QE6 - Element 115 (Solution Algorithm)
(1) Input Data: Date Format = DD/MM/YYYY
•
(1.1) National Institute of Standards & Technology (NIST): Revised - 07/12/2019
G
6.6743 .10
<---- Newtonian Constant of Gravitation
2
kg .s
3
2.897771955 .10 .( m .K )
KW
•
3
m
11 .
6.62607015 .10
h
<---- Wien Wavelength Displacement Law Constant
NA
34 .
( J .s )
Q e 1.602176634 .10
<---- Planck's Constant
1
23
6.02214076 .10 .
mol
<---- Avogadro's Constant
8.314462618 .
R
19 .
(C)
J
mol .K
<---- Molar Gas Constant
(1.2) Particle Data Group (PDG): Revised - 07/12/2019
me
0.5109989461
MeV
938.2720813 .
2
c
939.5654133
mp
mn
24
5.97217 .10
ME MS
h PDG
H0
9.777752 .( Gyr )
1.98841 .10
∆H 0
30
h PDG
.( kg )
RE RS
6.3781 .10
6
8
6.957 .10
0.005
9.777752 .( Gyr )
H0
H 0 = 67.4026129080527
.( m )
R0
km
s .Mpc
8.178 .( kpc )
T0
∆H 0 = 0.500019383590893
2.7255 .( K )
km
s .Mpc
∆T 0
0.0006 .( K )
(1.3) Planetary: Revised - 07/12/2019
24
0.07346 .10
MM MJ
1898.19 .10
24
.( kg )
h PDG
0.674
Exact Values (Definitions): Updates Not Required
AU 149597870700 .( m )
•
<---- Electric Charge (Elementary Charge)
16
pc 3.08567758149 .10 .( m )
<---- https://nssdc.gsfc.nasa.gov/planetary & http://nssdc.gsfc.nasa.gov/planetary/factsheet/
RM RJ
( 1738.1 71492 ) .( km )
(2) Constants & Units
•
(2.1) Physical Constants (NIST Definitions - Updates Not Required)
c 299792458 .
m
<---- Speed of Light in Vacuum
s
m C12
•
α
3 kg
12 .10 .
mol
ε0
8.854187817 .10
12 .
F
m
<---- Permittivity (Electric Constant)
µ0
7 N
4 .π .10 .
2
A
<---- Permeability (Magnetic Constant)
<---- Molar Mass of Carbon 12
(2.2) Atomic / Nuclear / Fundamental Particle Characteristics (NIST Definitions - Updates Not Required)
2 .π .Q e
2
m C12
m AMC
4 .π .ε 0 .h .c
R∞
12 .N A
2
α .m e .c
2 .h
3
re
α
4 .π .R
by substitution ---->
∞
re
1
4 .π .ε 0 .m e
.
Qe
2
c
Above: equations for " α ", " m AMC " {AMC = Atomic Mass Constant}, Rydberg's Constant " R ∞ " & Classical Electron Radius " r e "
2
ω Ce ω CP ω CN
•
λh
2 .π .c .
me mp mn
h
<---- "h-bar" form of the Compton Frequency (as stated in QE3, pg. 30: this is the only instance where the "h-bar" form of Planck's Constant, i.e. Dirac's Constant, is applied)
(2.3) Planck Characteristics (Dimensional Definitions - Updates Not Required)
G .h
c
3
mh
Riccardo C. Storti
h .c
G
th
G .h
c
5
ωh
1
th
Note: NIST utilizes the "h-bar" form, i.e. Dirac's Constant. However, Planck's Constant is utilised to define Planck properties herein
1
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•
(2.4) General Definitions (Updates Not Required)
4. . 3
πr
3
V( r )
•
eV
ρ m( r , M )
M
g( r, M )
G .M
M BH( r )
2
V( r )
r
2
c .r
2 .G
R BH( M )
2 .G .M
c
γ
2
(2.5) Units of Measure (Definitions - Updates Not Required)
Qe
.J
<----Electron Volt (definition): NIST
C
Jy
10
W
26 .
2.
Ns newton .s
Lyr c .yr
( mΩ µΩ nΩ pΩ fΩ aΩ zΩ yΩ )
( mT µT nT pT fT aT zT yT )
Scale 1 .( Hz )
Scale 1 .( ohm )
( mJ µJ nJ pJ fJ aJ zJ yJ )
Scale 1 .( J )
( mV µV nV pV fV aV zV yV )
Scale 1 .( T )
Scale 1 .( volt )
( mgm µgm ngm pgm fgm agm zgm ygm )
( mJy µJy nJy pJy fJy aJy zJy yJy )
Scale 1 .( Jy )
( mpc µpc npc ppc fpc apc zpc ypc )
( kJ MJ GJ TJ PJ EJ ZJ YJ )
Scale 2
( kV MV GV TV PV EV ZV YV )
Scale 1 .( s )
( kJy MJy GJy TJy PJy EJy ZJy YJy )
( ks Ms Gs Ts Ps Es Zs Ys )
6
10
9
10
12
10
15
10
18
10
21
10
24
Scale 1 .( W )
Scale 1 .( Pa )
Scale 1 .( newton )
( mSt µSt nSt pSt fSt aSt zSt ySt )
Scale 1
( mm µm nm pm fm am zm ym ) Scale 1 .( m )
Scale 2 .( Hz )
Scale 2 .( W )
Scale 2 .( Pa )
( kPa MPa GPa TPa PPa EPa ZPa YPa )
( keV MeV GeV TeV PeV EeV ZeV YeV ) Scale 2 .( eV )
( ms µs ns ps fs as zs ys )
Scale 1 .( pc )
( kW MW GW TW PW EW ZW YW )
Scale 2 .( volt )
10
( mN µN nN pN fN aN zN yN )
Scale 1 .( gm)
( kHz MHz GHz THz PHz EHz ZHz YHz )
Scale 2 .( J )
3
( mPa µPa nPa pPa fPa aPa zPa yPa )
Scale 1 .( Ns )
( mNs µNs nNs pNs fNs aNs zNs yNs )
Scale 1 .( gauss )
( kSt MSt GSt TSt PSt ESt ZSt YSt )
10
( mW µW nW pW fW aW zW yW )
( mgs µgs ngs pgs fgs ags zgs ygs )
µ
Scale 1
m Hz
( mHz µHz nHz pHz fHz aHz zHz yHz )
•
0.57721566490153286060651209008240243104215933593992
( kN MN GN TN PN EN ZN YN )
Scale 2 .( newton )
( kΩ MΩ GΩ TΩ PΩ EΩ ZΩ YΩ )
Scale 2 .( ohm )
( kT MT GT TT PT ET ZT YT )
Scale 2 .( Jy )
Scale 2 .( T )
Scale 2
3
10
10
6
9
10
10
12
10
15
10
18
10
21
10
24
( kLyr MLyr GLyr TLyr PLyr ELyr ZLyr YLyr ) Scale 2 .( Lyr )
( kK MK GK TK PK EK ZK YK )
Scale 1 .( A )
( mA µA nA pA fA aA zA yA )
( mC µC nC pC fC aC zC yC )
Scale 1 .( C )
( kA MA GA TA PA EA ZA YA )
( kC MC GC TC PC EC ZC YC )
Scale 2 .( K )
Scale 2 .( A )
Scale 2 .( C )
( kyr Myr Gyr Tyr Pyr Eyr Zyr Yyr ) Scale 2 .( yr )
( meV µeV neV peV feV aeV zeV yeV )
Scale 1 .( eV )
( kpc Mpc Gpc Tpc Ppc Epc Zpc Ypc ) Scale 2 .( pc )
Scale 2 .( s )
( mK µK nK pK fK aK zK yK )
Scale 1 .( K )
(2.6) Computational Initialisation & Graphical Range Variables (Updates Not Required | Do Not Modify)
1
r x1
1
3
m g1
1
Riccardo C. Storti
η
4.595349
TW
3 .( Myr )
MG
11
6 .10 . M S
ωt
rnd( 1 ) .( Hz )
tt
1
ωt
2
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(3) Electro-Gravi-Magnetics (EGM)
K PV ( r , M )
r .c
r .c
2
2
C PV n PV , r , M
2 .G .M
G .M .
2
2
π .n PV
r
n PV
ω PV n PV , r , M
r
3 . . .
