Revising the Planck Unit Values and Determining the Gravitational Constant II As the alternative numerical expression, symbol use, and unit labels facilitate greater information density in maps, increased search and sort capability in digitized literature, and superior value comparison in tables, Geometrical Dimensional Analysis exposes a key similarity of values. With the structuring of definitions and formulas of fundamental constants into the lattices of logic, the vector spaces, the factoring pathway maps projected by acceptance of the International System of Units (S.I.), identities and patterns of relationship are displayed which correct the estimates of the Planck units and indicate a specific value for the constant of gravitation. Proposing that [G] has numerical value 6.6917625079...e-11 , exactly the same as other quantities with different units, the implication is that the difficulties in relating gravity to other forces and the gravitational to other constants has involved an inadequacy in the definition or use of the quantity calculus. With the atomic units of mass, length, and frequency as the unit vectors defining the Corrsin diagrams(006) of GJN017 and GJN018, both known and unsuspected factoring combinations within the atomic units become visible, validating the premise that unit systems can be treated as vector spaces(027) and inviting a similar display of the Planck units, as in diagram GJN020. As an overlay of the two natural unit systems, each of GJN023 and GJN024 is, at any point, a dimensionless ratio of a Planck unit numerator to an atomic unit denominator, relating together all of the quantities portrayed in the two individual unit system maps. For better understanding of that metaratio, however, [hB], [c], and [G] as unit vectors form yet another view of the Planck unit system in GJN016, where it is more obvious which quantities, lying in the plane created by adopted [hB] and defined [c], cannot be changed, and which entities, not in that plane, will be altered with the adjustments required to [PM], [PL], and [Pf]: just as the product [PL][Pf] must match [v0][aa] as equal to [c] and both [c][PL][PM] and {[PL]^2}[PM][Pf] must equal [hB], [PL][PM] must be as equal to [hB]/[c] as is [Me][a0][aa], [PM]/[Pf] must match both [Me]{[aa]^2}/[2af] and [hB]/[c^2], and [G]{[PM]^2}, [PM]{[PL]^3}{[Pf]^2}, and {[PQ]^2}/[k] must all be as identical to [hB][c] as are {[Q0]^2}[Ke]/[aa] and [Me][v0^2][a0]/[aa]. While the need for some more consistent set of Planck units thus becomes obvious, determination of the one correct set, and therefore of the value of the gravitational constant as the factor combination {[PL]^3}{[Pf]^2}/[PM], that arises from a very near miss in a value archive as [G] is adjusted to reflect contemporary