Color print Values table 1280 X 960 GIF Grayscale print Tutorial back, Atomic constants map Symbol key Tutorial end Wedges as displacement into the fourth dimension Color print 1280 X 960 GIF B & W print Color print 1280 X 960 GIF B & W print The Periodic Table of Planck Unit Constants Determines the Exact Value of the Newtonian Gravitational Constant Numerical patterns used to extrapolate unseen marks on slide rule scales and unlisted values in logarithm tables for hundreds of years combine in this periodic table of fundamental constants to show that only one numerical value for the Newtonian gravitational constant aligns the pervasive patterns of near misses among the constants into exact numerical matches. The mismatches found in the quantity calculus archive for any other [G] value reaffirm that proof: the exact numerical value of the Newtonian gravitational constant is 6.6917625607...e-11 = 10^-10.17445947721306... = T-10.1744595 Numbers between dollar signs below refer to locations in graphics above : projections of that vector space structuring into a lattice of logic the values of the Planck unit constants with the magnitudes expressed as common logarithms in 2D portrayals of a 3D map, but including representation of displacement into 4D. Multiplication by the factor {[k]^[1/2]} is signified by a wedge expanding in front of the 2D depiction plane, toward the viewer, and division by that factor of {[k]^[1/2]} is represented by a wedge expanding away from view, toward being behind the 2D depiction plane: Moving two wedges toward in front of the image is multiplication by electric constant [k] (= permittivity) in (Farad per Meter)^+1 and moving two wedges toward being behind the image is division by [k] in (Farads per Meter)^+1 . It is important to note that in the context of the atomic units and their mappings, GDA discussion alludes to multiplication by the Coulomb constant [Ke] = 1/{[4Pi][k]} represented by displacement in 4D as if moving behind the depiction plane while discussion in the context of these Planck unit spaces alludes to multiplication by [k] represented by displacement in the opposite direction, toward being in front of the depiction plane. This is just different terminology for the same conceptual situation with one important advantage: because the square of charge is defined in the atomic context as [action][velocity]/[Coulomb constant] : {[Q0]^2} = [hB][v0]/[Ke] with [Ke] = 1/{[4Pi][k]} and [v0] = [c][aa] , much of that vector space is populated by constants with tweaks : occurrences of one constant which has units combined with one or more constants which have no units. Defining [Planck charge]^2 as [action][velocity][k] = [hB][c][k] : {[PQ]^2} = [hB][c][k] and not {[PQ]^2} = [hB][c]/({[4Pi][k]}^-1) , the Planck unit vector space is rendered