Re: The falsity of Einstein's continuum


"Joe Fischer" <efischer@xxxxxxxxx> skrev i en meddelelse
news:5ov7t1tanqoav65u6jb0bsraadts1rd0tg@xxxxxxxxxx
> On Sun, "Ole D. Rughede" <ole.rughede@xxxxxxxxx> wrote:
>
> >"Joe Fischer" skrev :
> >> On Sun, "Ole D. Rughede" <ole.rughede@xxxxxxxxx> wrote:
> >> >Only elliptical orbits go by Keppler's law.
> >> >That is as the trace of a fix point on a small circle
> >> >rolling without friction on the inside of a great circle,
> >> >and when the small and the great circles are as 1:2.
> >>
> >> Can you explain this better, or provide a link?
> >
> >Make yourself a model Joe. You just need two
> >rulers at a right angle, and a third ruler with a central
> >point for a drawing pen or pencil and some removable
> >pins making a right line with the pencil-point.
> >You fasten one pin in the distance a from the penpoint,
> >the other pin in distance b from the pen.
> >Let the pins follow your right angel rulers turning the
> >drawing-ruler 90 degrees, and the pen will draw a
> >beatiful quater perifery of an ellipse with the half-axes
> >a and b.
>
> But you said two great circles, one inside the other.

And here I gave you another example working precise
like the rolling circles, you are going to try.
>
> In beginning astronomy, they suggest using a
> loop of string and two push-pins to draw an ellipse.
> >> An ellipse can have any eccentricity 0.0 to 1.0,
> >> with the 1.0 case being a parabola, but still one of
> >> the cases of being an ellipse. The circle is also
> >> an ellipse with an eccentricity of 0.0.
> >
> >Eccentricity 1 is a straight (double) line of a length
> >equal to twice the great half-axis a with b = 0.
>
> Eccentricity 1.0 conic section is a parabola.

You have just demonstrated the validity of your former
statement regarding ellipses. Strange isn't it? That a straight
line may be both an ellipse and at the same time a parabola?
May that be because of their familiarity as conic sections?
>
> >It is the trace of a fix point on the perifery of your
> >small circle rolling without friction on the inside of
> >a great circel of radius twice the smaller one.
> >Eccentricity 0 means a = b, why it is a circle of
> >radius r = a = b.
>
> Yes, here is a circle drawn to 1/8 inch precision.
>
> o

Very fine! Let's make a conus of hight a cm and this fine
circle as its base. Make a cut along a plane in touch with
the conic surface, and you have a line as a conic section
showing the strange ellipse-parabola of e = 1, and of
length a little bit longer than a. - You may calculate the
length, if you know the radius of your circle.

Now let the radius diminish. We still have a cone! Let
the radius be infinitesimal small. We still have a cone?
But waw! Has it changed into just a line like a light-ray
of only length a cm, which is both a straight line, an
ellipse, and a parabola?
>
> >You see, the whole geometry incuding Euclidean
> >may be represented in elliptic geometry!
>
> Even hyperbolas?

What do you think you could do with your straight line?
>
> >> So how can the 1:2 ratio circles describe any
> >> of the many shapes and sizes of an ellipse.
> >
> >You show with your model.
> >>
> >> >Here we have a hypocycloid orbit meaning another
> >> >ratio than 1:2 between our circles.
>
> I still am not able to see that.

Take your great and small circles. Make the small circle a
little bit smaller, and try to draw an ellipse as explained.
What do you see?
>
> >> A parabola has what is called a parameter of
> >> 2, with the circle have a parameter of 1.
> >> Could this be what you meant (probably not).
> >
> >No. You will have to study geometry!
> >>
> >> Also note that the anomaly of the orbit of
> >> Mercury is ~5500 seconds of arc per century, while
> >> the previously unaccounted for, and the additional
> >> advance of the apsides predicted by Einstein being
> >> only ~43 seconds of arc.
> >
> >We are here talking exclusively about the 43 seconds.
> >Perturbations from the other planets are accounted for.
>
> And you can draw 43 seconds?

Certainly, and so can you. Make two pen-dots in distance
1 cm from each other on a piece of paper, and tell me at
which distance that is the ends of an angle of 43 arc sec.
>
> >> I don't see how the two great circles could
> >> be used to generate anything resembling the large
> >> advance of the apsides caused by the perturbations
> >> of all the planets, plus the additional advance of 43
> >> seconds.
> >> Joe Fischer
> >>
> >Oh, very easily. You are a mechanic. When you
> >have finished your ruler experiments, you may find out
> >how to make yourself a drawing tool with which to
> >make perfect complete ellipses of any eccentricity
> >0 </= e </= 1.
>
> I can't think of any use of an ellipse drawing tool.
>
> >(Spare the bigger hammer, if you can't make it move
> >at a first trial. It's a question of finesse).
>
> I use the hammer very precisely.
>
> >Your next step will be to calculate very easily the
> >the total length of the ellipse perifery as 4aE, and to
> >find out why the total energy of an orbiting planet
> >is exactly proportional to the great half-axis a.
>
> Not likely, I don't do math.

I cannot believe that you don't count your money.
The great mathematician Poincaré once has said that
everything in mathematics can be understood from
just adding 1 once again. That's like counting money.
>
> >Then you may turn to the construction of some fine
> >apparatus with which to draw the most beautiful
> >hypo- and epi-cycles. And another one for drawing
> >cycloides and ket-lines. Maybe also the many other
> >fascinating geometric curves you may see in:
>
> I made parabolic drafting tools 30 years ago,
> they have a number of uses.

Such as?
>
> >Schaum's Outline Series: Mathematical Handbook of
> >Formulas and Tables, McGraw Hill Book Company,
> >New York, St. Louis, San Francisco, Toronto, Sydney.
> > - I guess in many reprints through the years. -
> >Originally by M. R. Spiegel, Rensselaer Polytechnic
> >Institute, September 1968.
> >Ole
>
> I have a few books older than that, Airy,
> "Gravitation", 1834, and another that describes
> geometry verbally.

Will you sell me the book? Name a prize!

My oldest book is C. Plinii, De mundi historia,
Liber 11, Francoforti ex officina Petri Brubachij,
Anno MD LIII (that is AD 1553), in which
Plinius the elder refers the observation of a Nova
long before Tycho Brahe's famous observation of
his Stella Nova in Cassiopeia 11. November 1572.
Tycho was born 14. December 1546, thus almost
26 years old when he made the observation which
he described in the book "De nova Stella".
>
> But why do you mention drawing where
> 43 seconds is mentioned?
>
> Joe Fischer
>
To illustrate how we may percieve what it going on
in the Mercury orbit. Did we succeed in that?

Ole


.

Relevant Pages
Quantcast