[Physics] Physics Digest, Vol 14, Issue 5

[Ruud Loeffen]

Hello Carl.

Your remarks about the Lagrangian points are interesting.

In fact Tufail Abbas and I tried to connect the concept of Lagrangian
point with "a-sol".  This a-sol is nothing but  proposed as most
probabilistic orbit in our solar system at a Radial Distance of about
8,8+11 meter away from the sun, which is analogous to Bohr Orbit of
Hydrogen Atom.  That is also the Distance to the Sun that fall between Jupiter
and Saturn.   However, yet we could not calculate to find any connection
between "Lagrangian" and "a-sol Distance".
Our paper  (Wave function of solar system
<https://drive.google.com/open?id=1Ro3PuiVIZGB2KXMjWsuB2S4BqYosfjWE> )
mentions this Distance in equation 2.3.
We stated:

*" Bohr radius of Hydrogen is the most probabilistic radius of the
electron, derived by formula a0 = re/α2 . Using the same definition we
shall define asol as per equation 2.3." *
In Appendix C you find the value for the Radial Distance asol
(8.803E+11 meter)


At this distance (8.803E+11 meter) away from the Sun  the Root Mean Square
Velocity (VRMS) is exactly 12278 meter per second. Jupiter is orbiting at a
velocity of about 13100 meter per second. The Lagrangian Point L2 from
Jupiter has an orbiting  velocity of 12624 meter per second at a Radial
Distance of: 8.32E+11 meter (derived from GM equals v^2 * Radial Distance).

If you are interested, you can find our calculations about the Lagrangian
points at: https://drive.google.com/open?id=1Bjlqmzuiqx426egdh1yAXdYjBDaMc
rcGh464Db_9_AU
<https://drive.google.com/open?id=1Bjlqmzuiqx426egdh1yAXdYjBDaMcrcGh464Db_9_AU>
Down Under the calculations you will find two graphs that express the
relation between the Distance of the planet to the Sun with the Orbital
Speed of the planet. In the graph you can see, that the 12278 point is the
lowest point near the edge (it depends on how you stretch the image)
I wonder: Is the Distance at L2 point of Jupiter the point that is the best
possibility for mass to "hang on" in orbit around the sun?



https://www.integrandoconhecimento.com/single-post/2016/07/13/%C3%89-assim-que-J%C3%BApiter-protege-a-Terra-contra-aster%C3%B3ides


*Best regards.Ruud Loeffen.*

On Mon, Apr 9, 2018 at 5:06 AM, <cj at mb-soft.com> wrote:

> I might have an idea for you guys.  About two hundred years ago, Laplace
> and Lagrange worked out the gravitational consequences of Newton's laws of
> gravitation.  It's really interesting stuff.  That was all "simple"
> (Euclidean) calculus, and one of the consequences that they figured out the
> Lagrange L4 and L5 points, both for Jupiter and for the Earth.  A company
> is even discussing building a HOTEL at the Earth's L4 point.
>
> In any case, I think that if you duplicate the math of Lagrange and
> LaPlace, your understanding of gravitation may grow.
>
> Further, there are some more advanced gravitational effects at both L4 and
> at L5, where the objects there follow very peculiar Lissajous orbits (in
> three dimensions).  I believe that math requires Riemannian Calculus to
> predict the orbits.  The Jupiter Trojans also move around in Lissajous
> orbits around each other.
>
> In any case, I think these objects might provide for you a more thorough
> math of the gravitation.  Many years ago, I duplicated much of Lagrange's
> Calculus (all simplly based on Newton's equations) and I think I learned a
> lot from that "homework".  As of yet, I have not tried to do the math
> regarding the Lissajous orbits.
>
> The Jupiter Trojans include thousands of asteroids in both groups.  Their
> Lissajous orbits are really complex, where they rarely hit each other, even
> in such tight orbits.  I don't think anybody knows yet WHY they don't
> collide more.  The Earth Trojans are pretty rare, mostly in our L4 and I
> think that only a couple small objects have been found in our L5 as of yet.
>
> Carl Johnson
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>
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