. 2 c G M. K
PV ( r , M )
π .r
T PV n PV , r , M
1
c
λ PV n PV , r , M
ω PV n PV , r , M
3 .M .c
U m( r , M )
ω PV n PV , r , M
2
3
4 .π .r
3
h .
4
ω PV( 1 , r , M )
3
2 .c
U ω ( r, M )
108 .
Ω ( r, M )
U m( r , M )
12 . 768
EΩ
m γγ
mγ
H U5( r , M )
dH dt H γ
m γγ
.ln
mγ
rπ
Nγ
rν
( 3 .π )
h
7 .µ .
5
U m( r , M )
5
µ
2
32
256
2
H α .H γ
. 5 .ln 1 .µ 2
2
Hγ
5 .µ
Hγ
. µ mh
.ln ( 3 π ) .
M
4
µ
3
4
2
.
r
2
7 .µ
n Ω ( r, M )
7 .µ
.
5
mh
5 .µ
rε
4
12
Ω ( r, M )
1
ω Ω ( r, M )
n Ω ( r , M ) .ω PV ( 1 , r , M )
mγ
512 .h .G .m e
c . π .r e
2
.
n Ω r e, m e
ln 2 .n Ω r e , m e
r π.
1 . me
9
2 mp
2
λx
2 .µ
4.
π
µ
mx
λx
Hα
2
ωh
λx
tα
1
Hα
2
.
4 .µ . λ x ω h
µ
π
( 4 .µ ) .c
St T
2 .µ
γ
EΩ
h .ω Ω r e , m e
2
T U2( H )
K W .St T .ln
Hα
.H5 .µ
2
H
5
2
.
M
λh
Ω ( r, M )
1
.
ω CP
c .ω Ce 27 .ω h .ω Ce ω CP
.
.
5
4
4
1 .
1
32 .π
3 ω
ω CN
CN
2
2
U ω ( r, M )
U ω ( r, M )
1
Nγ
81 .
2
26 .µ
r
ρ U5( r , M )
λh
3 .H U5( r , M )
2
8 .π .G
A U5( r , M )
1
H U5( r , M )
R U5( r , M )
c .A U5( r , M )
M U5( r , M )
V R U5( r , M ) .ρ U5( r , M )
1
Given
dH dt
T U2 H U5 r x1 .R 0 , m g1 .M G
T0
r x1
m g1
η
H U5 R 0 , M G
Riccardo C. Storti
Hα
1
t EGM
Predicted Galactic Radius
0.988785473962701
m g1 = 1.00215256472725
η
H EGM
η
H U5 R 0 , M G
r x1
Find r x1 , m g1 , η
H U5 R 0 , M G
R 00
r x1 .R 0
R 00 = 8.08628760606697 ( kpc )
Predicted Galactic Mass (Virial)
MG
m g1 .M G
M G = 6.01291538836348 .10
11
MS
•
Note
Predicted Galactic Mass is utilised herein
because it is not a PDG listed value
4.59534958578387
A U5 R 0 , M G
R EGM
R U5 R 0 , M G
M EGM
M U5 R 0 , M G
T EGM
T U2 H EGM
3
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(4) dgE Spreadsheet Calculator
Calculator 1
•
G = 6.6743 10
3
m
11 .
h = 6.62607015 10
2
34 .
2
kg .
m
s
kg .s
th
G .h
c
5
c = 2.99792458 .10
t h = 1.35138507828468 10
2
.
4 .µ . λ x ω h
St T
µ
π
( 4 .µ ) .c
2 .µ
43 .
s
ωh
8
m
3
K W = 2.897771955 10 .m .K
s
1
42
ω h = 7.3998153159224 10 .Hz
th
λ x 4.
km
= 3.2407792894458 10
.
s Mpc
3
2 .µ
π
1
µ
λ x = 2.69870895208366
µ
Hα
ωh
λx
20 .
7
yr = 3.1556926 .10 ( s )
Hz
42
H α = 2.74198346220664 10 .Hz
61
H α = 8.46087689814736 .10
km
.
s Mpc
2
9 5
10 s
St T = 4.41360590772282 10 .
m
T U2( H ) K W .St T .ln
Hα
.H5 .µ
2
H CMBR
H
H U5 R 0 , M G
H ∆CMBR
H U5 R 0 , M G
H CMBR∆
H U5 R 0 , M G
T 0 = 2.7255 ( K )
∆T 0 = 6 .10
4
( K)
Given
K W .St T .ln
Hα
H ∆CMBR
5 .µ
.H
∆CMBR
2
T0
∆T 0
K W .St T .ln
Hα
H CMBR
H ∆CMBR
H ∆CMBR
H CMBR
H CMBR
Find H ∆CMBR , H CMBR , H CMBR∆
H CMBR∆
H CMBR∆
H CMBR
2
= 67.1181447977434
67.1450938090621
1
Hα
H CMBR∆
5 .µ
.H
CMBR∆
km
s .Mpc
H CMBR = 0.026949011318742
= 14.5685359530647 ( Gyr )
H CMBR∆
km
s .Mpc
km
.
s Mpc
H CMBR
1
H ∆CMBR
H CMBR
km
.
s Mpc
T U2
∆T 0
= 14.5685359530647
1
1
H ∆CMBR
T0
T0
14.5743867417478
1
H CMBR
2
1
H ∆CMBR
67.0912006738519
1
= 70.8560221441252
.
13.8 ( Gyr )
Riccardo C. Storti
K W .St T .ln
T0
H ∆CMBR = 0.02694412389147
H CMBR∆
H CMBR
5 .µ
.H
CMBR
1
T0
( Gyr )
14.5626888000112
T0
H CMBR
1
= 5.85078868307819 ( Myr )
H CMBR∆
1
= 5.84715305355053 ( Myr )
1
H CMBR
1
H CMBR∆
1
=
5.85078868307819
5.84715305355053
∆T 0
∆T 0
2.7249
= 2.7255
( K)
2.7261
( Myr )
1
= 2.80770894815354 ( K )
.
13.8 ( Gyr )
4
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•
Calculator 2
19
kpc = 3.08567758149 10 .m
H U5( r , M )
m γγ
.ln
h
( 3 .π )
m γγ = 3.19515507344683 10
7 .µ .
32
µ
256
2
. µ mh
.ln ( 3 π ) .
4
M
µ
2
eV
7 .µ
2
7 .µ
r
.
45 .
.
mh
5 .µ
c
λ h = 4.05135054323488 10
3
35 .
m
mh
h .c
8
m h = 5.45551186133462 10 .kg
G
M X1
MG
MS
11
M X1 = 6.01291538836348 .10
5
2
.
M
λh
G .h
λh
2
26 .µ
r
M X2
λh
R 01
M X1
R0
M X3
∆R 0
R 02
M X1
R0
M X4
M X1
M X5
M X1
M X6
M X1
∆R 0
0.25 .( kpc )
∆R 0
Given
T U2 H U5 R 01 , M X1 .M S
T0
T U2 H U5 R 01 , M X3 .M S
T0
T U2 H U5 R 01 , M X5 .M S
T0
T U2 H U5 R 02 , M X2 .M S
T0
∆T 0
T U2 H U5 R 02 , M X4 .M S
T0
∆T 0
∆T 0
T U2 H U5 R 02 , M X6 .M S
T0
∆T 0
M X1
M X1
5.42445048870899 .10
M X2
M X2
7.45991407114055 .10
M X3
M X3
5.18883120819766 .10
Find M X1 , M X2 , M X3 , M X4 , M X5 , M X6
M X4
11
11
11
=
M X4
11
7.13588107695813 .10
11
M X5
M X5
5.67080411927548 .10
M X6
M X6
7.79871019227623 .10
M X1
M X2
M X3
M X4
M X5
M X6
M X5
M X4
11
=
5.42445048870899 .10
11
7.45991407114055 .10
11
=
5.18883120819766 .10
11
7.13588107695813 .10
11
=
5.67080411927548 .10
11
7.79871019227623 .10
11
=
5.67080411927548 .10
11
7.13588107695813 .10
T U2 H U5 R 01 , M X1 .M S
T U2 H U5 R 02 , M X2 .M S
=
T U2 H U5 R 01 , M X3 .M S
T U2 H U5 R 02 , M X4 .M S
=
T U2 H U5 R 01 , M X5 .M S
T U2 H U5 R 02 , M X6 .M S
=
T U2 H U5 R 01 , M X5 .M S
T U2 H U5 R 02 , M X4 .M S
=
M X7
M X5
M X4
2.7255
2.7255
2.7261
2.7261
( K)
T 0 = 2.7255 ( K )
( K)
T0
∆T 0 = 2.7261 ( K )
T0
∆T 0 = 2.7249 ( K )
2.7249
2.72489999859608
2.7249
2.7261
( K)
<---- Permissible Milky Way Galactic Mass multiplier range (between " M X5 " & " M X4 ")
( K)
11
M X7 = 6.40334259811681 .10
2
H U5 R 01 , M X5 .M S
H U5 R 02 , M X4 .M S
Riccardo C. Storti
11
=
67.0912006738519
67.145093809062
km
.
