                                          ³
  ³      K     =   Gain in original mass of the Sun, the     ³
  ³                amount of relativistic augmentation       ³
  ³                due to the Sun's gravity                  ³
  ³                                                          ³
  ³            =   4.226490       x 10 to 27 grms            ³
  ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´
  ³                                                          ³
  ³      Mbh   =   Mass of a black hole having an event      ³
  ³                horizon equal to the Sun's radius R       ³
  ³                                                          ³
  ³            =   4.689536679    x 10 to 38 grms            ³
  ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ


 TABLE 1-A      ESTABLISHED VALUES
  ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
  ³                                                          ³
  ³        R   =   Existing Sun radius                       ³
  ³            =   6.96265 x 10 to 10 cms                    ³
  ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´
  ³                                                          ³
  ³        C   =   Speed of light                            ³
  ³            =   2.99792458 x 10 to 10 cms/sec             ³
  ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´
  ³                                                          ³
  ³        G   =   Universal gravitational constant          ³
  ³            =   6.6720 x 10 to -8 cms3/grms secý          ³
  ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´
  ³                                                          ³
  ³        CR  =   A physical constant for Mass/Radius       ³
  ³                ratio of a black hole                     ³
  ³            =   6.735275620 x 10 to 27 grs/cm             ³
  ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´
  ³                                                          ³
  ³        GH  =   Golden Harmonic Ratio                     ³
  ³            =   1.61803398875                             ³
  ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

 TABLE 2

  ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
  ³                                                          ³
  ³  Planetary masses  -  Data is from tables found at the   ³
  ³                       back of the following reference:   ³
  ³                                                          ³
  ³          UNIVERSE  by Don Dixon,  Houghton Mifflin Co.,  ³
  ³          Boston,   1981                                  ³
  ³                                                          ³
  ³      Moon        =     .0735  x 10 to 27 grms            ³
  ³                                                          ³
  ³      Venus       =    4.8683  x 10 to 27 grms            ³
  ³      Earth       =    5.976   x 10 to 27 grms            ³
  ³      Mars        =    6.4181  x 10 to 26 grms            ³
  ³      Jupiter     =    1.901   x 10 to 30 grms            ³
  ³                                                          ³
  ³      Sun         =    1.9888  x 10 to 33 grms            ³
  ³                                                          ³
  ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ




 TABLE 3

  Certain terms are used to generalize certain types of masses:
  ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
  ³                                                          ³
  ³  Low mass       -  Masses in the range of those found    ³
  ³                    in this solar system                  ³
  ³                                                          ³
  ³  Enhanced mass  -  Solar mass aggregates other           ³
  ³                    than the Sun, added or subtracted     ³
  ³                    to the Sun mass                       ³
  ³                                                          ³
  ³                    -  Specifically the mass of the       ³
  ³                    Sun plus 1/2 Jupiter, and mass of     ³
  ³                    the Sun minus 1/2 Jupiter, also mass  ³
  ³                    of the Sun minus mass of Venus        ³
  ³                                                          ³
  ³  Higher mass    -  Mass of a black hole, and in mass     ³
  ³                    range of a black hole                 ³
  ³                                                          ³
  ³                    -  Specifically the mass for a        ³
  ³                    black hole whose event horizon        ³
  ³                    is the radius of the Sun              ³
  ³                                                          ³
  ³                                                          ³
  ³  Originating mass  -  Original mass accumulation without ³
  ³                       any relativistic augmentation      ³
  ³                                                          ³
  ³  Augmented mass    -  Existing mass assumed to include   ³
  ³                       a change from the originating      ³
  ³                       mass due to relativistic effect    ³
  ³                       of gravity                         ³
  ³                                                          ³
  ³  Existing mass     -  As physically measured, with       ³
  ³                       any assumed augmentation present   ³
  ³                       in the measurement                 ³
  ³                                                          ³
  ³  Real mass         -  A real weight, in terms of a       ³
  ³                       physical weight, for instance      ³
  ³                       measured in grms as if weighed     ³
  ³                       on a scale                         ³
  ³                                                          ³
  ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

     Certain equations are used to generalize mass effects
     due to gravitational relativity. Certain term conventions
     are adopted for the sake of convenience in bookkeeping:


 EQUATION C     Determining a relativistic effect factor Em
                for a mass aggregate, in particular the Sun:

                 ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
                 ³         2G (MM)                Where MM is the mass
         Em  =   ³  1  Ä   ÄÄÄÄÄÄÄ                of the Sun, and R is
                \³          Cý R                  the radius of the Sun



