Pythagorean Grid, The reader may have noted on earlier graphs that the orbit of Mercury relates to the orbit of Mars, and Mars in turn relates to Uranus. If then, Mercury relates to Mars, and Mars to Uranus, it follows that in some way, Mercury must also relate directly to Uranus. This observation leads to the construction of the grid shown on fig 5 The grid, or matrix, is interesting in many ways, not least because it demonstrates how neatly the orbits are arranged in a bilateral Pythagorean pattern 'abc*ABC' that repeats itself four times. The grid illustrates how calculations can be made via a wide variety of different routes. It illustrates the symmetry in the mathematical arrangement that underlies the Solar System. Constructing a near-perfect grid The grid could be produced from (almost) pure maths, and would then be regarded as 'perfect'. We need to accept Earth as unity, and we need a knowledge of Mercury mean as a datum. These form a basis for calculating all the other orbits. To calculate all the orbits. First calculate 'V' from the Venus Equation, which fixes the Venus point on the 'y' axis. . ... V(9/4p) Use this value to calculate 'a' and 'b'. Use these to calculate 'c' from Pythagoras. Knowing that the values on the 'x' axis are ln30 times 'a','b', and 'c' we can calculate the values of A,B,C. and construct the near perfect 'matrix'. The orbits are then calculated from the node values of the grid, (illustrated) by raising to the inverted exponents. The calculated values deviate from the real orbits by about the same as those previously calculated in section one, from which we may conclude that the real System deviates from perfection by only a very small fraction of a percent. Fig 5 demonstrates how the entire known Solar System is contained within and limited by, the main equation. It also demonstrates that the equation does not itself reveal all the relationships. All the orbits can be calculated from any other.

Fig 5 [( p­(9/4p).Ln30) - F]­(2p/3) = 20p

[( AU(9/4p).Ln30) - F]­(2p/3) = Outer AU

Any point or distance on the diagram can be calculated by simple arithmetic. The nodal points reveal that there are two other subsidiary equation lines parallel to the main line.

Secondary Equation Fig 6 The lower of the secondary lines allows Mercury to relate directly to Uranus, Venus to Neptune, Earth to Pluto and Mars to the hypothetical Planet X. The equation for this line is similar to the main equation, except that the offset '-F' should be modified by adding +F2. F2 is the sum of upper case A+B+C. The values of upper case 'A,B,C,' are the same as the previously calculated lower case, a,b,c multiplied by Ln30. It follows that virtually any orbit can be calculated from virtually any other by adding or subtracting these values. Example. To calculate Pluto from Earth, (or Saturn) Calculate 'c' from Pythagoras. Sum a+b+c = 0.846486196 Multiply by Ln30 (3.401197382) A+B+C = F2 = 2.879066635 Calculating through the secondary line from Earth :- Earth is unity, one AU, and unity raised to the power of (9/4p) remains as unity. Unity multiplied by Ln30 minus F brings us to the Saturn point, which is calculated as 2.900425284.

Fig 6 Secondary Equation [( AU(9/4p).Ln30) -F + F2]­(2p/3) = Outer AU

Add the sum A+B+C and we get 5.779491919, which when raised to (2p/3) and returned to astronomical units yields the figure 39.41830761 AU. This is the same as the figure calculated from P2 (above). It is equal to Pluto mean, within 0.0525% of Nortons figure. Repeating the calculation from Mercury gives Uranus.(0.2%) Repeating from Venus gives Neptune.(0.2%) From Mars we get a figure that is the same as that calculated previously for planet X.

Trigonometry We have observed that the rule of Pythagoras can be applied to the calculation of orbits with a great expectation of success. The rule of Pythagoras applies, in its original form, to right-angled triangles, and there are no triangles visible on any of the figures provided. It follows that right-angled triangles are implied. The values of 'a,b,c' are related by Pythagoras as if they were the sides of a right angled triangle. It is only a small step of logic and maths to abstract the values from the matrix and configure them as triangles. If this is done using the calculated figures above, four identical triangles can be formed from the vertical axis. (Inner System) Four identical but larger triangles can be formed from the horizontal axis. The latter are Ln30 times larger than the former. The triangles can be constructed from the segments a,b,c and A,B,C, taken in succession but in different sequences. Obviously, trigonometry can be applied to these implied triangles, and the corner values calculated. Since the corners all represent orbits, the results are exactly the same results as those already obtained. All the triangles are 'similar' in the sense of the mathematical meaning used in geometry. They all have the same internal angles. The nominal angles are :- 35.879 degrees, 54.12 degrees. 90 degrees. Tan 35.879 is orbit of Venus in AU. Note...The ratio b/a is the same as B/A and is numerically the same as the mean orbit of Venus in AU (i.e. the ratio Venus/Earth)