estimates. =================================++================================= **In format Txx.xxxxxxx = 10^xx.xxxxxxx... , recent publication(322) has [G] located in the middle of modern experimental results(322) at T-10.1743792 = 6.693e-11 in {Meter^3)/[(Kilogram)(Second^2)], or (Newton)(Meter^2)/(Kilogram^2), or (Farad)(Meter)(Volt^2)/(Kilogram^2), or (Meter)/[(Farad)(Second^2)(Tesla^2)], or (Farad)(Meter)(Ohm)(Watt)/(Kilogram^2), or (Meter)(Weber^2)/[(Henry)(Kilogram^2)], or (Coulomb^2)(Meter)/[(Farad)(Kilogram^2)], or (Meter^3)(Ohm)/[(Henry)(Kilogram)(Second)], or (Ampere^2)(Weber^2)/[(Kilogram^2)(Newton)], or (Coulomb)(Meter^3)(Tesla)/[(Kilogram^2)(Second)]. In (Henry)/(Meter) or (Newton)/(Ampere^2), quantity [d]{[aa]^2} and those which are identical to it all have a numerical value of 6.6917625...e-11 as T-10.1744595 , quite close to T-10.1743792 and even more centered in that result range. In fact, that near miss not only stands out in the values table, it is also true that if [G] and immutable product [d]{[aa]^2} both have that numerical value of T-10.1744595 , so that [PM] is T-7.6628219 , [PL] is T-34.7909227 , and [Pf] is T+43.2677434 , a number of dimensioned and dimensionless quantities acquire identical numerical values. While a uniform map such as those above will locate numerical values in parallel planes, the revised Planck unit maps now exhibit important new alignments. There are now numerous instances where significant quantities with dissimilar units share a line parallel to that which transfixes both [G] and [d] : a line of multiplication by some power of the factor [G]/[d] = [c^2][PL]/([PM][d]) = [c^4][k][PL]/[PM][d], which equals {[aa]^2}(Coulomb^2){Meter^2)/[(Kilogram^2)(Second^2)], or [PC][PL]/[PM] which is [aa](Coulomb){Meter)/[(Kilogram)(Second)] . In the comparison table, values in the first column are based on [G] as T-10.1744595 , and those in the second column derive from the recently published NIST values(023f). The "dissimilar" quantities which share a given numerical value are denoted by differing numbers of dollar signs and those with units will lie on one of the lines of coincidence mentioned above. Notice that the NIST adopted values of the Planck units produce results which fail to match those values required by the dimensional analysis, that different combinations of those NIST values as factors can produce differing numerical results for the same end product, and that some of the identical numerical occurrences which exist only for the proposed values of [PL], [PM], [Pf], and [G] have significant implications: {[aa]^2} as compared to [G][k][c^2] = [G]/[d] and therefore also [PL]/[PM] contrasted with {[aa]^2}/{[k][c^4]} = {[aa]^2}[d]/[c^2], [PM] in contrast to [PQ][c]/[aa] or [Pf] to [PQ][c^3]/{[aa][hB]}, [PL] contrasted with [Me]{[aa]^3}/[PQ][2af] = [PQ][aa][d]/[c], [PC] in contrast to [c^2]/{[d][aa]} and to [PM][aa]/[PL], [G]/[k] as compared to {[E0]/[H0]}^2 = {[v0][d]}^2 = {[z0][aa]}^2 = {([He][a0][d])/[hB]}^2 = {[aa]^2}[d]/[k] = 4{[aa]^4}{[RK]}^2 , and [Fe]/[Fg] = ([Q0]^2)[Ke]/([G][Me][Mp]) = [aa]{[PM]^2}/{[Me][Mp]} = {[PQ]^2}[aa][PM][d]/{[Me][Mp][PL]} = ([aa]^2)[PM][a0]/([Mp][PL]) = {[PQ]^2}[aa]/{[G][k][Me][Mp]} = ([aa]^3)[PM][Pf]/([Mp][2af]) in contrast to [c^4][a0][k]/[Mp] or to [PC][a0][aa]/[Mp] . While it is interesting to compare the alignment factor above to his magnetic charge and tempting to declare an insufficiency of bases in the S.I. similar to that proposed by Desloge(102)(103), this report intentionally declares only "inadequacy". The issue of measurements not only includes notable argument for fewer base units instead of more(030)(056)(235), it possesses all the potential for misunderstanding and confusion to be inferred from centuries of controversy and such contentions as distinguishing straight length from arc length(076), having separate units for lengths in different frames of reference(169), and proposals that length differs in the direction of an electron's travel(100) or can change when measured from a different scale(087). More physical dimensions in the microcosm(029)(055), gravity screening investigations(059), Foucault pendulum anomalies during solar eclipses(323), spacecraft trajectory abnormalities(316), even claims of antigravity experiments(324) are due consideration as an understanding of gravity remains elusive. With visible proof that the Planck units can be related to the other constants well enough to correct incompatibilities with them, because the adjusted set combines as factors to produce a numerical value shared by [G] and quantities with factors which are significant in defining any system of units(027)(123)(245)(261)(262), and considering the pattern alignments by such significant numerical coincidences, the proposal here is that reconsideration is called for of the mathematical logic found at the foundation of all of physics. To that end, this writer is pursuing and joins others in recommending a general review of the works by authors such as Birge(223)(262)(263), Bridgman(067)(251), DeBoer(147), Esnault-Pelterie(235), Hall(082), Karapetoff(232), Maxwell(090), Page(261), Palacios(124), Petley(077), Sena(245), Silsbee(066), Tuninsky(148), Varner(123), and Weber(233), as well as the comments on the subject by Abraham(056) and Jackson(136) and the more officially sanctioned publications(023)(288)(313). ** The CODATA 2006 adjustment of the fundamental constants specifically states that both the Fixler et al results and the Bernoldi et al results play no significant part in the officially