 EQUATION C-1   Determining how much mass augmentation relativistically
                occurs in the mass aggregate of the Sun:

         (MM)  -  ((MM) x Em)  =  Km           Where K is the actual mass
                                               augmentation increased on
                                               the Sun's original mass
                                               due to gravity


 EQUATION C-2   Determining a relativistic effect factor for a mass
                aggregate, such as the Sun plus X, where X is anything:


                  ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
                  ³         2G (MM+X)
         Ex  =    ³  1  Ä   ÄÄÄÄÄÄÄÄÄÄÄ
                 \³           Cý R



 EQUATION C-3   Determining how much mass augmentation relativistically
                occurs in a mass aggregate, such as the combined mass
                of the Sun + X , when both are confined in radius R :

                   (MM+X)  -  ((MM+X) x Ex)  =  K+x


 EQUATION C-4   For example, determining a relativistic effect factor
                for such as the Sun plus 1/2 Jupiter combined:

                     ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
                     ³         2G (MM+1/2j)
         E+1/2j  =   ³  1  Ä   ÄÄÄÄÄÄÄÄÄÄÄ
                    \³            Cý R



 EQUATION C-5   Determining how much mass augmentation relativistically
                occurs in a mass aggregate, such as the combined masses
                of the Sun and 1/2 Jupiter, when both are confined in
                radius R :

         (MM+1/2j)  -  ((MM+1/2j) x E+1/2j)  =  K+1/2j

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º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º
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º VERIFYING A MASS OF MM FOR THE SUN              º
ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ

      An aggregate mass MM (being the mass of the Sun) found to have
      intrinsic relativistic consequences, can be easily verified.

      If starting with an estimated Sun mass, for instance;
      (1.989 x 10 to 33 grms); and assuming that the Sun mass is
      already relativistically augmented, the gravitational relativistic
      mass increase of a Sun mass of  (1.989 x 10 to 33 grms)  is found
      (using Equations C and C-1),  to be slightly less than the mass
      difference between Venus and Mars.

      That is:    Venus mass   is   4.8683   x 10 to 27 grms
                  Mars  mass   is    .64181  x 10 to 27 grms
                  Venus - Mars is   4.226490 x 10 to 27 grms

                  whereas the mass augmentation Km of a
                  Sun mass of (1.989 x 10 to 33 grms) is
                  (4.218033 x 10 to 27 grms), which is low.

      If the Sun's mass is gradually increased, eventually a
      mass aggregate will be found, in which the relativistic
      mass augmentation K is precisely (Venus - Mars), that is:

           K  =  4.226490 x 10 to 27 grms.

      The point of agreement occurs when the mass aggregate
      for the Sun MM is found to be  (1.990993 x 10 to 33 gms).

      For instance, suppose arbitrary units of Neptune's mass are
      systematically added to a base mass of (1.989 x 10 to 33 grms).
      A break point will be reached. At + 18N units of Neptune's mass
      the relativistic augmentation (Km) of the aggregate mass will be
      marginally less than (Venus  - Mars). And at + 19N units of
      Neptune's mass, the relativistic augmentation (Km) of the
      aggregate mass will be marginally more than (Venus - Mars).

      And so somewhere between (base + 18N) and (base + 19N) is a solar
      mass component whose resulting augmentation (K) is exactly equal
      to (Venus - Mars). The search can now be narrowed to (base + X),
      where (+ X) falls somewhere between (+ 18N and +19N).

      Fine tune fiddling back and forth using smaller and smaller
      increments for X, eventually closes in on a result for;

         (base + 18N + X)

         in which the relativistic mass augmentation
         from (base + 18N + X) when using Equation D
         below, equals (Venus - Mars) exactly.

 EQUATION D
                                          Where b is a base mass
             ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ       (1.989 x 10 to 33 grms)
             ³         2G (b+X)
       E =   ³  1  Ä   ÄÄÄÄÄÄÄÄ           And so (b+X) - ((b+X) x E) = K,
            \³           Cý R             and K = (Venus - Mars) exactly,
                                          when (b + X) is exactly
                                          (1.990993 x 10 to 33 grms)


      EQ D  can be written so that (b+X) is standardized as MM, so that:


 EQUATION E
                                           Where MM is an inferred Sun
               ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ      mass, so MM - ((MM) x Em) = K
               ³         2G MM             where K = (Venus - Mars),
         Em =  ³  1  Ä   ÄÄÄÄÄ             and Em is the relativistic
              \³         Cý R              effect factor for mass MM



      In other words the inferred Sun mass MM presents a solar
      mass factor whose relativistic gravitational augmentation (K)
      is exactly equal to the mass difference between Venus and Mars.