both free of tweaks and free of the need to discuss and consider reciprocals of reciprocals. Since customary, popular Planck charge [PX] is defined by [PX]^2 = [hB][c]/[Ke] , this means that {[PQ]^2} = {[PX]^2}/[4Pi] . This choice is important in the maps because it bestows a singular elegance upon the definition of that group of relationships, that class of vectors wherein lies the quintessence of determining the one value that the Newtonian gravitational constant [G] must have. In the triplet of graphics immediately above, GJN169X, GJN169Y, and GJN169Z, the Plank constants vector space is reproduced with an emphasis on that vector which proceeds from the plot point for the magnetic constant [d] (= permeability) to [G], the same vector and relationship represented by displacement from the origin to two wedges in front of location $40$ in the map. That vector's identity is [k]{[PL]^5}{[Pf]^4}/[PM] , it is [k][c^4][PL]/[PM] , and that vector's identity is {[PQ][PL]}^2 [c^2]{[PQ]^2}/{[PM]^2} = -------- : {[PM][PT]}^2 unadjustable [c^2] multiplied by unadjustable {[PQ]^2} , all divided by {[PM}^2} , square of the Planck mass value that will be set by adjustment of the value of [G] . With the Planck constants space modeled on the template of the self validating atomic constants space, where pre-existing, pre-defined, unadjustable constants populate, singly or in combinations, a space which is coherent, the question here is whether [G] is to have that one numerical value that will endow the Planck space with that same state of coherency. Either one accepts that the highlighted vector and all those identical to it have exactly the same numerical value as the square of the fine structure constant and that this space is coherent, or this Planck constants space consists partly of vectors with the numerical values of constants and partly of vectors with values which are only near misses to those of familiar constants. History records that the development and acceptance of the periodic table of the elements in chemistry included the completion of a pattern, a missing element that was later observed in the spectrum of the sun and thus named helium when attained. The completion of pattern here, too, is too elegant to be wrong. Due to the precedent of coherence in the atomic units vector space, due to the pervasive numerical coincidences found in both these graphics and in the quantities archive, and especially due to the identities of many of the coincidences involved, it is unreasonable to accept any other value for [G] . The vector emphasized in the maps above must have the numerical value of the square of the fine structure constant at 10^-4.2736694 and [G] must have the numerical value 10^-10.1744595 : {[PQ][PL]}^2 -------- <=> {[aa]^2} , and [G] <=> [d]{[aa]^2} . {[PM][PT]}^2 