The Triangular System of Planetary Motion

The solar system is a circular motion system , but as I will now demonstrate for the first time, the mechanism by which it's bodies move in relation to the Sun is based on the triangle. Kepler stumbled upon the idea that a trianglular mechanism governed how the planets moved in 1595 while in the middle of a lecture on the conjunctions of Saturn and Jupiter. Each set of three points he wrote on the blackboard corresponded to a conjunction and formed almost  precise equilateral triangles. These triangles rotated around the board to form two circles, with the radius of one half that of the other one, approximating to the distances of Jupiter and Saturn. 

Thus, a triangular pattern determined the distances between two planets moving with a circular motion. This may have something to do with the fact that a circle is constructed using three points just like a triangle. He was then inspired by this discovery to fit the five Platonic polyhedra solids into an arrangement that corresponded to the known distances at the time between the six known planets. His completed model was magnificent but a little bit on the complex side (and proven to be a failure over time). He actually missed out on something much more simpler and even more remarkable which I will now demonstrate. He could have realised this after 1619, when he discovered his third law but at that stage his focus had shifted to the musical harmony of the planets. 

Keplers Third Law states that :

D³ 𝞪 T²

So if the distance of a planet from the Sun is doubled,

2³ = T²

T² = 8

T = √ 8

The change in orbital period is the square root of eight or 2.82. The planet will take 2.82 times longer to travel around the Sun.

Now we can work out the change in velocity. Remember the formula speed equals distance over time from school ?


V = D / T

V = 2 / √ 8

V = 2 / 2.82

V = 0.707


Or we can use my own formula V = √ √ F. The change in the force of gravity when the distance is doubled is 1/2² or 25% . The double square root of 0.25 is 0.707.

So, to sum up when:

Distance = x 2

Orbital Period = √ 8

Velocity = 0.707 


The great beauty of these numbers is that they are represented perfectly by Pythagoras's Triangle. Once again, remember from school, the square on the hypotenuse is equal to the sum of the squares on the other two sides. If the two sides are both two, then the longer side (hypotenuse) is equal to the square root of  2² + 2², i.e. √ 8, thus representing the change in orbital period.

The connecting line between the 90 degree angle and the centre of the hypotenuse is equal to half of √ 8 or 1.41.

1.41 divided by the side representing distance 2, equals 0.707. Thus this centre line represents the change in velocity.

Incidentally, Sine 45 degrees also gives 0.707.

So, the solar system is not a complex polyhedral system as Kepler believed, but is actually governed by a much simpler triangular mechanism. The secret to the Harmony of the Planets and the Mysterium Cosmographicum lies not with Plato and his solids but with the first known Greek mathematician and philosopher, Pythagoras of Samos, and his right angled triangle.

Why didn't Newton give credit to Kepler ?

On Page 108 of Newton's Principa, he introduces for the first time Kepler's Third Law, without actually naming it's originator :

COR. 6. If the periodic times are in the sesquiplicate ratio of the radii

The sesquiplicate is the square root of the cube, in this case, the Orbital Period is proportional to the square root of the distance cubed. Kepler's third law states that :

D^3 𝞪 T^2

Therefore,

T 𝞪 √ D^3



He then inputs this into a simple speed = distance over time formula :

V = D / T

V= D / √ D^3

V = √ 1 / D

Then, combining the centripetal force formula, V^2 / R, with the above, he arrives at the groundbreaking force equals the inverse of the distance squared formula :

the centripetal forces will be in the duplicate ratio of the radii inversely :

At this point, Newton stops to give credit to other english physicists for the famous formula :

as Sir Christopher Wren, Dr. Hooke, and Dr. Halley have severally observed

But he has omitted the origin of his starting point, Johannes Kepler, a giant whose shoulders Newton was standing on more than anyone else.