       That is:   Equation E determines Em
           and:   MM - ((MM) x Em) = K
           and:   K = 4.226490 x 10 to 27 grms

                      which is precisely (Venus - Mars)
 which also is:       4.226490 x 10 to 27 grms


      This instantly presents an interesting situation. The inferred
      mass of the Sun MM appears to involve a relativistic gravitational
      mass amalgamation which is greater than the mass of the Sun alone.

      The interesting kink is that the masses of Venus and Mars
      are found expunged into space, at long distance orbits around
      the Sun. This orbital existence is not explained at this point
      and so is noted only as a comment.

      The other interesting point of view is that although the mass
      of Mars for instance is very small compared to the mass of the
      Sun, the mass of Mars is nonetheless highly visible. This is
      something like the high visibility of the electron's tiny
      binding energy unit in comparison to the mass of the Proton.



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º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º
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º SPECIFIC MASS QUANTA EFFECT º
ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ


  As described under 'A Comparison Between Gravitational And Special
  Relativity' (found directly under the 'General Introduction for
  Part 2', below), gravitational relativity includes at least two
  variable source terms for its effect. These source terms are the
  aggregate mass, and the mass's confining radius. It means that
  different quantities of mass can be said to occupy the same area.
  In which case there can be (in result) different or identical
  relativistic mass augmentations, depending on discrete combinations
  of how much mass is said to be added or subtracted to the initial
  mass aggregate, confined in the same or in different radii.

          For instance in mass aggregates which are in the range
          of the size of the Sun, here, discrete extra mass in the
          same radius (the Sun's radius) can produce a relativistic
          factor Ex which when arbitrarily applied to yet another
          discretely different mass aggregate, can produce a K
          augmentation which is otherwise gained from yet another
          different mass aggregate.

          For instance, the Sun mass MM, plus 1/2 the mass of Jupiter,
          can provide via EQ C-2 an effect factor (E+1/2j) which when
          applied to the same mass aggregate, via EQ C-3, results in
          K+j .

          But if E+1/2j is applied to a different mass aggregate, for
          instance to MM-1/2j, a value slightly departed from K+j must
          result. The resulting slightly lower value in fact once again
          happens to be K exactly (the mass difference between Venus
          and Mars).


      The formal description for this enhanced mass state is:

 EQUATION E-1

                  ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ      (MM+1/2j) is the
                  ³         2G (MM+1/2j)         aggregate of the Sun
       E+1/2j  =  ³  1  Ä   ÄÄÄÄÄÄÄÄÄÄÄ          mass plus 1/2 the mass of
                 \³            Cý R              Jupiter, confined in the
                                                 existing Sun radius R

 EQUATION E-2

               (MM-1/2j)  -  ((MM-1/2j) x E+1/2j)  =  K

               where K equals the mass of (Venus - Mars), and
               (E+1/2j) is the relativistic effect of the slightly
               denser aggregate of the inferred Sun mass MM plus 1/2
               the mass of Jupiter, when confined in the Sun's radius R.

          In keeping with state-like mass aggregates, if EQ E-1 is
          rewritten so that the initial mass aggregate used in EQ E-1
          is now MM-1/2j, and a resulting effect (called E-1/2j) is
          used in a rewritten form of EQ E-2, then a relativistic mass
          augmentation equal to K once again results; that is:

 EQUATION E-3

               (MM+1/2j)  -  ((MM+1/2j) x E-1/2j)  =  K

               where K equals the mass of (Venus - Mars).

 EQUATION E-4

          The bifurcation of Jupiter mass around the mass of the Sun
          to form coherent relativistic states can be generalized as:

               E+1/2j  of mass  M+1/2j  applied to  M-1/2j  yields  K
               Em      of mass  MM      applied to  MM      yields  K
               E-1/2j  of mass  M-1/2j  applied to  M+1/2j  yields  K


 EQUATION E-5

          Such a bifurcation around the mass of the Sun
          can be generalized as:

               E+x  of mass  M+x  applied to  M-x  yields  Kx
               E    of mass  M    applied to  M    yields  Kx
               E-x  of mass  M-x  applied to  M+x  yields  Kx

          However, the augmentation quantity Kx only equals known
          augmentation value K, when M+x and M-x are specifically
          MM+1/2j, and MM-1/2j. That is, when 1/2 quantas of Jupiter's
          mass are added, and subtracted, to the inferred mass MM of
          the Sun.

