By
ignorance I posted in the No new theories policy and I received a warning
“please don’t post here unless your theory has been published in a pear
reviewed paper. Also, if you have ideas regarding current ACCEPTED THEORY,
please use the SPECULATION FORUM to post them in”, by Sonata Design Xbox 360,
Fernanda Founder, http://www.advancedphysics.org/forum
Thus here I
am in the SPECULATION FORUM to present some REASONING ABOUT the ACCEPTED THEORY
of THEORY OF RELATIVITY. Thus I will be bound to Einstein’s formulas/equations
and I will try to evaluate such theory. Maybe like the way a student found an
unknown root for an equation (or system of equation) and is able to show that
mathematically such solution, to find such unknown root, is very sound. Thus we
may evaluate Theory of Relativity following the accepted theory and the
possible results from Einstein’s equations. Just a mathematical reasoning, I
guess, and its implications.
SECOND LAW OF UNIVERSAL GRAVITATION:
other deduction (exact one, from classic equation)
Eo
= mo . c2 (internal energy at rest, at Vo=0)
m1 =mo. (1 – V12/c2)-1/2
E1
= mo . c2 . (1 – V12/c2)-1/2
= m1 . c2
DIFERENTIATING first left pair:--à (1)
dE = mo
. c2 . ( -1/2) . (1 – V2/c2)-1/2
–1 . ( - 2 . V/c2) . dV -----à (2)
dE = mo
. V . (1 – V2/c2)-3/2 .
dV -----à (3)
F . V = P
(Power = Force x Velocity) Multiplying both sides by "dt" ---à (4)
Notice
that E = Energy = Power x time dE = P
. dt and replace with (3)
F.
V. dt = P . dt = dE = mo
. V . (1 – V2/c2)-3/2 .
dV ---à (5) Divide all by V . dt
F = mo
. V . (1 – V2/C2)-3/2 .
dV / (V . dt) --à (6) dV /dt = a = acceleration
F = mo . a . (1 – V2/c2)-3/2 -----à (7)
This is the total force F required to apply to reach a given velocity V
Let
us define b=
-V2/c2 and <"n"=
-3/2 With (1+b)n obtained by
Taylor’s
series for (1 + b)n = 1 + n/1.(b)+(n).(n-1)/(1.2).b2+n.(n-1).(n-2)/(1.2.3).b3
+
+
n.(n-1).(n-2).(n-3)/(1.2.3.4).b4 +
n.(n-1).(n-2).(n-3).(n-4)/(1.2.3.4.5).b5... easy to write next
terms... (8)
From
equations (7) and (8) we obtain the combined equation (using Taylor’s series):
F = mo . a . (1 – V2/c2)-3/2 = mo . a . { {1 + 3/2 . (V/c)2 +
3/2 .5/2 /(1.2).(V/c)4 + 3/2 . 5/2 . 7/2/(1.2.3).(V/c)6
+...} ---à (9)
F = mo . a . { 1 + 3/2 . (V/c)2
+ 15/8.(V/c)4 + 35/16.(V/c)6 + + 315/128 . (V/c)8 + 693/256 . (V/c)10
+ ...} easy to compute more
terms...(10)
Let us
separate the terms that have (V/c) (from right side) and put them into
evidence:
F = mo . a . { 1 } + mo
. a . (V/c)2 . { 3/2 +
15/8.(V/c)2 + 35/16.(V/c)4 + 315/128 . (V/c)6 + 693/256 . (V/c)8
+ ...}
F = F1 + F2nd = TOTAL APPLIED FORCE TO ACCELERATE =
CONVERTIONAL INERTIA ACCELERATION FORCE + GRAVITY INERTIAL ACCELERATION FORCE (it is what mathematics is telling us; I am
only an ignorant, and maybe this is not the proper interpretation).