In judging the evidence for a [G] value that differs so considerably from most laboratory experiment results, it is important to remember the scope of the problem. A typical textbook on physics discusses a mass of 215 kg on the surface of the earth endowed with a charge identical in magnitude to an opposing charge at earth's center so that the gravitational attraction by the entire mass of the planet is offset. In his book Six Easy Pieces, Richard Feynman explains how two grains of sand thirty meters apart would attract each other with an electrical force of three million tons without a balancing of charges, if instead of likes repelling everything attracted everything else. Still another thought experiment might make the point more succinctly. As stated by that same Nobel prize winner in that same book, the ratio of gravitational attraction relative to the electrical repulsion between two electrons is 1/[4.17 x 10^42] : 10^-42.6+... In a standard static electricity setup involving two small masses with equal and like charges hung by insulating threads, the force [F] of repulsion is calculated to be the Coulomb constant [Ke] multiplied by the square of the charges [Q]^2, all divided by the square of the distance [L] between them: [F] = [Ke]{[Q]^2}/{[L]^2} . If the initial distance is one centimeter and that force is to be reduced to the strength of the gravitational force between those two masses by altering only [L] , [L] cannot be made one meter : 1/{[10^2] x [10^2]} => [F] x [10^-4] , [L] cannot be made one kilometer : 1/{[10^5] x [10^5]} => [F] x [10^-10] , [L] cannot be made one hundred million kilometers = 2/3 of the distance to the sun = .66 astronomical units : 1/{[10^13] x [10^13]} => [F] x [10^-26] , [L] cannot be made one hundred million times as far as .66 A U = 66 million astronomical units : 1/{[10^21] x [10^21]} => [F] x [10^-42] , [L] must be at least twice that far, [L] must be at least two hundred million times as far as .66 A U: 1/{[10^21.3] x [10^21.3]} => [F] x [10^-42.6] . If that commonly exhibited, hands on, observational experiment of the electrostatic force is to be altered for observation of a force comparable to that of the gravitational force by changing only their distance of separation, those two little masses on threads must be more than 132 million astronomical units apart. While such an experiment is unlikely to take place, if it did, at least the experimenters would not be using relatively minute masses to emulate celestially observed gravitational interactions while immersed deep in the gravity well of one of those celestial bodies, trying to obtain as good a vacuum as possible, estimating outgassing properties of materials, and/or torsion factors of fibers, and/or temperature fluctuations, and/or tidal influences while they stand