adopted value for Newtonian gravitational constant [G], (Rev Mod Phys, Vol 80, No 2, Apr-Jun 2008, table XXVII and fig 2), but dimensional analysis still requires a set of Planck mass, Planck length, and Planck time values that correctly combine into all the quantities and there still exists a repeating, all-pervasive pattern of numerical coincidences among fundamental constants if [G] has the same numerical value as the product of the magnetic constant and the square of the fine structure constant. COMPARISON TABLE For third column POWER OF TEN values below, calculate the value of the quantity listed using CODATA 2010 values as seen 17 June, 2013 (allascii.txt, as downloaded from http://physics.nist.gov/constants can be found here), express the result as a common logarithm, as a power of ten, then round off that value to the 7th decimal place. Symbol and label key Mappings Complete values table =================================++================================= $ = DIFFERENT DIMENSIONS, $$ = STILL DIFFERENT DIMENSIONS, etc. * as divider: value will vary with adjustment of value of [G] | as divider: value will NOT vary with adjustment of value of [G] WITH EACH VALUE AS A POWER OF TEN: G=T-10.1744595 CODATA 2006 CODATA 2010 =================================++============================================== [G] -10.1744595 * -10.1755956 -10.1756242 {[PL]^3}{[Pf]^2}/[PM] -10.1744594 * -10.1755968 -10.1756245 {[PL]^2}[Pf][c]/[PM] -10.1744594 * -10.1755965 -10.1756245 [c^2][PL]/[PM] -10.1744594 * -10.1755962 -10.1756244 [c^2]{[PL]^2}/{[a0][Me][aa]} -10.1744593 * -10.1755958 -10.1756243 ([Q0]^2)/([4Pi][aa][k]([PM]^2)) -10.1744593 * -10.1755966 -10.1756245 {[PQ]^2}/([k]{[PM]^2}) -10.1744595 * -10.1755962 -10.1756245 {([2af][Me]/[B0][PM])^2}/{[4Pi][aa][k]} -10.1744595 * -10.1755966 -10.1756245 in k2rmM2trNwtn = kgrmM3trs2nd = Cuulk2rmM3trscndTsla = fradMetrs2ndt2la = hnryk2rmMetrW2br = Fradk2rmMetrOhmmWaat = A2prk2rmnwtnW2br = Fradk2rmMetrV2tt = hnrykgrmM3trOhmmscnd $ [d]{[aa]^2} = [k]{[v0][d]}^2 -10.1744595 | -10.1744595 -10.1744595 $ [k]{[He][a0][d]/[hB]}^2 -10.1744595 | -10.1744595 -10.1744595 $ 4[k]{[aa]^4}{[RK]}^2 -10.1744597 | -10.1744595 -10.1744595 $ [k]{[z0]^2}{[aa]}^2 = [k]{[E0]/[H0]}^2 -10.1744595 | -10.1744595 -10.1744595 $ {4([aa]^2)}/({[Jf]^2}[c^2][Me][a0][Pi]) -10.1744595 | -10.1744595 -10.1744595 $ [d]{[E0]^2}/{[c^2][B0]^2} -10.1744595 | -10.1744595 -10.1744595 $ {[Q0]^2}{[d]^2}/{[4Pi][Me][a0]} -10.1744593 | -10.1744595 -10.1744595 in Hnrymetr = a2prNwtn = FradmetrO2mm = FradmetrH2rys2nd $$ ({[aa]^2}[PL]/[k][PM])^.5 -10.1744595 * -10.1750278 -10.1750420 $$ [aa][PQ]/{[c][k][PM]} -10.1744595 * -10.1750280 -10.1750420 in f12dk12mMetr = kgrmWebr = CuulfradkgrmScnd [PM] - 7.6628219 * - 7.6622533 - 7.6622393 {[hB][c]/[G]}^.5 - 