s Mpc
∆M X7
M X4
M X5
10
∆M X7 = 7.32538478841326 .10
2
H U5 R 01 , M X5 .M S
1
H U5 R 02 , M X4 .M S
1
=
5
14.5743867417478
14.5626888000112
( Gyr )
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H U8
A U1
H U5 R 01 , M X5 .M S
H U5 R 02 , M X4 .M S
H U8 = 67.118147241457
2
H U8
1
A U1 = 14.5685354226369 ( Gyr )
km
s .Mpc
H U5 R 01 , M X5 .M S
∆A U1
1
∆H U8
H U5 R 02 , M X4 .M S
H U5 R 02 , M X4 .M S
H U5 R 01 , M X5 .M S
2
∆H U8 = 0.026946567605071
km
s .Mpc
1
∆A U1 = 5.84897086830726 ( Myr )
2
T U2 H U8 = 2.72550005441243 ( K )
Summary
1. CMBR Range --> " T 0 ∆T 0 = 2.7249 ( K ) " to " T 0 ∆T 0 = 2.7261 ( K ) "
2. "R0" Range --> " R 01 = 7.928 ( kpc ) " to " R 02 = 8.428 ( kpc ) "
3. "MG" = " M X7 = 6.4033 .1011 " Solar Masses, +/- " ∆M X7 = 7.3254 .1010 " Solar Masses --> " M X5 = 5.6708 .1011 " to (multiplier) " M X4 = 7.1359 .1011 "
4. "H " = " H U8 = 67.1181
0
km
.
s Mpc
" +/- " ∆H U8 = 0.0269
km
.
s Mpc
km
km
" --> " H U5 R 01 , M X5 .M S = 67.0912
" to " H U5 R 02 , M X4 .M S = 67.1451
"
.
.
s Mpc
s Mpc
5. "T0" = " A U1 = 14.5685 ( Gyr ) " +/- " ∆A U1 = 5.849 ( Myr ) " --> " H U5 R 02 , M X4 .M S
1
= 14.5627 ( Gyr ) "
to " H U5 R 01 , M X5 .M S
1
= 14.5744 ( Gyr ) "
6. " T U2 H U8 = 2.72550005441243 ( K ) "
http://iopscience.iop.org/article/10.3847/0004-637X/829/2/108/pdf
1. The author states two overlapping ranges of Milky Way Solar Mass Multiplier
2. Range 1 = " 4.79 .1011 " to " 5.63 .1011 " Solar Masses
3. Range 2 = " 6.06 .1011 " to " 7.53 .1011 " Solar Masses
4. Author estimates --> " M GE 6.82 .1011 " Solar Masses; the author's estimate is non-compliant with CMBR (as shown below)
H U5 R 01 , M GE .M S
H U5 R 0 , M GE .M S
H U5 R 02 , M GE .M S
H U5 R 0 , M GE .M S
66.9793482654738
km
s .Mpc
= 67.0773848250119
67.1725785229535
H U5 R 0 , M GE .M S
1
= 14.5773886107784
H U5 R 02 , M GE .M S
1
14.5567302475191
T U2 H U5 R 01 , M GE .M S
T U2 H U5 R 0 , M GE .M S
T U2 H U5 R 02 , M GE .M S
14.5987252923595
( Gyr )
2.72240807157092
= 2.72459230222853
( K)
2.7267118149796
= 39.938050988434 ( Myr )
T U2 365 .H U5 R 0 , M GE .M S
= 69.1633324647007 ( K )
Correlation between Calculator 1 & 2
T U2 H U5 R 0 , M X7 .M S
= 99.9979387126516 ( % )
T U2 H U8
•
1
1
365
•
H U5 R 01 , M GE .M S
1
T U2 H U5 R 0 , M X7 .M S
= 2.06128734839828 .10
T U2 H U8
3
( %)
<---- Error
T U2 H U5 R 0 , M X7 .M S
T U2 H U8
=
2.72544387402463
2.72550005441243
( K)
Calculator 3
M EGM M U K λ .R 0 , λ x .λ h , K m .M G , m x .m h
Riccardo C. Storti
M EGM = 9.27483782974259 .10
52
kg
M EGM
M X7 .M S
10
= 7.28439768397071 .10
M EGM
= 4.66444939913931 .10
22
MS
6
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•
Analysis of Element 115
Fundamentals
m N_115
115
m A_115
m 115
m A_115 .m AMC
V S( r )
4. . 3
πr
3
290
m A_115
<---- Number of Neutrons in Element 115 Nucleus
m N_115 = 175
m 115 = 270.133289794324
GeV
c
3
2
m 115 = 4.81556329480416 10
V S r ν = 2.36869541389588 fm
3
m A_115 .V S_Av
V 115 = 691.493659190196 fm
r 115
3 .V 115
V S_Av
VS rν
kg
3
<---- Initial guesstimate for the Element 115 Nucleon Volume
V S_Av = 2.3844608937593 fm
2
<---- Initial guesstimate for the Nucleon ZPF Equilibrium Radius of Element 115 (minimum value)
ω Ω r 115 , m 115
3
ω Ω r 115 , m 115 = 3.22776593711433 .10 ( YHz )
ω PV 1 , r 115 , m 115 = 18.920834409487 ( GHz )
VS rπ
r 115 = 5.48571445303054 ( fm )
4 .π
27 .
<---- Initial guesstimate for the Mass-Energy value of Element 115 Nucleus
kg
3
V S r π = 2.40022637362271 fm
3
V 115
25 .
m AMC = 1.66053906717385 10
= 1.23319063538888
ω Ω r π,m p
Calculating The Required Signal Amplification Frequency for Element 115 (Gravity-B Wave Frequency)
9
rπ
5
r 115
.
m 115
2
ω Ω r π,m p
5
r 115 St ω
<---- Value of Harmonic Operator; this result implies that unity may be a value of significance
= 1.23319063538888
mp
ω Ω r ε ,m e
r π.
1
St ω
.
9
m 115
mp
2
St ω_115
1
ω Ω r 115 St ω_115 , m 115
=1
ω Ω r π,m p
r 115 ( 1 ) = 7.99995584982386 ( fm )
ω PV 1 , r 115 ( 1 ) , m 115 = 11.4410994697295 ( GHz )
C PV 1 , r 115 ( 1 ) , m 115 = 319.711134584291
ω PV 1 , R E , M E = 0.035822657862986 ( Hz )
C PV 1 , R E , M E = 6.23785621648859
Riccardo C. Storti
m
2
s
nm
2
s
r 115 ( 1 )
9
=2
rπ
rε
5
.
me
2
=2
mp
= 9.63162855239241
rπ
T PV 1 , r 115 ( 1 ) , m 115 = 87.4041872152033 ( ps )
T PV 1 , R E , M E = 27.9152932712249 ( s )
7
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Calculating The Minimum Gravitational Interaction Harmonic for The Amplified Element 115 Signal (Gravity-A Wave Harmonic)
N
421
n PV
N, 2
N .. N
Θ(t)
2
i .
n PV
π .n PV
.e
tt
π .ω t .n PV .t .i
<---- Unit Harmonic Operator
tt
ω t.
Re( Θ ( t ) ) d t = 99.9063923867319 ( % )
0
ω t.