in a pair of painted footprints. Finally, there is one more thing to keep in mind. With every new publication of CODATA values, it must be said again: there exists no recognized relationship between the Newtonian gravitational constant and any of the other constants. All the constants exist in the same universe and therefore have some kind(s) of relationship(s), but experiments involving forces 10^42 times as weak as tabletop setups will be conducted as if such relationships did not exist and cannot be affecting results. Using one dimension or more, do the math. Decide for yourself. GUNTERTABLE3 only print ---------------------------------++--------------------------------- GUNTERTABLE3 : for the Periodic Table of Planck Unit Constants ---------------------------------++--------------------------------- POWER OF TEN | COMMENTS, NOTES UNITS ---------------------------------++--------------------------------- AUN = Atomic unit of PUN = Planck unit of 0.0000000 1 = [10]^0 = [Anything]^0 $0$ = {[10]^0}{[PM]^0}{[PL]^0}{[Pf]^0}{{[k]^0} ORIGIN - 11.0528513 [k] = 1/{[4Pi][Ke]} Fradmetr=Cuulhrtzmetrwebr = [Q0]/{4[w0][v0]} = {[Jf]^2}[Me][a0][Pi]/4 hnryh2tzmetr = {[aa]^2}/([d]{[v0]^2}) = [10^7][Meter]/([4Pi][c^2][Henry]) = {[aa]^2}{[a0]^-2}{[2af]^-2}/[d] = [AUN permittivity]/[4Pi] = 1/{[c^2][d]} = 1/{2[v0][RK]} = 1/{2[aa][c][RK]} hrtzmetrohmm $0$ = [k] = ({[PL][Pf]}^-2)/[d] = Electric constant = permittivity - 7.6628219 [PM] = [PE]/[c^2] = {[Q0]^2}[d]/{[4Pi][aa][PL]} Kgrm = [Me][a0][aa]/[PL] = {[aa]^2}[Me][Pf]/[2af] = [hB]/{[PL][c]} = [z0]{[PQ]^2}/{[PL][c]} = [Pk][Bk][d][k] = [k]{[PL]^3}{[PB]^2} = [z0]{[PC]^2}/({[PL]^2}{[Pf]^3}) = ({[Q0]^2}[Ke]/{[G][aa]})^.5 $1$ = [PM] = {[hB][c]/[G]}^.5 = Planck Mass - 34.7909227 [PL] = [G][PM]/[c^2] = [a0][Me][aa]/[PM] Metr = [hB]/{[PM][c]} = [u0][Me]/{[c][Q0][PM]} = 1/{[z0][Pf][k]} $2$ = [PL] = {[hB][G]/[c^3]}^.5 = Planck length - 45.8437740 [PCA] = [PQ]/[PT0] = {[PQ]^2}/[PE] Frad $2$ = [PL][k] = [PL]/{[4Pi][Ke]} = PUN capacitance + 43.2677434 [Pf] = [c]/[PL] = [PM][2af]/({[aa]^2}[Me]) Hrtz = [PB]{[G][k]}^.5 = [hB]/({[PL]^2}[PM]) = ([G][PM]/{[PL]^3})^.5 $3$ = [Pf] = {[hB][G]/[c^5]}^-.5 = 1/[PT] = Planck frequency - 43.2677434 [PT] = 1/[Pf] = {[aa]^2}[Me]/{[PM][2af]} hrtz=Scnd = [PL]/[c] = 1/([PB]{[G][k]}^.5) = ([G][PM]/{[PL]^3})^-.5 $4$ = [PT] = {[hB][G]/[c^5]}^.5 = {[PL]^2}[PM]/[hB] = Planck time + 8.4768207 [c] = [z0]/[d] = 1/{[k][z0]} = [v0]/[aa] HrtzMetr = [aa][H0]/{[k][E0]} = 1/{2[aa][RK][k]} fradhnryhrtzMetr = {[G][PM]/[PL]}^.5 = 1/{[c][d][k]} fradMetrohmm=J12lk12m = [hB]/{[PM][PL]} = (1/{[k][d]})^.5 metrtslaVltt=Cuulf12dk12m = [f0]/{2[Rc]} = [E0]/{[aa][B0]} = [AUN velocity]/[aa] $5$ = [PL][Pf] = Light speed in vacuum = PUN velocity + 0.8139988 [Pp] = [hB]/[PL] = [PM][c] = [PE]/[c] HrtzKgrmMetr $6$ = [PM][PL][Pf] = Planck momentum - 