Exercise style ...

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   Good evening.                                                                                  

   A Let's, the article of the day is dedicated to the star among the "stars", I appointed the Sun.
This fascinating object, as useful as air and water to life, has always inspired poets and scholars since the dawn of time (especially the day actually). It is obvious inescapable.
Yet our star long remained a mystery absolute, for its operation as well as its physical characteristics. You have to go back very far in the past men to notice how it has influenced, guided and inspired. The architecture of the pyramids, the megalithic alignments, temples, all signs of adoration and fear shaped by humans for RÅ

A simple question, however, and the magnificent edifice of ancient celestial science collapses:

                               How far the earth is the sun ?

    Cruel question that remained unanswered for a long time precisely. From Anaximandre (560 BC) to Jones in 1931, changed the estimated 172 000 ..... 149 670 000 km: almost a 1000 error factor ! The real value is quite recent, since it is official since 1976 and is 149 597 870 km.

    It sees how Kikoidon, which raises the same question, will have to use reflection in turn and without instrumentation, obtain a suitable outcome.
He knows that the equation of Kepler does not help because it depends on the mass center (in this case the sun) and that this value it is not known. In fact, all this could stop there if nature had in his infinite goodness, offered an alternative route, a guide: the star of the shepherd! This very bright star in the sky always has been a haven for travelers astray. It has been known since forever and with this is not a star but a planet almost identical to ours and it is called Venus!

    We already know from the previous article that the key to success is K. Therefore remains to find a precise method to calculate the "K sun." If we succeed, this key will open all doors of our solar system.

What we know:

The sidereal period (Tt) of the Earth, which is a year or 365.25 days

The sidereal period (Tv) of Venus, known since antiquity, or 224.70 days

Earth and Venus around the sun (clear, though ...)

Earth and Venus have an almost circular orbit.
.
... Et voila!

A drawing worth sometimes a long discourt:


The angle b is 45 degrees. Tangent b = 1

R = Rsv + Rvt

Tt)2 / R3= (Tv)2/ Rsv3 = Ksoleil 

It can calculate the report as:

Tangent has = 0;726> a = 36 °

So Rsv = 0;726 x RVT R and R x = 0;273


    Without Newton in the case remain there, but we know from "La lune est une pomme" that Fi = Fg and therefore (without repeating the demonstration) as V = √2 (GM / R) where V = 2Pi R / T . M is the mass of the sun and R his distance of the object in orbit.
That seems to be complicated, but in fact it remains unknown as 2 (M and R) and 3 equations where R is the Earth-sun distance, the distance Rv Sun-Venus and M the mass of the Sun.

1)  R = √3( M x Tt2 x G / 4 pi2) > R = √3( M x Tt2 x 1.69 x 10-12) > R = 1.2 x 10-4 x √3( M x Tt2 )

2) Rv = √3( M x Tv2 x G / 4 pi2)  >  
Rv = 1.2 x 10-4 x √3( M x Tv2 )

3) 
Rv = R x 0.725  > Rv / R = 0.725


We can now choose the value of M for that equivalence 3) be respected.

For M = 2 x 1030 kg, we find :

 R = 1.2 x 10-4 x √3 ( 2 x 1030 x (365.25 x 24 x 3600)2 ) ≈ 1.5 x 1011 m.

Rv = 1.2 x 10-4 x √3 ( 2 x 1030 x (224.7 x 24 x 3600)2 ) ≈ 1.09 x 1011 m.  

Rv / R = 1.09 / 1.5 = 0.726

     Any value of M differs from the precision found. We are very close to the exact value of official distance (to rounding calculations nearby). We can therefore say with certainty that the mass of the sun is 2 x 1030 kg (a little less to complete the equation), that Venus is 109 million kilometers of solar center and the earth is a penalty less than 150 million km from its star!
     The solar képlérien is therefore Ksoleil = 9.37 x 10-27. This value will be "universal" to anything that might be found in orbit around the sun. That is the key to the solar system.

     Finally, even if this requires a significant amount of calculations, the result obtained by simple observation is of extreme precision. It seems surprising that the characteristics are found so long remained very rough! It must then believe that Kepler and Newton especially did not have scientific calculator ...

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