Im( Θ ( t ) ) d t = 0
0
The results above demonstrate that the minimum Spectral Harmonic describing any Gravitational Acceleration Field (i.e. when it is Quantised over a Fourier Spectrum) is '421':
1. The '421'st' Spectral Harmonic denotes the sum of all Odd Harmonics from negative '421' to positive '421'
2. The sum of the first '421' Harmonics represents greater than '99.906(%)' of the Gravitational Acceleration within the field
3. As expected, only the Real terms in the Unit Harmonic Operator contribute to the calculation (i.e. the Odd Harmonics)
4. As expected, the Imaginary terms in the Unit Harmonic Operator do not contribute to the calculation (i.e. the Even Harmonics)
Various other solutions:
1. 'N = 1' --> ' 81.0569469138702 (%)'
2. 'N = 21' --> ' 98.1590617499417 (%)'
3. 'N = 101' --> ' 99.6026747610375 (%)'
Calculating The Minimum Gravitational Interaction Frequency for The Amplified Element 115 Signal (Gravity-A Wave Frequency)
t
10.5 .( s ) , 10.501 .( s ) .. 14.15 .( s )
a PV( r , M , t )
i .
C PV n PV , r , M .e
π .n PV .ω PV( 1 , r , M ) .t .i
1.
T PV 1 , R E , M E = 13.9576466356125 ( s )
2
ω PV N , R E , M E = 15.081338960317 ( Hz )
n PV
1.
T PV 1 , R E , M E
2
Magnified View (Fund. Period Midpoint)
1 .T
PV 1 , R E , M E
2
Gravitational Acceleration
13.825
1
9.81
a PV R E , M E , t
= 7.53882671341663 ( Hz )
1.
T PV 1 , R E , M E
2
<---- Peak-to-Peak period about midpoint (approx.)
<---- Peak-to-Peak frequency about midpoint (approx.)
13.825 .( s )
g R E, M E
9.8
Hence, from the Peak-to-Peak graphical measurements (above & left), we may deduce that the Steady-State
Gravitational Acceleration Harmonic Frequency (for physical interaction) is given by:
9.79
ω G n PV , r , M
9.78
13.8
13.85
13.9
13.95
t
Time
14
14.05
14.1
T G n PV , r , M
λ G n PV , r , M
Riccardo C. Storti
13.825 .( s ) = 0.132646635612453 ( s )
8
1.
ω PV n PV , r , M
2
1
ω G n PV , r , M
c
ω G N, R E , M E
ω G N , R E , M E = 7.54066948015852 ( Hz )
T G N , R E , M E = 0.132614219815795 ( s )
4
λ G N , R E , M E = 3.97567429243296 .10 ( km)
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Note: the period calculated is generally consistent with the minimum duration required to
mechanically transmit Impulse (i.e. changes in Momentum). This implies that a reduction in
Gravitational Acceleration of 99.9(%) is sufficient to mimic a 100(%) reduction; if a wavefunction is
delivered 180 degrees phase shifted from the Earth's Gravitational Acceleration harmonic.
Magnified View (Fund. Period Midpoint)
1 .T
PV 1 , R M , M M
2
10.58 .( s )
Gravitational Acceleration
1.626
1
a PV R M , M M , t
g R M, M M
<---- This result verifies & confirms the preceding methodology
= 9.73051013075158 ( Hz )
1.
T PV 1 , R M , M M
2
1.624
10.58 .( s )
T PV ( 1 , r , M )
1.622
Therefore;
a G( r , M )
ω PV( 1 , r , M ) .
a PV( r , M , t ) d t
<---- Gravitational Acceleration
0 .( s )
1.62
10.5
10.55
10.6
10.65
10.7
10.75
10.8
10.85
t
Time
M bh
9
10 .M S
R bh
a G R M,M M
a G R E, M E
a G R J, M J
=
a G R S, M S
a G R bh , M bh
1.
( mm )
4
R BH M bh
9.78922958202892
a GG R E , M E
99.9063923867319
a GG R J , M J
= 99.9063923867319
a GG R S , M S
99.9063923867319
273.943457291216
s
1.5202129754301 .10
1
a GG( r , M )
R BH( M )
2 .G .M
c
<---- Schwarzschild Radius
2
4
a GG R M , M M
24.7641706632374
g( r, M )
a GGG( r , M )
1
<---- " .( mm ) " Avoids computational singularity at the Event Horizon
1.62143821847817
m
a G( r , M )
a GG( r , M )
2
4
a GGG R M , M M
99.9063923867319
a GG R bh , M bh
( %)
99.9063923867319
a GGG R E , M E
0.093607613268087
a GGG R J , M J
= 0.093607613268099
a GGG R S , M S
0.093607613268065
a GGG R bh , M bh
ω G N, R M , M M
0.093607613268054
9.85231401432347
ω G N, R E , M E
ω G N, R J , M J
( %)
7.54066948015852
2.05143419319885
=
1.00283122226903
ω G N, R S, M S
0.093607613268054
( Hz )
1.26721951777966 .10
ω G N , R bh , M bh
6
Determining the Amplification Factor via Graphical Measurements of Amplitude (Gravity-A Wave)
m
9.8137 .
2
s
g R E , M E = 0.015298368065009
m
<---- Peak | Trough ---->
2
s
g R E, M E
C PV 1 , R E , M E
m
m
9.7842 .
= 0.014201631934991
2
2
s
s
Hence ---->
m
9.8137 .
2
s
g R E, M E
g R E, M E
C PV 1 , R E , M E
9.8137 .
C PV 1 , R E , M E
= 407.746511914299
m
C PV 1 , R E , M E
g R E, M E
2
s
= 439.23516995
m
9.7842 .
2
s
g R E, M E
9.7842 .
m
2
s
= 423.490840930576
2
1.62606 .
m
2
s
g R M , M M = 3.10256980707102 .10
3
m
2
s
<---- Peak | Trough ---->
g R M,M M
1.62117 .
m
2
= 1.78743019292904 .10
s
3
m
2
s
Hence ---->
C PV 1 , R M , M M
m
1.62606 .
2
s
g R M,M M
g R M,M M
C PV 1 , R M , M M
1.62606 .
m
2
s
C PV 1 , R M , M M
= 333.016452173592
= 578.04035864
m
1.62117 .
2
s
C PV 1 , R M , M M
g R M,M M
g R M,M M
1.62117 .
m
2
s
= 455.528405408763
2
Riccardo C. Storti
9
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Thus
C PV N
2,R M,M M
3
2.4425692429591 .10
C PV N
2 , R E, M E
C PV N
2 , R J, M J
C PV N
2 , R S, M S
0.412674288458195
9
9
2 , R BH 10 .M S , 10 .M S
22.9008136987051
C PV N
0.014746705003519
=
A F N, R M , M M
7.63992547877658 .10
3
A F N, R E , M E
4.61250904592164 .10
4
A F N, R J , M J
m
0.037305276821577
2
1.29077233733126 .10
6
9
9
A F N , R BH 10 .M S , 10 .M S
7.16297032584813 .10
7
C PV n PV
A F n PV , r , M
s
= 1.16684321520688 .105
A F N, R S, M S
<---- Required Amplitude
C PV 1 , r 115 ( 1 ) , m 115
<---- Critical Harmonic | Amplification Factor Harmonic ---->
N = 421
2 , r, M
N
<---- Amplification Factor (AF)
4
A F N , R E , M E = 4.61250904592164 .10
2 = 423
For values of "N > 21", " a GG( r , M ) " may be usefully approximated utilising a single sinusoid as follows:
•
Form over " T PV( 1 , r , M ) "
T PV ( 1 , r , M )
g PV1( N , r , M )
g( r, M )
ω PV ( 1 , r , M ) .C PV ( N
sin 2 .π .ω PV( N , r , M ) .t
2 , r, M ) .
dt
g S1( N , r , M )
0 .( s )
•
g PV2( N , r , M )
g( r, M )
2 , r, M ) .
ω PV ( N , r , M ) .C PV ( N
sin 2 .π .ω PV( N , r , M ) .t
dt
g S2( N , r , M )
0 .( s )
g PV3( N , r , M )
g( r, M )
2 .ω PV( N , r , M ) .C PV( N
sin 2 .π .ω PV( N , r , M ) .t d t
2 , r, M ) .
0 .( s )
2
s
g S1 N , R E , M E = 99.9041878756607 ( % )
g PV2( N , r , M )
g PV2 N , R E , M E = 9.78901358795248
g( r, M )
m
2
s
g S2 N , R E , M E = 99.904188006012 ( % )
g S3( N , r , M )
g PV3( N , r , M )
g PV3 N , R E , M E = 9.78901358795248
g( r, M )
m
2
s
g S2 N , R E , M E = 99.904188006012 ( % )
Simplified form
g PV4( N , r , M )
•
g( r, M )
m
1
Form over " .T PV( N , r , M ) "
2
1.