33.9769238 [hB] = [h]/[2Pi] = [PM][PL][c] hrtzJuul=HrtzKgrmM2tr = {[Q0]^2}/{[4Pi][k][v0]} = [B0][Q0]{[a0]^2} CuulM2trTsla = {[Q0]^2}[Ke]/[v0] = [Q0][w0]/[Pi] = [He]/{[4Pi][Rc][c]} = {[Q0]^2}[RK]/[2Pi] = [u0][Me]/[Q0] = [G]{[PM]^2}/[c] *7* = {[Q0]^2}[v0][d]/([4Pi]{[aa]^2}) = {[PQ]^2}[z0] = AUN action $7$ = [PM]{[PL]^2}[Pf] = [Me]{[a0]^2}[2af] = PUN action + 44.0817422 [FBH] = [FPX] = [FPC] = [4Pi][FPQ] = [c^4]/[G] Nwtn = {[PQ]^2}/({[PL]^2}[k]) = [d]{[PC^2]} = [hB][c]/{[PL]^2} = {[PX]^2}/({[PL]^2}[4Pi][k]) = [PE]/[PL] = [PPw]/[c] = {[PM]^2}[G]/{[PL]^2} = [c^2][PM]/[PL] = [c][PM][Pf] = {[Q0]^2}[Ke]/({[PL]^2}[aa]) = [z0][k][c^3][PM]/[PL] = {[a0]^2}[Fe]/({[PL]^2}[aa]) = {[Fe]^2}[Mp]/([Me][Fg]{[aa]^4}) $8$ = [PM][PL]{[Pf]^2} = Planck force + 9.2908195 [PE] = [PM][c^2] = [FBH][PL] Juul=MetrNwtn = {[PQ]^2}/{[k][PL]} = {[PC]^2}[z0]/[Pf] C2ulfrad=A2prhrtzOhmm $9$ = [PM]{[PL]^2}{[Pf]^2} = Planck energy - 25.5001032 [hBc] = [hB][c] = [PM][PL][c^2] C2ulfradMetr=JuulMetr = {[PQ]^2}[Ke][4Pi] = {[PQ]^2}/[k] A2prHnryMetr=H2tzKgrmM3tr = {[Q0]^2}[Ke]/[aa] = {[PC]^2}{[PL]^2}[d] fradH2tzK2rmMetrt2la = {[PX]^2}[Ke] = ({[Me][2af]/[B0]}^2)/{[aa][4Pi][k]} M2trNwtn $10$ = [PM]{[PL]^3}{[Pf]^2} = [PE][PL] = [FBH]{[PL]^2} = [G]{[PM]^2} - 36.5529545 {[PQ]^2} = [hB][c][k] = [G][k]{[PM]^2} FradJuul=C2ul = [k][c^2][PM][PL] = {[Q0]^2}/{[4Pi][aa]} AmprKgrmtsla = [Me][a0][aa]/[d] = [PM][PC]/[PB] A2prKgrmMetrnwtn = {[PM]^2}{[Pf]^2}/{[PB]^2} hnryKgrmM2tr=H2tzK2rmt2la = {[PX]^2}/[4Pi] = {[Popular Planck charge]^2}/[4Pi] $10$ = [PM]{PL]^3}{[Pf]^2}[k] = [PL][PM]/[d] = [GDA Planck Charge]^2 - 18.2764773 [PQ] = ({[hB][c][k]}^.5) = [Q0]/({[4Pi][aa]}^.5) Cuul = [PC][PT] = [PM][Pf]/[PB] Amprhrtz=HrtzKgrmtsla = [PX]/{[4Pi]^.5} = [Popular Planck charge]/{[4Pi]^.5} $11$ = {[PM]^.5}{[PL]^1.5}[Pf]{[k]^.5} = GDA Planck charge + 24.9912662 [PC] = [PQ][Pf] = ([k]{[c]^3}[PM][Pf])^.5 CuulHrtz = ({[hB][c]/[d]}^.5)/[PL] = {[FBH]/[d]}^.5 Ampr=F12dHrtzJ12l = [PM][Pf]{[G][k]}^.5} = [Pf]{[hB][c][k]}^.5 F12dH2tzK12mMetr = [Q0][Pf]/({[4Pi][aa]}^.5) h12yM12rN12n $12$ = {[PM]^.5}{[PL]^1.5}{[Pf]^2}{[k]^.5} = PUN current + 27.5672968 [PT0] = [PE]/[PQ] = [PB][PcQ] = [PC][z0] Vltt = [hB][k]/[PQ] = [PQ]/{[PL][k]} = [PH0]/{[k][Pf]} cuulJuul $13$ = {[PM]^.5}{[PL]^1.5}[Pf]{[k]^-.5} = PUN electric potential + 62.3582195 [PE0] = [FBH]/[PQ] = [PE]/{[PQ][PL]} metrVltt = [z0][PB]/[d] = [z0][PH0] = [PQ]/([k]{[PL]^2}) cuulNwtn = [z0][PB][c^2][k] = [c][PB] = [PC]/{[k][c][PL]} Cuulfradmetr $14$ = {[PM]^.5}{[PL]^-.5}[Pf]{[k]^-.5} = PUN electric field + 86.0962908 [PQD] = [PQ]/{[PL]^3} = [c][PB][k]/[PL] Cuulm3tr $15$ = {[PM]^.5}{[PL]^-1.5}[Pf]{[k]^.5} = PUN charge density + 97.1491421 [PEg] = [PB][Pf] = [PQ]/([k]{[PL]^3}) m2trVltt = [FBH]/{[PQ][PL]} = [z0][PB]/{[d][PL]} cuulmetrNwtn=HrtzTsla $15$ = {[PM]^.5}{[PL]^-1.5}[Pf]{[k]^-.5}=PUN electric field