15  The advance of Mercury's perihelion

    Newton's gravitational expression is as follows according to the particle outside and inside of the sphere.

    ...............Equ.15.1
     - radius of the sphere;   r - distance between the particle and the sphere;  M - mass of the sphere;   m - mass of the particle.
    Why Newton's theory can not explain the advance of Mercury's perihelion?  What is the real reason? We had analyzed the ruler, clock and mass in the gravitational field, noticed that these parameters are variational. however, Newton's theory takes all these parameters as constant. In other words, the gravitational field is more weaker the Newton's theory is more preciser. Since the Mercury is more near to the sun, this variation can't be ignored. If we convert these parameters into that in the flat space, they can meet the Newton's theory.
     Let the ratio of the two distances is
   
    R0_distance in non-gravitational field.
    Rg_ distance in gravitational field,
    Rruler in the gravitational field:
    ...............Equ.15.2
    So:
    ...............Equ.15.3
   By reason of maths, the formula above can not be integral at present, Certainly, we can also solve this problem by computers. Here, we will make use of approximation to solve it. First, a curve are described with the relation between r-L in the gravitational field as showed in the Fig. 15.01.

Fig. 15.01 the relation between R and L in the sun gravitational field

   The ratio of the distances is equal to the one of the two areas, i.e. A0 / AL. It can be proved that Equ: :    ...............Equ.15.4
    The ratio of the two distances is approximately equal to the ratio of the two scales of the half distances from the Mercury to the Sun. We can also educe the relation of m with the same method. So the Newton gravity in flat space is as follows.
   
    Place the equation above into the equation 15.4, then unfold it and ignore small variables.
    ...............Equ.15.5
    Placing F into Binai formula, we can get the following equation.
   

    Let:
          
    Then the equation above will be as follows:
   
    Let:
    £¬  £¬  So£º     
   Select a suitable axis, then:
   
   
   
    The equation above is the Mercury's orbit equation because that:
   
   The procession of the Mercury revolving around the sun one round is calculated as follows
   
   
    
   
   The cycle of the Mercury is 87.969 days. In one year of the earth, the Mercury rotates 4.1521 rounds. So, the procession in a century is as follows.
   
   this calculating result is: 43¡¨.00. The result from the general theory of relativity is: 43¡¨.89. The actual observation is: 43¡¨.37.
   Of course, we know that this is the result by the mean of approximation. Strict solution should be much closer the observation.
   The following is the expression of general theory of relativity for reader reference .
   
   The readers who are interested in this field can calculate the Equ.15.3 to obtain its precise results by computers. The Newton's theory can solve completely the advance of Mercury's perihelion if we understand the arcanum. The sun's gravitational field which at the Mercury is stronger than other, change of distance and mass is much notable.

Zhan, Li Kui 6/18/2007

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