The following graphs are a proof of Newton’s mechanical laws about mass, distances and attraction forces. Unfortunately these laws do not confirm the elliptical orbit of the planets as said Kepler. Since 1609 we have been educated to accept Keplerian orbits and mathematicians have proved, even today, the exactitude of celestial mechanic. Do these mathematicians have cheated us?

Yes; shame for them. It is not late to correct mathematicians’ tricks and to approve a new celestial mechanic for the orbits of the planets. The orbits are not elliptical but cardioidal looking spirals; billions of spirals. So, there are no eccentricities, no Sun at one focus of an ellipse, no aphelion, no perihelion, no equality of swept out areas in equal interval of time.
It is difficult to change the perception of the community, the agreements of scientists, but shall we keep our mouth closed and obey the wrong education? No. Scientist should explore the realities and should not insist on wrong agreements.
Fig.1 is about Newton’s universal attraction law.

F=G*M*m/D^2

Since ( G,M,m) are known values the graph of F*D^2=Ct is an hyperbola.


Fig.1

That is:
When we know (G,M,m), the value of the Constant is known. Then, given the distance (D) between two masses, (D^2) is evaluated and the attraction force (F) is found. Graphically (F) is the length of the segment under the graph.

Newton has a second mechanical law: F=m*dV/dt
This means, when a mass (m) is accelerated by a difference of velocity (dV) a force (F) should have created this acceleration. No force, no variation in the velocity of the mass.
Graphically (D^2) shape is a parabola.
When we know (D),we find (D^2).
We translate this parabola to our known values: F=f0+f and D^2=d0^2+d^2
We say:
When d=d.max f=0 .This is the max.equlibrium position of the planet-Sun system.
When d=0 f=f.max. This is the crash condition of the planet-Sun system
Fig.2
Graphically we know (d),we know (d^2),we know (f)
Then, for unit evaluation, assuming (m=1 and dt=1)
F=m*dV/dt is transformed to be F=1*dV/1= dV and as we have F=f0+f
f=F-f0=dV-f0 will represent, in the mean time, the difference of velocity.
Now we may attempt to draw the trajectory of our planet, graphically.



Fig.2

dV is a radial velocity difference (dVr=Vr2-Vr1), variable as the length of the segment (f). Its direction is on the ray Sun-planet. It is a vector, while a perpendicular vector velocity (Vp) is an innate, constant velocity, due to Fattraction=Fcentrifugal. Vp is the imperative velocity for the equilibrium of the bodies. Without Vp bodies may not keep their equilibrium. Vp explain also why the bodies have to cycle one around the other; the celestial movement.Fig.3

To draw the trajectory of the planet, we start with (d^2=0 ; f=Vr2): values from the hyperbola.
An excel table may help us to understand the values (f).
We may arrange in the interval (d^2) as many evaluation lines as we want.
In this drawing example 16 lines are chosen. So that:
When d^2=0; f=Vr=2 and when d^2=16; f=0
f=0 has the meaning for Vr=0 at the max.distance between Sun-planet.
If we choose billions of working lines, we will get the trajectory of the planet for billions of cycles of the planet around the Sun.




Fig.3

The trajectory is a spiral; a cardioidal looking spiral. The planet has to come back to crash into the Sun. This is not an elliptical path as said Kepler. Mathematicians who have tricked Newton’s laws have to correct their reasoning. Their wrong reasoning is due to write Vp as variable. Vp is an innate velocity and is Constant.
They know, in polar coordinates:

Vp=r*dAlfa/dt=Ct then they write dVp/dt=0 then a trick and they say:
1/r*d(r*Vp)/dt=0 from there, after integration, they find r*Vp=Constant which means:
“areas swept out in equal time interval are equal”. Kepler’s second law.
This is a big cheat.
Kepler himself has refused his first law about elliptical orbit in 1618; fifty years before Newton. He understood, at that time, “the estimated elliptical orbit of the planets is tending to be circular, and the eccentricity will tend to zero, the eccentricities are not constant for eternity”: that was his third law about periods. With his third law, he meant “no eccentricity, no ellipse, no areas equality”. necattasdelen@ttmail.com

Your version / copy ogf this book has no diagrams - yet the book cannot be understood without them.

One of the vesions at Google Books has the diagrams (though not perfect) - see :-

http://books.google.com/books?id=xX0UAAAAQAAJ&dq=editions:OCLC312093471&source=gbs_navlinks_s