          (It should be noted that the bifurcation results of EQ E-4
          are not perfect exactitudes. The three resulting values of
          K happen to look the same for masses in the range of this
          solar system. For higher mass densities for example MM
          times 1000, confined in the same radius R, the three K
          values (shown as Kx in EQ E-5) are noticeably separated).


  ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
ÛÄ´     VERIFYING THE COHERENT 1/2j STATES     ³
  ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

  Equations E-1, E-2, E-3, and E-4, were not easily found without a
  prior insight and a discovery. In question is how come a unit of 1/2
  the mass of Jupiter has been arbitrarily used to arrive at a seeming
  non arbitrary result, this result being where K is twice again
  calculated, as summarized in Equation E-4.

      An original intention was to see if the total mass of the solar
      system could be inferred to be in any way involved in some sort
      of interphasing between different mass aggregates in this solar
      system's gravitational relativity. This thought itself came from
      an original impression that the real mass of the Sun was in the
      range of base  (1.9891 x 10 to 33 grms), and inferred mass MM
      would be the real Sun mass (base) plus Jupiter's mass, since
      (MM - base) closes in on an excellent approximation of Jupiter's
      real mass at  (1.901 x 10 to 30 grms), when using EQ D to infer
      mass MM.

         For a while it was looking good. It seemed that if MM was the
         mass of the (Sun + Jupiter), and a mass value just slightly
         larger than the total mass of the solar system was substituted
         in EQ C-2, then a mass augmentation of K was again found when
         the factor Ex of EQ C-2 was substituted in EQ C-3, when
         Jupiter's mass was subtracted from the solar total mass
         aggregate and the result of this reduction substituted for
         MM+X in EQ C-3.

         In the exploration, a mass term Mt was adopted for the solar
         mass total, plus some little extra, to give mass term Mtx.
         And mass term Mtx-j denoted the solar total minus the mass
         of Jupiter.

         The value of Mtx could be rigorously inferred, as being
         exactly the mass aggregate needed in EQ C-2 to result in
         a mass augmentation effect equal to K in EQ C-3, when mass
         aggregate Mtx gave augmentation effect Etx, which was used
         to find the augmenting effect on mass Mtx-j, as in:









 EQUATION F

               ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
               ³         2G Mtx
        Etx =  ³  1  Ä   ÄÄÄÄÄÄ
              \³          Cý R


         and a mass aggregate of (Mtx - Jupiter) was substituted
         in EQ C-3, giving:



 EQUATION G
                  (Mtx-j)  -  ((Mtx-j) x Etx)  =  K

         In other words, the thinking was heading along a line that a
         sort of formal relativistic interphasing might be occurring,
         whose boundary was spread between the base mass of the Sun,
         and the total mass of the solar system. For instance between
         the Sun, and (Sun + Jupiter), and (Sun + planets + moons),
         and (Sun + planets + moons - Jupiter). The problem was in that
         little extra mass bit, (the x of Mtx). What might it represent?

         It was suddenly and unexpectedly found that the value
         of Mtx as rigorously inferred, turned out to be exactly
         (MM + 1/2 Jupiter). This was not a percentage of error
         type of equality. The figures that suddenly appeared on
         hand were identical to 8 significant digits.

         In other words, the rigorously determined value for Mtx,
         and MM+1/2j, were identical to 8 significant figures.

  Which dramatically changed the picture.

         It was now easy to think that MM instead of being
         a (Sun mass + Jupiter) aggregate, represented the
         real mass of the Sun itself. In other words, MM
         could well be the real mass of the Sun.

            It was also easy to perceive a formal verification for the
            quanta bifurcation factor involving 1/2 the mass of Jupiter.

            By using Equations F and G to find a result equal to K,
            a mass quanta increment of (+X) added upon MM eventuates in
            an interphase involving (MM-X) for the K result, only when
            X is exactly 1/2 Jupiter, when using the same inferencing
            technique as was used to infer MM in the first place, as
            described above under 'Verifying a Mass of MM For The Sun'.

            A slightly more accurate inferencing for MM itself was thus
            made possible. In order for Equations E-1 to E-4 to yield
            results definitely equal to K, the value of MM is adjusted
            to the greater accuracy of  (1.99099305 x 10 to the 33 grms).