T PV ( N , r , M )
2
•
g PV1 N , R E , M E = 9.78901357518014
Form over " T PV( N , r , M ) "
T PV ( N , r , M )
•
g PV1( N , r , M )
g( r, M )
C PV( N
Similarity between forms
Riccardo C. Storti
2 , r, M ) .
1
cos( π )
π
g S4 N , R E , M E
g S4( N , r , M )
g PV3( N , r , M )
g( r, M )
g PV4 N , R E , M E = 9.78901358795248
m
2
s
g S4 N , R E , M E = 99.904188006012 ( % )
= 99.9977935538785 ( % )
a GG R E , M E
10
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Gravity-A-Wave Amplifier Design Solution
N
405
<---- Harmonic Limit | Harmonic Distribution ---->
U ω ( r, M ) .
U ωPV n PV , r , M
n PV
2
4
n PV
4
n PV
1 , 3. .. ( N
2)
U ω ( r, M )
h .
4
ω PV ( 1 , r , M )
3
2 .c
<---- Spectral Energy Density | Spectral Poynting Vector ---->
S ωPV n PV , r , M
c .U ωPV n PV , r , M
Gravity-A-Wave Source (Moscovium)
h .
ω PV 1 , r 115 ( 1 ) , m 115
2
2 .c
N A.
4
W
11
= 6.31619709443397 .10
<---- Poynting Vector of one Moscovium Atom (utilising the Fundamental Frequency)
2
m
h .
ω PV 1 , r 115 ( 1 ) , m 115
2
2 .c
4
= 3.80370279705844 .10
W
13
2.
<---- Poynting Vector per Mole | Poynting Vector per kilogram ---->
m mol
1
23
N A = 6.02214076 .10
mol
1
. h .ω
PV 1 , r 115 ( 1 ) , m 115
m 115 2 .c2
4
kg
m 115 .N A = 0.29
= 1.31162165415808 .10
14
mol
W
2
m .kg
Gravity-B-Wave Source (Earth + Zero-Point-Field)
S ωPV n PV , R E , M E = 1.63318710237298 10
46 .
4
= 1.63318710243369 10
46 .
<---- Earth + Zero-Point-Field (ZPF): Sum of changes between Spectral Poynting Vectors of the first " N = 405 " Modes
2
m
n PV
h .
ω PV N , R E , M E
2
2 .c
W
W
<---- Earth + Zero-Point-Field (ZPF): Spectral Poynting Vector at " N = 405 "
2
m
S ωPV n PV , R E , M E
1
n PV
= 3.71683794853084 .10
h .
ω PV N , R E , M E
2
2 .c
P ω n PV , r , M
P ω N , R E , M E = 8.34888451584373 10
4
<---- This demonstrates that the sum of the changes between Spectral Poynting Vectors equals the value of the Spectral Poynting Vector at " N = 405 "
r
r 115 ( 1 )
2
.
<---- Power Flow through a Surface Area of Radius 'r' | Required Moscovium Power Amplification Factor ---->
6
38 .
( W)
ω PV 1 , r 115 ( 1 ) , m 115
6
P ω 1 , r 115 ( 1 ) , m 115
P AF N , R E , M E = 1.64356822251301 .10
( W)
ω PV n PV , r , M
P AF_2 N , R E , M E = 1.64356822251301 .10
P ω n PV , r , M
P AF n PV , r , M
32 .
P ω 1 , r 115 ( 1 ) , m 115 = 5.07973103974856 10
Riccardo C. Storti
( %)
4
2 h .
4 .π .r .
ω PV n PV , r , M
2
2 .c
P AF_2 n PV , r , M
9
4
<---- Alternative representations of 'P AF' ---->
P AF_3 n PV , r , M
4
2
n PV .K PV( r , M ) .
r 115 ( 1 )
P AF_3 N , R E , M E = 1.64356822251301 .10
11
r
6
33
.
r 115 ( 1 )
r
.
M
m 115
4
<---- This form demonstrates that the greatest
numerical contribution arises from the mass ratio
•
•
" n PV 1 " with respect to Moscovium
" K PV 1 " with respect to the Refractive Index
contribution of the Moscovium & may be
usefully neglected from all calculations
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Key Design Criteria (KDC)
Atomic Moscovium
<---- Required Amplifier Pulse (Burst) Frequency | Amplifier Signal Frequency ---->
ω G N , R E , M E = 7.25408821725463 ( Hz )
ω PV 1 , r 115 ( 1 ) , m 115 = 11.4410994697295 ( GHz )
T G N , R E , M E = 0.137853300104814 ( s )
T PV 1 , r 115 ( 1 ) , m 115 = 87.4041872152033 ( ps )
Signal Wavelength ------------------->
λ PV 1 , r 115 ( 1 ) , m 115 = 26.203116124738 ( mm )
Required Signal Amplification ---->
A F N , R E , M E = 4.79383618286205 .10
Required Power Amplification ---->
P AF N , R E , M E = 1.64356822251301 .10
λ PV 1 , r 115 ( 1 ) , m 115 = 1.03161874506842 ( in )
4
6
Metallic Moscovium (Spherical Configuration)
δ Mc
gm
13.5 .
3
cm
V Mc M Mc
3
r Mc M Mc
δ Mc
4 .π .r Mc( 500 .( gm) )
r Mc( 500 .( gm ) )
20.6783496966467
r Mc( 1 .( kg ) )
4 .π .r Mc( 1 .( kg ) )
26.0530880598924
r Mc( 5 .( kg ) )
= 44.5501539190659
r Mc( 10 .( kg ) )
56.1296766986877
r Mc( 100 .( kg ) )
120.927722619927
( mm )
ω PV 1 , r Mc( 1 .( kg ) ) , 1 .( kg )
ω PV 1 , r Mc( 5 .( kg ) ) , 5 .( kg )
4
ω PV 1 , r Mc( 10 .( kg ) ) , 10 .( kg )
Riccardo C. Storti
2
4 .π .r Mc( 5 .( kg ) )
=
249.406795121216
1.83764497840302 .10
2
n PV K PV( r , M )
ω PV 1 , r Mc( 1 .( kg ) ) , 1 .( kg )
cm
395.908608943436
2
4.
ω PV 1 , r Mc( 500 .( gm) ) , 500 .( gm)
53.7330651338823
3
2
ω PV 1 , r Mc( 5 .( kg ) ) , 5 .( kg )
ω PV 1 , r Mc( 10 .( kg ) ) , 10 .( kg )
ω PV 1 , r Mc( 100 .( kg ) ) , 100 .( kg )
2.
r Mc M Mc
33
.
r Mc M Mc
r
r
.
M
M Mc
4
S Mc M Mc
P ω 1 , r Mc( 500 .( gm) ) , 500 .( gm)
32.6591103833768
P ω 1 , r Mc M Mc , M Mc
4 .π .r Mc M Mc
2.25342778761299
30.2382444297678
P ω 1 , r Mc( 1 .( kg ) ) , 1 .( kg )
2.62868895283832
= 25.2867630785227
P ω 1 , r Mc( 5 .( kg ) ) , 5 .( kg )
= 3.75894410305878
( Hz )
2
23.4123744900041
P ω 1 , r Mc( 10 .( kg ) ) , 10 .( kg )
4.38491745436146
18.1273512929403
P ω 1 , r Mc( 100 .( kg ) ) , 100 .( kg )
7.31448316119827
10
47 .
( W)
4
S Mc( 500 .( gm) )
4.19374510275621
3.08184591466634
= 1.5071538452799
1.10755799578684
4
ω PV 1 , r Mc( 100 .( kg ) ) , 100 .( kg )
P AF_4 n PV , r , M , M Mc
85.2959241190006
4 .π .r Mc( 100 .( kg ) )
4
3 .
V Mc M Mc
4 .π
2
2
4 .π .r Mc( 10 .( kg ) )
ω PV 1 , r Mc( 500 .( gm) ) , 500 .( gm)
h .
2
2 .c
M Mc
0.39803570587148
4
10
45 .
W
2
m
4.19374510275621
S Mc( 1 .( kg ) )
3.08184591466634
S Mc( 5 .( kg ) )
= 1.5071538452799
S Mc( 10 .( kg ) )
1.10755799578684
S Mc( 100 .( kg ) )
0.39803570587148
10
45 .