F1 = mo . a (Newton’s
traditional law, for common INERTIA)
F2nd = mo . a . (V/c)2 . { 3/2 + 15/8.(V/c)2 + 35/16.(V/c)4
+ 315/128 . (V/c)6 + 693/256 . (V/c)8 + ...} = as we can see it is a DIRECT and
EXPLICIT function of (V/c). Thus in the usual Physics of low velocities, V/c is
negligible and thus is the SECOND FORCE OF GRAVITATION
Integral
of F2nd . dL (along the length where Force F2nd is being applied) = ENERGY
STORED INTO THE PARTICLE BEING ACCELERATED, as INTERNAL GRAVITATIONAL INERTIAL
ENERGY. If the particle is de-accelerating (under a break), then such INTERNAL
GRAVITATIONAL INERTIAL ENERGY is used to “resist” against the de-acceleration:
INERTIAL EFFECT. Thus it is like storage of energy from the first type of
gravitational energy.
F2nd
Law of Gravitation (against increasing velocity) = F – (Mo . a) = Faditional
to provide ENERGY WHICH IS STORED AS “GRAVITATIONAL INERTIAL ENERGY” and we
reason as being increase of “tangible mass”.
You can see this is the OTHER “ROOT” reasoning, from the same EINSTEIN’s
equation and classic reasonings. But they are only mathematics speculations. RED INTO MASS "Mo" accelerating in Velocities
"V" near to velocity of light ("C"):
SECOND LAW OF UNIVERSAL GRAVITATION: F2nd = mo .
a . {1 + 3/2 . (V /c)2 + 15/8 . (V /c)4
+ ... }
EFFECTS OF FIRST AND SECOND LAW OF UNIVERSAL
GRAVITATION
Let us examine the effect of several
V/c values on traditional "g" values, for a particle leaving Earth,
vertically (outward): Using equation
(10):
F= mo . a . { 1 + 3/2 . (V/c)2 + 15/8.(V/c)4
+ 35/16.(V/c)6 + + 315/128 .
(V/c)8 + 693/256 . (V/c)10 +
V/c = 0 g = mo. a = mo. g (g = 9.822
m/s2 approx.; see above discussion)
F=mo . g 0% error
V = 8 km/s (required to orbit
around Earth, as satellite) c=300,0000 km/s (rough)
V/c = 8/300,000 = 2.66667 . 10-5
Using in above equations (Taylor’s series development):
F = mo. g . 1.0000000011 (error = 0.000 000 1067
%)
Using V/c = 11 km/s (to depart from
Earth gravitational field)
F = mo. g . 1.0000000020 (error = 0,000 000
2017%)
CONCLUSION: we can neglect the 2nd GRAVITATIONAL LAW EFFECTS FOR OUR
PRACTICAL VELOCITIES OF TRAVELLING FROM EARTH.
V/c = 110 km/s = 396,000 km/h
(10 times greater than required to leave Earth)
F = mo. g . 1,0000002017 (error = 0,000 020 166
7 %)
V/c = 1,100 km/s = 3,960,000
km/h (100 times greater than required to leave Earth)
F = mo. g . 1.0000201670 (error = 0,002 016 700
6 %)
V/c = 11,000 km/s = 39.600,000
km/h (1,000. times greater than required to leave Earth)
F = mo. g . 1.0020200611 (error = 0.202 006.1111
6 %) STARTS MAKE EFFECTS
V/c = 110,000 km/s = 396.00,000
km/h (10,000. times greater than required to leave Earth)
F = mo. g . 1.2417967051 (error = 24.179 670 5056 %) GREAT EFFECTS
V/c = 220,000 km/s = 792,000,000 km/h (20,000. times
greater than required to leave Earth)
F = mo. g . 3.0167357854 (error = 201.6735785400%)
HUGE EFFECTS
We should take into account that we are using the
approximate formula, based on Taylor's series, just to separate (to stress, to
show up) the two type of gravity in the formula, splitting their effects.
For so great velocity, as 220,000 km/s we should use the
more rigorous (the exact) formula, as we deducted (in so simple way) from
Einstein’s formula in (7) above (we deducted)
F
= mo . g. [1 – (V/c)2](-3/2)
V/c = 220,000 km/s = 792,000,000 km/h (20,000. times
greater than required to leave Earth)
F = mo. g . 3.182172866 (error = 218,2172866
%) HUGE EFFECTS; difference with above 201.673 is due to Taylor’s series
was not computed with much greater number of terms of series.