         It made the explorations involving solar mass total aggregates
         Mt and Mtx not important. This avenue of reasoning was dropped,
         and is mentioned above only to reveal how a quantal value of
         ñ 1/2 Jupiter as displayed in Equations E-1 to E-4 came to be
         an issue.



  ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
ÛÄ´     OTHER MASS AGGREGATE STATES     ³
  ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

      In applying such interphasing logic to the solar system, the
      study is narrowed to include only mass quantities which currently
      exist; these being the Sun, and certain planets.

      In the case of a bifurcated Jupiter mass, a theoretical attribute
      is identified. This is where mass aggregates and resulting
      gravitational relativistic effects can phase in and out (in a
      continuation of certain coherent effects), through a range of
      mass densities confined within a single constant radius.

         A form of harmonic interphasing through a realm of masses
         is definitely sensed.

         In gist; a higher relativistic effect from an enhanced mass
         aggregate is applied to a lower mass aggregate, such that
         the resulting augmentation is lower or different than would
         be expected for either the originating enhanced mass, or the
         reduced mass.

         This type of reasoning should only be speculative, except that
         the mass augmentation which actually results when +1/2 Jupiter
         and -1/2 Jupiter are involved, is already a recognized quantity,
         this being mass term K, already independently seen for a mass
         aggregate which is other than an effect that is expected
         straight across for an enhanced or diminished sum of the Sun
         plus or minus 1/2 Jupiter.


  ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
ÛÄ´     OTHER MASS EFFECT COHERENCIES      ³
  ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

      Other mass effect coherencies seem to occur. One involves the
      mass of the Earth (Me), which, when subtracted from mass MM,
      yields an aggregate mass whose relativistic effect factor
      (herein called Ee), which when applied to mass aggregate MM,
      results in a discrete mass split which is precisely equal to
      the mass of the Earth Me minus K.

      This formula (as exemplified in EQ H and I below), might at first
      seem tautological until further studies show that a relativistic
      factor Ex for any mass aggregate (M + X) or (M - X) does not phase
      in perfectly to an exact result for (MM - (MM x Ex)) = X - Kx for
      any value assumed for mass X. Only certain precise values of ñ X
      are seemingly phased in a coherency. For instance when:


          1.  X equals the mass of Earth
          2.  X equals the mass of Venus
          3.  X equals ñ 1/2 the mass of Jupiter



      The case of X being equal to ñ 1/2 the mass of Jupiter
      has already been demonstrated in Equations E-1 to E-4.

      When X equals the mass of Venus, then a mass split resulting
      in a discrete relativistic augmentation, also incorporates the
      mass of Mars. This is shown further below in Equations Q to S.

      A formal description for the interphasing state involving
      the Earth is as follows:

 EQUATION H

              ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
              ³         2G (MM-Me)         Where (MM-Me) is mass MM
      Ee  =   ³  1  Ä   ÄÄÄÄÄÄÄÄÄ          minus the mass of the Earth Me.
             \³           Cý R             MM is the mass of the Sun


 EQUATION I

    MM - ((MM + Me) x Ee) =  Me - K        Where Me is the mass of Earth,
                                           and K is (Venus - Mars)


      This formula (as exemplified in EQ I), might at first seem
      exciting until it is recognized that it is rather a sort of
      strange tautology.

      That is, further exploration shows that a relativistic factor Ex
      for any low mass aggregates in the range available for this solar
      system, for instance (MM + X)  or (MM - X), phases in to a seeming
      predictable result where:

          when Ex is determined as the relativistic effect factor
          for mass MM-X  (for instance using EQ H), then:

                MM - ((MM+X) x Ex) = Xx  = (X - K)

          where Xx = (X - K) results for any
          reasonable value assumed for mass X.

      But for higher masses (much beyond MM), the equality actually
      breaks down, demonstrating that there was no tautological
      equality to begin with.

      A formal description for showing the breakdown is:


 EQUATION J

              ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
              ³         2G (M-X)           Where (M-X) is mass M minus
      Ex  =   ³  1  Ä   ÄÄÄÄÄÄÄ            any other mass X, and radius
             \³          Cý Rx             Rx is the same for any values
                                           of (M-X), then:

 EQUATION K

      M - ((M) x Ex) = Kx            And:



 EQUATION L

     M - ((M+X) x Ex) =  Xx          And:


 EQUATION M

     Xx - X = Kx                     Where:


     Xx + Kx = X                     And:

     Xx = X - Kx                     Where X is the original arbitrary
                                     mass that was subtracted from M in
                                     EQ J, and was then added to M in
                                     EQ L








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