W
2
m
12
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The graph below demonstrates that the lumped mass form of Metallic Moscovium raises the Required Power Amplification factor considerably
Metallic Moscovium PAF
15
5 .10
500 .( gm )
10 .( kg )
P AF_4 N , R E , M E , 500 .( gm )
Required Power Amplification
15
4 .10
P AF_4 N , R E , M E , 500 .( gm )
3.70497096101203 .10
15
P AF_4 N , R E , M E , 1 .( kg )
3.17606406297293 .10
15
P AF_4 N , R E , M E , 5 .( kg )
= 2.22107173901574 .1015
P AF_4 N , R E , M E , 10 .( kg )
1.90400038375625 .10
15
P AF_4 N , R E , M E , 100 .( kg )
1.14141824266309 .10
15
15
3 .10
P AF_4 N , R E , M E , M Mc
P AF_4 N , R E , M E , 10 .( kg )
2 .1015
1 .1015
0.1
1
10
100
M Mc
Moscovium Mass (kg)
Metallic Moscovium (Right Circular Cone Configuration)
r Mc( 500 .( gm ) )
h Mc M Mc
r Mc( 1 .( kg ) )
3 .V Mc M Mc
π .r Mc M Mc
2
h Mc( 500 .( gm) )
20.6783496966467
82.7133987865867
26.0530880598924
h Mc( 1 .( kg ) )
r Mc( 5 .( kg ) )
= 44.5501539190659
h Mc( 5 .( kg ) )
= 178.200615676263
r Mc( 10 .( kg ) )
56.1296766986877
h Mc( 10 .( kg ) )
224.518706794751
r Mc( 100 .( kg ) )
120.927722619927
h Mc( 100 .( kg ) )
483.710890479708
( mm )
104.21235223957
h Mc( 1 .( kg ) )
( mm )
λ PV 1 , r 115 ( 1 ) , m 115
h Mc M Mc
r Mc M Mc
l Mc
atan
λ PV 1 , r 115 ( 1 ) , m 115
r Mc M Mc K Mc
r Mc M Mc( 1 )
h Mc M Mc( 1 )
Riccardo C. Storti
2
3 . M Mc
λ PV 1 , r 115 ( 1 ) , m 115
4 .π δ Mc
h Mc M Mc K Mc
= 14.0362434679265 ( deg )
2
r Mc M Mc K Mc
2 .atan
2
r Mc M Mc( 1 )
h Mc M Mc( 1 )
λ PV 1 , r 115 ( 1 ) , m 115
4 .π .
δ Mc .
3
K Mc
M Mc K Mc
4 .r Mc M Mc K Mc
2
17 .r Mc M Mc K Mc
= 28.072486935853 ( deg )
2
<---- Cone Angle
= 0.994274418961037
λ PV 1 , r 115 ( 1 ) , m 115
<---- Height to Radius Ratio for all values of " M Mc " (i.e. constant)
4
r Mc M Mc
3
r Mc( 1 .( kg ) )
= 3.97709767584414
3
l Mc K Mc
l Mc( 1 )
M Mc( 1 ) = 1.01737533001258 ( kg )
M Mc( 1 ) = 2.24292866745659 ( lb )
h Mc M Mc( 1 ) = 104.812464498952 ( mm )
h Mc M Mc( 1 ) = 4.12647498027369 ( in )
r Mc M Mc( 1 ) = 26.203116124738 ( mm )
r Mc M Mc( 1 ) = 1.03161874506842 ( in )
17 .r Mc M Mc K Mc
l Mc( 1 ) = 108.03821550262 ( mm )
<---- Hypotenuse of Cone
= 4.12310562561766
r Mc M Mc( 1 )
13
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Metallic Moscovium (Wedge Elements)
t Mc K Mc
r Mc M Mc K Mc
t Mc( 1 ) = 6.55077903118449 ( mm )
4
<---- Assume the thickness of the Wedge Element to be 1/4 wavelength | Predicted number of circular discs per cone ---->
D Mc K Mc
h Mc M Mc K Mc
t Mc K Mc
D Mc( 1 ) = 16
AW
AW
1. .
hb
2
4 .r Mc M Mc( 1 )
V W1 A W .
M W VW
VC
<---- Area of wedge
1. .
2
π r Mc M Mc( 1 ) .h Mc M Mc( 1 )
3
2
r Mc M Mc( 1 )
4
V W .δ Mc
b 2 .r Mc M Mc( 1 )
h h Mc M Mc( 1 )
A W = 27.4641317858601 cm
2
r
M Mc( 1 )
2 Mc
4 .r Mc M Mc( 1 ) .
4
1.
h Mc M Mc( 1 ) .2 .r Mc M Mc( 1 )
2
h Mc M Mc( 1 ) .r Mc M Mc( 1 )
4 .r Mc M Mc( 1 ) .r Mc M Mc( 1 )
4 .r Mc M Mc( 1 )
2
2
A W = 4.2569489407062 in
r Mc M Mc( 1 )
4. .
π r Mc M Mc( 1 )
3
3
V W1
r Mc M Mc( 1 )
3
V W1 = 17.99114586125 cm
3
3
V W1 = 1.09788708100792 in
<---- Approximate Mass of Wedge Element (rough guesstimate)
M W V W1 = 242.880469126875 ( gm)
1. .
2
π r Mc M Mc( 1 ) .4 .r Mc M Mc( 1 )
3
AW
3
VC
4. .
π r Mc M Mc( 1 )
3
3
V C = 75.3611355564871 cm
3
3
V C = 4.5988186508875 in
<---- Volume of Cone
https://math.stackexchange.com/questions/2790734/second-method-to-find-the-volume-of-a-slice-of-a-cone
HC
h Mc M Mc( 1 )
RC
aC
1
2
2 . .H C .R C .acos
6
RC
1.
2
H C .a C . R C
3
Simplifying yields: V Slice
V W2
VC
2 .V Slice
r Mc M Mc( 1 )
1
4.
acos
8
3
R
Riccardo C. Storti
8
2.
1
7.
28
R
2
1 . 63
3
64
1 .
ln 8 . 1
384
tan θ 2_3
64
2
aC
2
= 28.8538842412795 cm
3
aC
.r
Mc M Mc( 1 )
3
3
V W2 = 1.07727455472977 in
3.
1
7.
14
R
2
14
63
RC
V Slice = 28.8538842412795 cm
3
<---- Volume of Wedge Element
<---- Mass of Primary Wedge Element (EGM) M W V W2 = 8.40650667904419 ( oz )
R
8
3
<---- Half the thickness of the Wedge Element
a aC
8
RC
1 .H C . 3 .
a C ln
6 RC
aC
2
V W2 = 17.6533670739282 cm
M W V W2 = 238.32045549803 ( gm )
tan θ 2
aC
RC
aC
tan θ 2_4
R
8
4.
3
7.
28
R
2
tan θ 2_5
R
8
5.
1
7.
7
R
2
tan θ 2_6
R
8
6.
5
7.
28
R
2
tan θ 2_7
R
8
7.
3
7.
14
R
2
tan θ 2_8
R
8
1
7.
4
R
2
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Atoms of Moscovium
atan
1
28
Disc 1
θ2
atan
θ 2_3
atan
θ 2_4
Disc 3
atan
θ 2_5
atan
atan
¼ R Typ.
3½ R
4R
Direction of Gravitational Wave Propagation
θ 2_8
28
θ 2_4
1
2.04540848888723
θ3
4.08561677997488
6.11550356628541
θ 2_5 = 8.13010235415598
10.1246716553978
θ 2_6
12.0947570770121
θ 2_7
14.0362434679265
θ 2_8
5
3
θ2
( deg )
θ2
θ 2_3
θ2
θ3
2.04540848888723
2.04020829108765
θ4
θ 2_4
θ 2_3
θ4
θ5
θ 2_5
θ 2_4
θ6
θ 2_6
θ 2_5
θ7
θ 2_7
θ 2_6
θ8
θ 2_8
θ 2_7
θ 5 = 2.01459878787057
1.99456930124184
θ6
1.97008542161428
θ7
1.94148639091438
θ8
2.02988678631053
( deg )
<---- Slice Angles
1
4
2.
V Slice = 111.293553502078 ( gm)
7
MW
V Cylinder
V Mill
V Mill = 150.722271112974 cm
V Cylinder
V Mill
VC
= 66.6666666666667 ( % )
V Cylinder
N Cylinder .
1 . 1 . .7 .