(Using Taylor's series, I developed in several terms, I
got:
F = mo. g . 3,0167357854 (error = 201,6735785400%)
HUGE EFFECTS)
Thus, only for LINEAR ACCELERATORS, and something like
that, is that it is required to use the effects of the SECOND LAW OF UNIVERSAL
GRAVITATION on EARTH, in which can be “even” generated a NEGATIVE GRAVITATION
EFFECT, as if EXPELLING AN OBJECT OUT OF A STAR, instead of just attracting it
(as from the FIRST LAW OF UNIVERSAL GRAVITATION): that is very easy to understand
evaluation the effects of 2nd Law of Gravitation in the orbit of passing nearby
tangible matter of light energy particles. BUT REMEMBER, these are only
SPECULATIONS that are result of examining Einstein’s FORMULA from THEORY OF
RELATIVITY limits, as if trying to understand the effects of a possible hidden
root. savelli_curitiba @hotmail.com
********************** My ANSWER,
after posting Above messages, split in two parts *****************
I am not
Galileo Galilei. But Celso Savelli Gomes
I know all
"Wises" of Catholicism were not interested in sharing ideas with him
and that they decided he could not keep sharing his own ideas around, in
Forums. Thus the simplest solution adopted by those Wise Men was to judge him:
"You are banned for these specific reasons:..... You are to never more to
say Earth is moving around. Just to be sure on it, you are to remain in prison,
forever. And the date when the ban will be lifted will be: Never".
I guess
this is the message ADVANCED PHYSICS FORUMS is providing, as if some Medieval
(Inquisition) reasoning. Just being blind to not so orthodox things. This is
exactly as that group of scientists-theologians did with Galileo.
When in
fact a site (Forum) like yours is exactly for such "open review of ideas
and reasoning", even somewhat variant of classic orthodox Physics, just to
screen out what can be demonstrated as being wrong.
And in your
case I followed your own rules. Because all I presented was limited to the
"classic Physics", including the Theory of Relativity, and by the
classic Mathematics. I guess (and hope) this is the truth. I departed from the
FORMULAS of Classic Theory of Relativity, from Einstein's, and I remain bound
to them, ALL THE WAY. The only thing is that I included and evaluated the
results that I got, only mathematical solutions (as if new root FOR THE SAME
Einstein's EQUATIONS), as comparing what could be their meaning.
But adding
up such values, the result is exactly the same as provided by Einstein's
formulas, because they departed from Einstein's reasoning. It is as if A = B +
C. And it was obtained A = D + E (as if another mathematical root) and such
"strange result" is evaluated, but it is also "Einstein's son
result".
I would
like you revise your message, which is quite like the one provided to Galileo
Galilei by some "scientific intolerance Inquisition decision", and
now without a fair trial and judgment by the Academic community. And now not
even having a chance to see you demonstrate in a trial that Galileo's
proposition A = C + D is "absurd, wrong" because of "this, this
... and that". I guess SCIENTIFIC and ACADEMIC FORUMS are exactly for
such, not for:
"You
have been banned for the following reason: Please find another forum to share
your ideas with. Date the ban will be lifted: Never". Blue Skinny. April
15, 2006.
I guess you
could suggest a more open-minded Forum that I could try, as if suggesting to
Galileo Galilei to move to China or Japan, Earth extremities.
Best
regards, sincerely yours, Celso Savelli Gomes
I hope you
provide some answer and if possible lift the "ban".
Linked author’s sites in:
http://www.anti-relativity.com/forum/viewtopic.php?t=239
(CONVENTIONAL MASS
“mo” NOT INCREASING WITH HUGE VELOCITIES.)
http://br.geocities.com/celsosavelligomes/SECOND_LAW_GRAVITATIONexactly.htm
http://geocities.yahoo.com.br/celsosavelligomes/SECOND_LAW_OF_UNIVERSAL_GRAVITATION.htm