7.6628219 * - 7.6622538 - 7.6622395 {[aa]^2}[Me][Pf]/[2af] - 7.6628219 * - 7.6622540 - 7.6622394 [Me][a0][aa]/[PL] - 7.6628220 * - 7.6622537 - 7.6622394 {[PQ]^2}[z0]/{[c][PL]} - 7.6628220 * - 7.6622537 - 7.6622394 ([Q0]^2)[d]/{[4Pi][aa][PL]} - 7.6628218 * - 7.6622537 - 7.6622394 in Kgrm = C2ulm2trOhmmScnd = CuulScndTsla = C2ulfradm2trS2nd = C2ulHnrym2tr = A2prm2trOhmmScnd = Fradm2trW2br = FradM2trT2la $ [PQ][c]/[aa] - 7.6628219 | - 7.6628217 - 7.6628218 $ [PC][PL]/[aa] - 7.6628218 | - 7.6628218 - 7.6628219 in CuulMetrscnd = AmprMetr $$ [c^4][PL][k]/{[aa]^2} - 7.6628218 * - 7.6633900 - 7.6634043 in FradM4trs4nd [PL] -34.7909227 * -34.7914909 -34.7915052 {[hB][G]/[c^3]}^.5 -34.7909228 * -34.7914908 -34.7915051 [hB]/{[PM][c]} = [a0]([Me][aa]/[PM]) -34.7909227 * -34.7914913 -34.7915052 [G][PM]/[c^2] -34.7909228 * -34.7914903 -34.7915049 1/{[z0][Pf][k]} -34.7909227 * -34.7914906 -34.7915051 in Metr = fradMetrScndohmm $ [Me]{[aa]^3}/[PQ][2af] = [PQ][aa][d]/[c] -34.7909228 | -34.7909228 -34.7909227 $ [PM][aa]/[PC] -34.7909228 | -34.7909224 -34.7909226 $ [PM][aa]/{[PQ][Pf]} -34.7909227 | -34.7909221 -34.7909226 in amprKgrm = cuulKgrmScnd $$ [c^2][PQ]/{[PM][Pf][aa]} -34.7909227 * -34.7920592 -34.7920876 in CuulkgrmM2trscnd $$$ [PM][d]{[aa]^2}/[c^2] -34.7909228 * -34.7903542 -34.7903402 in HnryKgrmm3trS2nd [Pf] +43.2677434 * +43.2683113 +43.2683258 {[hB][G]/[c^5]}^-.5 +43.2677435 * +43.2683115 +43.2683258 [2af][Pp]/([p0][aa]) +43.2677434 * +43.2683117 +43.2683259 [2af][a0]/([PL][aa]) +43.2677434 * +43.2683116 +43.2683259 [2af][PM]/([Me]{[aa]^2}) +43.2677435 * +43.2683120 +43.2683259 [2af][PE]/[He] +43.2677434 * +43.2683120 +43.2683259 in Hrtz $ [PC][c]/{[aa][PM]} +43.2677435 | +43.2677431 +43.2677433 $ [PQ][c^3]/{[aa][hB]} +43.2677434 | +43.2677435 +43.2677434 in AmprkgrmMetrscnd = CuulM3trjuuls4nd $$ [PM][aa]/{[PQ][PL]} +43.2677434 * +43.2688802 +43.2689084 $$ [PQ][d][aa]/{[PL]^2} +43.2677433 * +43.2688798 +43.2689083 in cuulKgrmmetr = CuulHnrym3tr {[E0]/[H0]}^2 = {[v0][d]}^2 = {[z0][aa]}^2 + 0.8783918 | + 0.8783918 + 0.8783918 {([He][a0][d])/[hB]}^2 = {[aa]^2}[d]/[k] + 0.8783918 | + 0.8783918 + 0.8783918 4{[aa]^4}{[RK]}^2 + 0.8783916 | + 0.8783918 + 0.8783918 in O2mm = H2rys2nd = fradHnry = a2prC2ulf2ad $ [G]/[k] + 0.8783918 * + 0.8772557 + 0.8772271 $ [hB][c]/([k]{[PM]^2}) + 0.8783919 * + 0.8772547 + 0.8772268 $ {[PL]^3}{[Pf]^2}/{[PM][k]} + 0.8783919 * + 0.8772545 + 0.8772268 in C2ulf2adk2rmM2tr = fradk2rmM3trNwtn = fradkgrmM4trs2nd $$ {[c][G]/[aa]}^2 + 0.8783918 * + 0.8761196 + 0.8760623 in k2rmM8trs6nd [G][c^2][k] = [G]/[d] - 4.2736694 * - 4.2748054 - 4.2748341 [c^4][PL][k]/[PM] - 4.2736694 * - 4.2748061 - 4.2748343 {[PC]^2}{[PL]^2}/{[PM]^2} - 4.2736692 * - 4.2748064 - 4.2748343 in Fradk2rmM3trNwtns2nd = hnrykgrmM4trs2nd = A2prk2rmM2tr $ {[aa]^2} - 