R R
2 8 2
7 . 2
R
32
2
1
3
A 2_3
3
4 .π .r Mc M Mc( 1 )
V Cone
V Cylinder
B C N Cylinder
2' 3' 4' 5' 6' 7' 8'
<---- Average Mass of Secondary Wedge Elements (EGM)
2
3
V Cylinder π .r .h 4 .π .R
A2
2
π .r .h
3
3
A 2_4
3
V Mill = 9.197637301775 in
<---- This demonstrates that 2/3 of the Discs utilised are milled-off to form the cone.
It is assumed that the material removed is smelted & reprocessed into new Discs
3
B C( 3 ) .D Mc( 1 ) = 80
<---- Minimum Cone Batch Size to produce zero waste
7 . 2
R
16
2.
V Slice = 3.92576457146589 ( oz )
7
V Cylinder = 13.7964559526625 in
<---- Volume of material removed to form Cone
1 . . 2.
πr h
3
1
B C( 3 ) = 5
1 . 2 . .7 .
R R
2 8 2
3
V Cylinder = 226.083406669461 cm
MW
1 . 3 . .7 .
R R
2 8 2
21 . 2
R
32
A 2_5
1 . 4 . .7 .
R R
2 8 2
7. 2
R
8
A 2_6
1 . 5 . .7 .
R R
2 8 2
35 . 2
R
32
Disc 16
A 2_7
1/8 R Typ.
θ 2_3
14
atan
θ2
3
28
θ 2_7
1
θ2
7
θ 2_6
8 7 6 5 4 3 2
1
14
1 . 6 . .7 .
R R
2 8 2
21 . 2
R
16
A 2_8
1 . 7 . .7 .
R R
2 8 2
49 . 2
R
32
¼R
7
2R
32
7
A2
R RC
R C = 26.203116124738 ( mm )
R C = 1.03161874506842 ( in )
16
A2
A 2_3
21
A 2_3
A 2_4
32
A 2_4
A 2_5
r Mc M Mc( 1 )
2.
7
A2
1.50194470703922
3.00388941407845
4.50583412111767
A 2_5 = 6.0077788281569
8
A 2_6
35
A 2_6
A 2_7
32
A 2_7
A 2_8
21
A 2_8
16
A3
7.50972353519612
9.01166824223534
10.5136129492746
cm
2
A2
A 2_3
A2
A2
A3
1.50194470703922
1.50194470703922
A4
A 2_4
A 2_3
A4
A5
A 2_5
A 2_4
A 5 = 1.50194470703922
A6
A 2_6
A 2_5
A6
A7
A 2_7
A 2_6
A7
A8
A 2_8
A 2_7
A8
1.50194470703922
cm
2
1.50194470703922
1.50194470703922
1.50194470703922
49
32
Riccardo C. Storti
15
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A2
A2
3.00388941407845
A3
A3
3.00388941407845
A4
0.46560379038974
0.46560379038974
A4
3.00388941407845
.
A
2
5 = 3.00388941407845
3.00388941407845
A6
3.00388941407845
A7
3.00388941407845
A8
cm
2
A2 A3 A4 A5 A6 A7 A8
<---- This demonstrates that each mated Cross-Sectional Area (e.g. 2 fused to 2 Prime, 3 fused to 3 Prime etc.) to produce an additional wedge is equal
1 . .7 .
R R
4 2
A1
1 . .1 .
R R
2
8
15 . 2
R
16
A1
15 .
r Mc M Mc( 1 )
16
2
A 1 = 6.43690588731096 cm
A1
2
2 .A 2
2
15 . 2
R
16
7 . 2
2.
R
32
15
15
7
7
= 2.14285714285714
0.46560379038974
.
A
2
5 = 0.46560379038974
0.46560379038974
A6
0.46560379038974
A7
0.46560379038974
A8
2
in
<---- Ratio of Primary to Secondary
Wedge Cross-Sectional Area's
A 1 = 0.997722407978015 in
M W V W2
MW
= 2.14136801278055
2.
V Slice
7
223 .( gm)
M WL
<---- Mass of Wedge Element (Lazar): https://www.gravitywarpdrive.com/Anti-Matter_Reactor.htm
M WL
V WL
V WL = 16.5185185185185 cm
δ Mc
V R_L
VC
V Slice_L
V WL
4.
1
acos
3
8
V R_L 2 .V Slice_L 2 .
1 . 63
3
K PV_L
64
4.
1
acos
3
8
3
VC
4.
1
acos
3
8
3
3
r Mc M Mc( 1 )
1 .
ln 8 . 1
384
63
1 . 63
1 .
ln 8 . 1
384
3
64
64
M Mc( 1 )
= 23.4250279585 ( % )
M W V W2
= 30.5909716112 ( % )
M W 2 .V Slice
M WL = 7.86609351475643 ( oz )
<---- Removed Cone Material (Lazar)
<---- Volume of a Lazar Slice (repeating the previous method)
63
64
.R 3
L
VC
V WL 2 .
R L = 26.3737675743646 ( mm )
1 .
ln 8 . 1
384
64
3
V R_L = 3.59079680398933 in
.R 3
L
V WL
1 . 63
3
3
M W V W2
<---- Volume of Wedge Element (Lazar)
V WL = 1.00802184689817 in
V R_L = 58.8426170379686 cm
RL
2.
<---- Ratio of Primary to each Secondary Wedge Mass | Proportion of Total Anti-Matter Fuel contained in Primary Wedge ---->
4.
1
acos
3
8
1 . 63
64
3
1 .
ln 8 . 1
384
63
64
.R 3
L
<---- Refracted Fundamental Wavelength of Moscovium based upon Lazar Wedge Element
63
64
R L = 1.03833730607735 ( in )
2
K PV_L = 0.987100868384605
RL
<---- Refractive Index value being less than Unity implies that " δ Mc " may be incorrect
Hence, performing substitutions into a preceding form, we may calculate a Lazar prediction for the Mass Density of Moscovium as follows:
VC
M WL
δ Mc_L
2.
4.
1
acos
3
8
Riccardo C. Storti
1 . 63
3
64
1 .
ln 8 . 1
384
63
64
.r
Mc M Mc( 1 )
3
M WL
δ Mc_L M WL
VC
2.
1
4.
acos
8
3
1 . 63
3
64
1 .
ln 8 . 1
384
16
63
64
.r
Mc M Mc( 1 )
3
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δ Mc_L( 223 .( gm ) ) = 12.632151082914
δ Mc_L( 223 .( gm) )
gm
cm
3
= 93.5714895030667 ( % )
δ Mc
Height & Radius of the Lazar Wedge Element
h Mc M Mc K PV_L
Physical Dimensions vs Refractive Index
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
r Mc M Mc K PV_L
1
h Mc M Mc K PV_L
r Mc M Mc K PV_L
=
=
105.495070297458
( mm )
26.3737675743646
4.15334922430938
( in )
1.03833730607735
Thickness of the Lazar Wedge Element
Dimension (m)
r Mc M Mc K PV_L
h Mc M Mc( 1 )
h Mc M Mc K Mc
r Mc M Mc K Mc
= 6.59344189359115 ( mm )
4
r Mc M Mc K PV_L
0.1
= 0.259584326519337 ( in )
4
"Sports Model" as reported by Ken Wright
h UFO
r Mc M Mc( 1 )
φ UFO
16 .( ft )
52 .( ft ) 9 .( in )
h UFO
φ UFO
=
4.8768
16.0782
( m)
0.01
K Mc
Refractive Index
Quality Assurance
S ωPV 1 , R E , M E = 4.8563036685538 10
W
55 .
2
m
W
h .
ω PV 3 , R E , M E
2
2 .c
4
h .
ω PV 5 , R E , M E
2
2 .c
4
h .
ω PV 7 , R E , M E
2
2 .c
4
h .
ω PV 9 , R E , M E
2
2 .c
4
S ωPV 3 , R E , M E = 3.30228649461658 10
54 .
S ωPV 5 , R E , M E = 1.07809941441894 10
53 .
S ωPV 7 , R E , M E = 2.52527790764797 10
53 .
S ωPV 1 , R E , M E
S ωPV 5 , R E , M E
Riccardo C. Storti
S ωPV 3 , R E , M E
2
m
W
2
m
W
2
m
h .
ω PV 1 , R E , M E
2
2 .c
4
h .
ω PV 3 , R E , M E
2
2 .c
4
h .
ω PV 5 , R E , M E
2
2 .c
4
h .