gradient - 53.0674000 [PQq] = [PQ][PL] = [hB]/{[PB][PL]} CuulMetr $16$ = {[PM]^.5}{[PL]^2.5}[Pf]{[k]^.5} = PUN electric dipole moment - 87.8583227 [PQQ} = [PQ]{[PL]^2} = [hB]/[PB] CuulM2tr $17$ ={[PM]^.5}{[PL]^3.5}[Pf]{[k]^.5}=PUN electric quadrapole moment -115.4256195 [P18] = [G][PM][k]/{[Pf]^2} Kgrmt2la=C2uljuulM2tr = {[PQ]^2}/([PM]{[Pf]^2}) FradM2tr=JuulM2trv2tt = [PQ]/{[PB][Pf]} = {[PQ]^2}{[PL]^2}/[PE] Cuulhrtztsla $18$ = {[PL]^3}[k] = [PM]/{[PB]^2} = PUN electric polarizability -177.7838390 [P19] = {[PQ]^3}{[PL]^3}/{[PE]^2} C3ulj2ulM3tr = [PE]/{[PE0]^3} = [P18]/[PE0] = PUN 1st hyperpolarizability $19$ = {[PM]^-.5}{[PL]^3.5}{[Pf]^-1}{[k]^1.5} -240.1420585 [P20] = [PE]/{[PE0]^4} = [PQq]/{[PE0]^3} C4ulj3ulM4tr = ({[PQ][PL]}^4)/{[PE]^3} = [P18]/{[PE0]^2} JuulM3trv3tt $20$ = {[PM^-1}{[PL]^4}{[Pf]^-2}{[k]^2} =PUN 2nd hyperpolarizability + 53.8813988 [PB] = {[PM]/([k]{[PL]^3})}^.5 = [PC][d]/[PL] Tsla = [PQ]/([k][c]{[PL]^2}) AmprHnrym2tr=Cuulfradhrtzm2tr $21$ = {[PM]^.5}{[PL]^-1.5}{[k]^-.5} = PUN magnetic flux density - 44.5905793 [Pu0] = [PC]{[PL]^2} =[PQ][PL][c] =[PE]/[PB] AmprM2tr = [hB][c]{[PL][k]/[PM]}^.5 = PUN magnetic dipole moment $22$ = {[PM]^.5}{[PL]^3.5}{[Pf]^2}{[k]^.5} - 98.4719780 [P23] = [hB][c][k]{[PL]^2}/[PM] C2ulkgrmM2tr = [PE]/{[PB]^2} = {[PQ]^2}{[PL]^2}/[PM] Juult2la=hnryM4tr $23$ = {[PL]^5}{[Pf]^2}[k] = {[PL]^3}/[d] = PUN magnetizability - 10.6136554 [PQM] = [PQ]/[PM] = {[G][k]}^.5 = [Pf]/[PB] Cuulkgrm = ([PL]/{[PM]]d]})^.5 = ({[hB][c][k]}^.5)/[PM] Hrtztsla = {[c^2][k][PL]/[PM]}^.5 = [Planck charge]/[Planck mass] $24$ = {[PM]^-.5}{[PL]^1.5}[Pf]{[k]^.5} = PUN specific charge - 15.7004466 [Pww] = [PC][PL][d] = [PQ][z0] Webr=amprJuul=M2trTsla = ({[hB][z0]}^.5) = [PC]/{[aBH][k]} AmprHnry=h12zJ12lO12m = ([G]{[PM}^2}[d])^.5 = [PB]{[PL]^2} CuulOhmm=f12dK12mMetr $25$ = {[PM]^.5}{[PL]^.5}{[k]^-.5} = [PE]/[PC] = PUN magnetic flux - 5.9007901 [d] = [H0]/[B0] = 1/{[c^2][k]} a2prNwtn=Hnrymetr = 4[B0][w0]{[aa]^2}/[Fe] = [z0]/[c] = {[z0]^2}[k] M2trnwtnT2la = [4Pi]{[aa]^2}[Me][a0]/{[Q0]^2} = [FPC]/{[PC]^2} c2ulKgrmMetr = [4Pi]{[aa]^2}[Fe]/{[i0]^2} = [FBH]/{[PC]^2} FradmetrO2mm = [4Pi]{[aa]^2}[Ke]/{[v0]^2} =[4Pi][FPQ]/{[PC]^2} fradh2tzmetr = [4Pi]{[aa]^2}[Ke][He]/([Me]{[v0]^4}) nwtnTslaWebr = [4Pi]{[aa]^2}[Ke][Pi][Jf][B0]/{[2af]^2} hrtzmetrOhmm = [4Pi]{[aa]^2}{[Ke]^3}[20H][Me]/{[a0]^6} = 2{[aa]^2}[RK]/[v0] = {[a0]^-2}{[2af]^-2}[4Pi]{[aa]^2}[Ke] = Vacuum permeability $26$ = {[PL]^-2}{[Pf]^-2}{[k]^-1} = Magnetic constant - 26.3141020 [PcQ] = [c][PL] = {[PL]^2}[Pf] hrtzM2tr $27$ = {[PL]^2}[Pf] = [PE]/{[PM][Pf]} = PUN circulation + 52.5585629 [PPw] = [PE][Pf] = [PM][c^2][Pf] = [c^5]/[G] Waat = [Pw0]{[PC]^2}[4Pi][aa]/{[i0]^2} = {[PC]^2}[z0] A2prOhmm $28$ = [PM]{[PL]^2}{[Pf]^3} = PUN power + 59.7821889 [PH0] = [PB]/[d] = [c^2][k][PB] Amprmetr=metrohmmVltt = [FBH]/([PB]{[PL]^2}) m2trNwtntsla=hnryMetrTsla = [PQ][c]/{[PL]^2} = [PC]/[PL] = PUN magnetic field strength $29$ = {[PM]^.5}{[PL]^.5}{[Pf]^2}{[k]^.5} +113.6635876 [k]{[PE0]^2} = [PC][PB]/[PL] m2trNwtn=Juulm3tr = [c^2][k]{[PB]^2} = {[PB]^2}/[d] AmprmetrTsla=H2tzM2trT2la = [PE]/{[PL]^3} = [FBH]/{[PL]^2} = PUN energy density $30$ = [PM]{[PL]^-1}{[Pf]^2} = [k][PUN electric field]^2 +124.7164389 {[PE0]^2} = {[FBH]/[PQ]}^2 c2ulN2tn=m2trV2tt = {[z0][PB]/[d]}^2 = {[c][PB]}^2 = ([PE]/{[PQ][PL]})^2 $30$ = [PM]{[PL]^-1}{[Pf]^2}{[k]^-1} = [PUN electric field]^2 - 10.1744595 [G] = [hB][c]/{[PM]^2} = [c^2][PL]/[PM] k2rmM2trNwtn = {[PL]^3}{[Pf]^2}/[PM] = {[Pf]^2}/({[PB]^2}[k]) Juulk2rmMetr = {[PQ]^2}/([k]{[PM]}^2) = [c^4][PL]/[PE] H4tzjuulM5tr = [d]{[PL]^5}{[Pf]^4}/[PM] fradH2tzMetrt2la = [d][c^2]{[PQ]^2}/{[PM]^2} A2prk2rmnwtnW2br = [c^2][Me][a0][aa]/{[PM]^2} a2prC2ulH2tzk2rmM2trNwtn = {[Q0]^2}[Ke]/({[PM]^2}[aa]) fradh2ryhrtzkgrmM3trOhmm = {[a0]^2}[Fe]/({[PM]^2}[aa]) Fradk2rmMetrOhmmWaat = {[z0]/[d]}{[PL]^2}[Pf]/[PM] A2prfradh2tzk2rmMetr = {[PC]^2}/({[PM]^2}{[Pf]^2}[k]) C2ulh2tzk3rmmetrV2tt = ({[v0]^2}[a0]/[Mp]){[Fg]/[Fe]} Fradk2rmMetrV2tt = {[PL]^2}[Fe]/({[Me]^2}{[aa]^3}) hnryk2rmMetrW2br = {[QeM]^2}[Ke]{[Fg]/[Fe]}{[Me]/[Mp]} C2ulfradk2rmMetr = {[Ke]/[aa]}([2af][Me]/{[B0][PM]})^2 H2tzkgrmM3tr = {[i0]^2}[Ke]/({[PM]^2}{[2af]^2}[aa]) = ({[Q0]^2}[Ke]{[Fg]/[Fe]})/{[Me][Mp]} = {[a0]^3}[Me]{[2af]^2}/({[PM]^2}[aa]) = {[Q0]^2}/{({[Jf][Pi][PM]}^2)[aa][Me][a0]} = 4[Ke]({[Bm]/[hB]}^2){[Fg]/[Fe]}{[Me]/[Mp]} = [Ke]({[2af]/[B0]}^2){[Fg]/[Fe]}{[Me]/[Mp]} = {[w0]^2}{[v0]^2}/({[PM]^2}{[Pi]^2}[Ke][aa]) = [Ke]({[Eg0]^2}/{[B0]^4}){[Fg]/[Fe]}{[Me]/[Mp]} = {[Gye]^2}[Ke]({[Bm]/[ue]}^2){[Fg]/[Fe]}{[Me]/[Mp]} = [B0][Fg]{[2af]^2}{[a0]^4.5}/{[Fe][Mp]({[Ke][Me]}^.5)} = ({[Eg0]^2}/{[B0]^4}){[Ke][Me][2af]/([PM][Pf]{[aa]^3})} = {[Me]^-1}{[a0]^3}{[2af^2}{[Fg]/[Fe]}{[Me]/[Mp]} $31$ = {[PM]^-1}{[PL]^3}{[Pf]^2} = Newtonian gravitational constant - 42.4537446 [PM][PL] = {[PQ]^2}[d] = [Me][a0][aa] C2ulHnrymetr = {[Q0]^2}[d]/{[aa][4Pi]} = {[Q0]^2}[Ke]/{[c^2][aa]} KgrmMetr = 4[aa][k]{[w0]^2}/[Pi] = {[PX]^2}[d]/[4Pi] FradmetrW2br = [aa][Jf]{[Me]^2}/{4[k][B0]} = [hB]/[c] fradK2rmmetrt2la = [aa][Ke]{[Me]^2}/({[B0]^2}{[a0]^2}) fradHrtzK2rmMetrtslavltt = [aa][k][4Pi]{[B0]^2}{[a0]^4} = [Me][u0]/{[c][Q0]} = 2[aa][k][hB][RK] = [Mp][Rp]/[2Pi] = [Me][Re]/[aa] $32$ = [PM][PL] = [k][PUN magnetic flux]^2 + 96.7099462 [k]{[PB]^2} = [PM]/{[PL]^3} = {[Pf]^2}/[G] Kgrmm3tr $33$ = [PM]{[PL]^-3} = [k]{[PUN magnetic flux density]^2} +107.7627975 [PB]^2 = [PM]/([k]{[PL]^3}) T2la = {[PC][d]/[PL]}^2 = {[Pf]^2}/{[k][G]} fradKgrmm2tr $33$ = [PM]{[PL]^-3}{[k]^-1} = [PUN magnetic flux density]^2 + 15.7004466 [PJf] = [PC]/[PE] = 1/([PB]{[PL]^2}) webr=Amprjuul = 1/{[[PQ][z0]} = [c^2][k]/{[PC][PL]} amprhnry = {[aBH][k]/[PC] = 1/([PB]{[PL]^2}) m2trtsla=cuulohmm $34$ = {[PM]^-.5}{[PL]^-.5}{[k]^.5} = PUN Josephson constant + 2.5760306 [z0] = 2[aa][h]/{[Q0]^2} Ohmm=HnryHrtz=amprVltt = [E0]/{[aa][H0]} = [d][E0]/{[aa][B0]} = 4[aa]/[G0] f12dH12y = 4[w0][aa]/[Q0] = 4[aa]/{[Jf][Q0]} = [hB]/{[PQ]^2} cuulWebr = {[v0]^-1}[4Pi][aa][Ke] = 1/{[c][k]} = 2[RK][aa] fradhrtz = [Pw0][4Pi][aa]/{[i0]^2} = [d][c] = 4[aa]/{[G0] c2ulhrtzJuul = {[a0]^-1}{[2af]^-1}[4Pi][aa][Ke] = {[d]/[k]}^.5 $35$ = {[PL]^-1}{[Pf]^-1}{[k]^-1} = Impedance of vacuum + 5.9007901 1/[d] = {[PQ]^2}/{[PL][PM]} A2prnwtn=hnryMetr = 1/{[z0]^2}[k] = {[PC]^2}/[FBH] = [c]/[z0] = 1/{Permeability} $36$ = {[PL]^2}{[Pf]^2}[k] = [PM]/{[PE][k]} = 1/{Magnetic constant} + 16.9536414 [c^2] = {[v0]/[aa]}^2 H2tzM2tr=Juulkgrm = 1/{[k][d]} = ([E0]/{[aa][B0]})^2 = [G][PM]/[PL] C2ulfradkgrm = {[Q0]^2}[Ke]/{[aa][PM][PL]} = [PK][Bk]/[PM] A2prfradMetrnwtn = {[a0]^2}{[2af]^2}/{[aa]^2} = [hB][Pf]/[PM] fradhnryM2tr $36$ = {[PL]^2}{[Pf]^2} = [Speed of light in vacuum]^2 + 51.7445641 [aBH] = [c][Pf] = [G][PM]/{[PL]^2} H2tzMetr $37$ = [PL]{[Pf]^2} = [c^2]/[PL] = [FBH]/[PM] = PUN acceleration + 31.4008933 [PJf]^2 = [k][c]/[hB] = {[PC]/[PE]}^2 A2prj2ul=w2br = [k]/({[PQ]^2}[d]) = 1/({[PQ][z0]}^2) Fradkgrmm2tr = 1/{[hB][z0]} = 1/([G]{[PM}^2}[d]) a2prh2ry=c2ulFradhnry $38$ = {[PM]^-1}{[PL]^-1}[k] = [PUN Josephson constant]^2 + 42.4537446 {[PJf]^2}/[k] = [4Pi]/({[PX]^2}[d]) kgrmmetr = [aa]/{[Me][Re]} = 1/({[PQ]^2}[d]) = [c]/[hB] c2ulhnryMetr $38$ = {[PM]^-1}{[PL]^-1} = {[PUN Josephson constant]^2}/[k] - 40.6917128 [PI0] = [PL][d] = [PL]/{[c^2][k]} Hnry = [PM]/{[k][FBH]} = [z0]/[Pf] a2prMetrNwtn $39$ = {[PL]^-1}{[Pf]^-2}{[k]^-1} = PUN inductance - 4.2736694 [G]/[d] = [G][c^2][k] FradH2tzk2rmM3trNwtn = {[PC]^2}{[PL]^2}/{[PM]^2} = {[aBh]/[PB]}^2 hnryH2tzkgrmM4tr = ([PQ][PL]/{[PM][PT]})^2 = [c^4][PL][k]/[PM] A2prk2rmM2tr = ({[PQ]/[PM]}^2)[c^2] = [c^5][k]/{[PM][Pf]} H4tzM2trt2la = ({[PQ]/[PM]}^4)[PM]/{[PL][k]} [[C2ulH2tzk2rmM2tr]] $40$ = {[PM]^-1}{[PL]^5}{[Pf]^4}[k] = [c^2]{[PQM]^2} + 6.7791820 [G][c^2] = [c^4][PL]/[PM] H2tzk2rmM4trNwtn = {[PC]^2}{[PL]^2}/([k]{[PM]^2}) C2ulfradkgrmM3tr = {[PQ]^2}{[PL]^2}/({[PM]^2}{[PT]^2}[k]) H4tzkgrmM5tr $40$ = {[PM]^-1}{[PL]^5}{[Pf]^4} = [c^2]{[PQM]^2}/[k] - 8.0376248 ([PL]/{[PM][k]})^.5 CuulHnryHrtzkgrm=f12dk12mMetr $41$ = {[PM]^-.5}{[PL]^.5}{[k]^-.5} = [d][c][PQ]/[PM] - 13.5640504 {[G]/[c^2]}^.5 = {[k]^.5}[d][c][PQ]/[PM] k12mM12r $41$ = {[PM]^-.5}{[PL]^.5} = {[PL]/[PM]}^.5 - 2.1368347 $[PQ][PL]/{[PM][PT]} = [aBh]/[PB] [[CuulHrtzkgrmMetr]] = [Pu0]/{[PM][PL]} = {[c^4][k][PL]/[PM]}^.5 H2tzMetrtsla $42$ = {[PM]^-.5}{[PL]^2.5}{[Pf]^2}{[k]^.5} = [c][PQ]/[PM] + 3.3895910 [c]{[G]^.5} = [PC][PL]/([PM]{[k]^.5}) H2tzk12mM52r = [PQ][PL]/([PM][PT]{[k]^.5}) Cuulf12dkgrmM32r $42$ = {[PM]^-.5}{[PL]^2.5}[Pf] = {[c^4][PL]/[PM]}^.5 =================================++=================================