ω PV 7 , R E , M E
2
2 .c
4
S ωPV 7 , R E , M E = 3.98216900821411 10
= 4.8563036685538 10
W
55 .
2
m
= 3.30228649461658 10
54 .
W
2
m
= 1.07809941441894 10
53 .
W
2
m
= 2.52527790764798 10
53 .
W
2
m
53 .
W
2
m
n PV_Max
9
n PV
1 , 3. .. n PV_Max
S ωPV n PV , R E , M E = 3.98216900821411 10
2
n PV
17
53 .
W
2
m
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3
h .G .M . 2 .c .G .M .
2
K PV ( r , M )
2. 5
.
.
π
r
πc r
U ωPV_2( r , M )
U ωPV_2 R E , M E = 2.02486067401077 10
65 .
( Pa )
h .
ω PV 1 , R E , M E
3
2 .c
4
= 2.02486067401077 10
65 .
( Pa )
1
U ωPV_2 R E , M E
h .
ω PV 1 , R E , M E
3
2 .c
= 1.77635683940025 .10
13
( %)
4
Fuel Cone Machining Process (not to scale)
Step 1
Step 2
Step 3
Step 4
These images were procured from the Ken Wright Web-Site; please note that only 12 Discs are displayed, not the required 16
Quality Assurance
Ken Wright Asserts:
1. "The Element 115 fuel is machined into a long isosceles triangle shaped wedge with a conical point at the angle adjacent to the two equal length sides of the wedge for use as fuel in the reactor": EGM agrees
2. ".... it was mentioned that the fuel pellets were about the size of a 50 cent piece and weighed about 223 grams": important assertion (each pellet represents a Disc as shown in the image above)
3. "They are fused together in a manner to create a vertical cylinder": EGM agrees
4. "The cylinder is cut into a conical shape": EGM agrees
5. "The conical shape is sliced vertically at the center of the cone to form the wedged Element 115 fuel element that is installed into the Matter Anti-Matter Reactor": EGM agrees
•
Testing "Point 2" yields
V D( r , h )
2
π .r .h
<---- Volume of Disc | Mass of Disc ----> m D( r , h )
δ Mc .V D( r , h )
According to the information supplied above, the diameter of each Disc is "about the size of a 50 cent piece (US)":
1. This means that the value of radius calculated previously " r Mc M Mc( 1 ) = 26.203116124738 ( mm ) " is a reasonable approximation to apply as a value of disc diameter
2. Disc thickness is an open guesstimate; however, to be generous, we will apply the value calculated previously " t Mc( 1 ) = 6.55077903118449 ( mm ) "
VD
VD
r Mc M Mc( 1 )
2
r Mc M Mc( 1 )
2
mD
1
, t Mc( 1 ) = 3.53255322921033 cm
3
, t Mc( 1 ) = 0.215569624260352 in
r Mc M Mc( 1 )
2
223 .( gm )
Riccardo C. Storti
3
mD
mD
r Mc M Mc( 1 )
2
r Mc M Mc( 1 )
2
, t Mc( 1 ) = 47.6894685943395 ( gm)
<---- This result implies that the specifications supplied are incorrect
, t Mc( 1 ) = 1.68219650059244 ( oz )
, t Mc( 1 )
= 78.6145880742872 ( % )
<---- Discrepancy associated with the supplied specifications
18
www.deltagroupengineering.com
223 .( gm)
2
r Mc M Mc( 1 )
δ Mc .π .
2
223 .( gm)
r Mc M Mc( 1 )
π.
2
cm
.t
Mc( 1 )
30.61 .( mm )
δ Mc .π .
2
2
gm
= 46.2589075534523
2
cm
.t
Mc( 1 )
3
223 .( gm)
r Mc M Mc( 1 )
δ Mc .π .
2
3
2
1
= 1.2059841876 ( in )
223 .( gm )
.
t Mc( 1 )
r Mc M Mc( 1 )
δ Mc .π .
2
2
= 4.6760848165
<---- Required Moscovium Mass Density for zero discrepancy if the diameter is " r Mc M Mc( 1 ) " & the thickness is " t Mc( 1 ) "
<---- Required thickness for zero discrepancy if the diameter is the size of a 50 cent coin (US)
• https://en.wikipedia.org/wiki/Half_dollar_(United_States_coin)
= 22.4468060449376 ( mm )
223 .( gm)
30.61 .( mm )
π.
2
gm
= 63.1271450224826
2
223 .( gm)
<---- Required thickness for zero discrepancy if the diameter is " r Mc M Mc( 1 ) "
= 30.6319983638386 ( mm )
223 .( gm)
30.61 .( mm )
δ Mc .π .
2
2
1
= 0.8837325215 ( in )
t Mc( 1 )
223 .( gm )
.
30.61 .( mm )
δ Mc .π .
2
2
= 3.4265857447
<---- Required Moscovium Mass Density for zero discrepancy if the diameter is the size of a 50 cent coin (US) & the thickness is " t Mc( 1 ) "
The images below were procured from: https://www.gravitywarpdrive.com/Anti-Matter_Reactor.htm
Analysis
1. The base length of the Primary Wedge appears to be approximately 1"
2. For consistency with the preceding section, we shall assume its length to be the diameter of a 50 cent coin (US)
3. The height of the Primary Wedge appears to be approximately equal to 2-3 times the base length
4. The thickness of the Primary Wedge appears approximately 4-7(mm)
5. For consistency & generosity of outcome, we shall utilise the Disc Thickness from the preceding section for calculations
Assumptions
• The Volume of the Primary Wedge may be usefully approximated by a Triangular Prism
1. .
L P B P .H P
2
V P L P, B P, H P
<---- Volume of Triangular Prism (approximately equal to the Volume of the Primary Wedge) | Mass of Triangular Prism ---->
V P t Mc( 1 ) , 2 .r Mc M Mc( 1 ) , 4 .r Mc M Mc( 1 )
M P t Mc( 1 ) , 2 .r Mc M Mc( 1 ) , 4 .r Mc M Mc( 1 )
= 17.99114586125 cm
3
M P t Mc( 1 ) , 2 .r Mc M Mc( 1 ) , 4 .r Mc M Mc( 1 )
1 = 1.91339581796086 ( % )
M W V W2
M P L P, B P, H P
δ Mc .V P L P , B P , H P
= 242.880469126875 ( gm )
<---- Discrepancy between exact value (previous calculations) & the Triangular Approximation (discrepancy = negligible)
Considering a 50 cent coin size & various combinations of height configuration yields:
V P t Mc( 1 ) , 30.61 .( mm ) , 2 .30.61 .( mm )
V P t Mc( 1 ) , 30.61 .( mm ) , 3 .30.61 .( mm )
M P δ Mc .
xH
B P x H, L P
2
.L .B 2
P P
6.1378971854849
9.20684577822734
cm
3
M P t Mc( 1 ) , 30.61 .( mm ) , 2 .30.61 .( mm )
M P t Mc( 1 ) , 30.61 .( mm ) , 3 .30.61 .( mm )
=
82.8616120040461
124.292418006069
( gm)
<---- Configuration does not satisfy the 223(gm) mass condition defined above
• These results imply that the model is constructed to approximately half scale (1:2)
<---- Mass Density expressed as a multiple of Height to Base Length Ratio via " x H "
2 .223 .( gm)
x H .δ Mc .L P
Riccardo C. Storti
=
B P 3 , t Mc( 1 ) = 41.0009049793626 ( mm )
<---- Required base length to satisfy 223(gm) condition
19
www.deltagroupengineering.com
x H L P, B P
L P x H, B P
2 .223 .( gm)
2
x H t Mc( 1 ) , 30.61 .( mm ) = 5.38246830122279
<---- Required height to base ratio to satisfy 223(gm) condition
2
L P( 3 , 30.61 .( mm ) ) = 11.7531201612218 ( mm )
<---- Required thickness to satisfy 223(gm) condition
δ Mc .L P .B P
2 .223 .( gm)
δ Mc .x H .B P
δ Mc_2 x H , L P , B P
2 .223 .( gm)
2
x H .L P .B P
δ Mc_2 3 , t Mc( 1 ) , 30.61 .( mm ) = 24.2211073555026
gm
cm
3
<---- Required Moscovium Mass Density to satisfy 223(gm) condition
Bob Lazar (left) & Ken Wright (right)
Riccardo C. Storti
20
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