4.2736694 | - 4.2736693 - 4.2736693 is dimensionless $$ [d][PC]{[aa]^3}/[c^2] - 4.2736694 * - 4.2731011 - 4.2730869 in amprm2trNwtnS2nd = AmprHnrym3trS2nd [d] = 1/([c^2][k]) = {[z0]^2}[k] - 5.9007901 | - 5.9007901 - 5.9007901 in a2prNwtn = Hnrymetr $ [PQ]/([k][c][PM][aa]) - 5.9007901 * - 5.9013587 - 5.9013727 in CuulfradkgrmScnd $$ [G]/{[aa]^2} - 5.9007902 * - 5.9019262 - 5.9019549 in kgrmM3trs2nd [c] = [v0]/[aa] = [E0]/{[aa][d][H0]} + 8.4768207 | + 8.4768207 + 8.4768207 [aa][H0]/{[k][E0]} = [z0]/[d] + 8.4768207 | + 8.4768207 + 8.4768207 [PL][Pf] + 8.4768207 | + 8.4768204 + 8.4768207 [hB]/{[PL][PM]} + 8.4768207 | + 8.4768203 + 8.4768206 in Metrscnd = metrtslaVltt = AmprfradMetrvltt = hnryMetrOhmm $ [PM][aa]/[PQ] + 8.4768207 * + 8.4773893 + 8.4774032 in cuulKgrm $$ [PM]{[aa]^2}/({[PL]^4}{[Pf^3}[k]) + 8.4768206 * + 8.4779583 + 8.4779858 $$ {[aa]^2}/{[G][c][k]} + 8.4768207 * + 8.4779568 + 8.4779854 in fradKgrmm3trS3nd [Me][c^2] -13.0868697 | -13.0868697 -13.0868696 ([Q0]^2)[Ke]/({[aa]^2}[a0]) -13.0868695 | -13.0868697 -13.0868696 [Fe][a0]/{[aa]^2} = [He]/{[aa]^2} -13.0868696 | -13.0868697 -13.0868696 {[E0]^2}{[a0]^3][4Pi][k]/{[aa]^2} -13.0868697 | -13.0868697 -13.0868696 {[B0]^2}{[a0]^3}[4Pi]/[d] -13.0868697 | -13.0868697 -13.0868696 {[H0]^2}{[a0]^3][4Pi][d] -13.0868697 | -13.0868697 -13.0868696 [hB][c]/{[a0][aa]} -13.0868696 | -13.0868697 -13.0868696 {[PQ]^2}/{[a0][aa][k]} -13.0868697 | -13.0868697 -13.0868696 [PE][PL]/([a0][aa]) -13.0868696 | -13.0868693 -13.0868696 {[PM]^2}[G]/{[aa][a0]} -13.0868697 | -13.0868686 -13.0868693 [FBH]([PL]^2)/([aa][a0]) -13.0868696 | -13.0868697 -13.0868693 [PM]{[PL]^3}{[Pf]^2}/([aa][a0]) -13.0868696 | -13.0868699 -13.0868696 in Juul = C2ulfrad = NwtnMetr = FradV2tt = hnryM4trT2la $ {[PM]^1.5]{[PL]^.5}/([a0]{[k]^.5}) -13.0868697 * -13.0863009 -13.0862871 in f12dK15mm12r = KgrmmetrScndVltt = KgrmMetrTsla $$ {[PM]^2}[aa]/({[Pf]^2}{[PL]^2}[a0][k]) -13.0868697 * -13.0857320 -13.0857045 in fradK2rmm2trS2nd [PL]/{[PM][d]} = [G][k] -21.2273107 * -21.2284475 -21.2284757 [G][Me][a0]({[Jf][Pi]}^2)/[4Pi] -21.2273108 * -21.2284468 -21.2284754 {[PQ]^2}/{[PM]^2} -21.2273108 * -21.2284479 -21.2284758 in hnrykgrmM2tr = FradkgrmM2trs2nd = M4trs4ndv2tt = C2ulk2rm $ {[aa]^2}/[c^2] = {[aa]^2}[d][k] -21.2273108 | -21.2273108 -21.2273107 in m2trS2nd = FradHnrym2tr $$ [aa]({[k][PL]}^.5)/{[PM]^.5} -21.2273108 * -21.2278791 -21.2278932 in F12dk12m = CuulkgrmmetrScnd [c^2]/{[d][aa]} +24.9912662 | +24.9912662 +24.9912662 in hnryM3trs2nd = A2prkgrmMetr $ [PC] = {[k]([PL]^3)[PM]([Pf]^4)}^.5 +24.9912662 * +24.9918344 +24.9918486 $ {1/[PL]}{[hB][c]/[d]}^.5 +24.9912662 * +24.9918344 +24.9918486 $ [PQ][Pf] +24.9912661 * +24.9918341 +24.9918486 $ [PM][Pf]{[G][k]}^.5 +24.9912661 * +24.9918346 +24.9918488 $ ([G]{[PM]^2}/([d]{[PL]^2}))^.5 +24.9912661 * +24.9918349 +24.9918488 in Ampr = Cuulscnd = F12dK12mMetrs2nd = h12yK12mMetrscnd $$ [PM][aa]/[PL] +24.9912661 * +24.9924030 +24.9924312 $$ [c^2][aa]/[G] +24.9912661 * +24.9924023 +24.9924309 in Kgrmmetr [G]([PM]^2) -25.5001033 | -25.5001022 -25.5001029 [PM][PL][c^2] -25.5001032 | -25.5001028 -25.5001031 {[PL]^3}{[Pf]^2}[PM] -25.5001032 | -25.5001034 -25.5001032 {[PL]^2}{[PC]^2}[d] -25.5001031 | -25.5001031 -25.5001032 {[PQ]^2}/[k] -25.5001033 | -25.5001032 -25.5001032 ([Q0]^2)/{[4Pi][k][aa]} -25.5001031 | -25.5001032 -25.5001032 [hB][c] -25.5001032 | -25.5001032 -25.5001032 in KgrmM3trs2nd = C2ulfradMetr = A2prhnryMetr = JuulMetr $ [PQ][d][c][aa][PM] -25.5001033 * -25.4995346 -25.4995207 in CuulHnryKgrmscnd $$ [PC]{[PL]^2}[c^2]/[aa] -25.5001031 * -25.5006713 -25.5006856 in AmprM4trs2nd [G]/[c^2] = [G][d][k] -27.1281009 * -27.1292370 -27.1292656 [c^2]/[FBH] -27.1281008 * -27.1292372 -27.1292661 [PL]/[PM] -27.1281008 * -27.1292376 -27.1292658 [Me][a0][aa]/{[PM^2]} -27.1281009 * -27.1292380 -27.1292659 {[Q0]^2}[d]/([4Pi]{[PM]^2}[aa]) -27.1281008 * -27.1292380 -27.1292659 in kgrmMetr = k2rmmetrNwtnS2nd = C2ulHnryk2rmmetr $ [aa]/[PC] -27.1281009 * -27.1286691 -27.1286833 $ [PQ][d][aa]/{[PM][c]} -27.1281009 * -27.1286695 -27.1286834 in ampr = CuulHnrykgrmm2trScnd $$ [k]{[d]^2}{[aa]^2} = [d]{[aa]/[c]}^2 -27.1281008 | -27.1281009 -27.1281009 in FradH2rym3tr = Hnrym3trS2nd [PM][Pf] +35.6049215 * +35.6060580 +36.6060865 [c^3]/[G] +35.6049216 * +35.6060577 +36.6060863 [hB]/{[PL]^2} +35.6049215 * +35.6060579 +36.6060865 [FBH][d]/[z0] +35.6049215 * +35.6060579 +36.6060868 in Kgrmscnd = K2rmMetrnwtns3nd = Juulm2trScnd = HnrymetrNwtnohmm $ [PC][c]/[aa] +35.6049216 * +35.6054898 +36.6055040 in AmprMetrscnd $$ [aa]{[PM]^1.5}{[d]^.5}/{[PL]^1.5}) +35.6049215 * +35.6066267 +36.6066690 in KgrmmetrScndTsla {[PQ]^2} -36.5529546 | -36.5529545 -36.5529544 [k][c^2][PL][PM] -36.5529545 | -36.5529541 -36.5529544 [k][PM]{[PL]^3}{[Pf]^2} -36.5529545 | -36.5529547 -36.5529544 [[Q0]^2}/{[4Pi][aa]} -36.5529544 | -36.5529545 -36.5529544 [Me][a0][aa]/[d] -36.5529546 | -36.5529545 -36.5529544 [hB][c][k] -36.5529545 | -36.5529545 -36.5529544 [PL][PM]/[d] -36.5529545 | -36.5529541 -36.5529544 [G][k]{[PM]^2} -36.5529546 | -36.5529534 -36.5529541 in C2ul = FradJuul = hnryKgrmM2tr $ [PQ][PM][aa]/[c] -36.5529546 * -36.5523859 -36.5523719 in CuulKgrmmetrScnd $$ ([PM]^2}{[aa]^2}/[c^2] -36.5529546 * -36.5518174 -36.5511789 in K2rmm2trS2nd [Fe]/[Fg] = ([Q0]^2)[Ke]/([G][Me][Mp]) +39.3546349 * +39.3557711 +39.3557997 {[PQ]^2}[aa]/{[G][k][Me][Mp]} +39.3546349 * +39.3557711 +39.3557997 {[PQ]^2}[aa][PM][d]/{[Me][Mp][PL]} +39.3546348 * +39.3557717 +39.3557999 [aa]{[PM]^2}/{[Me][Mp]} +39.3546349 * +39.3557721 +39.3558000 ([aa]^2)[PM][a0]/([Mp][PL]) +39.3546349 * +39.3557717 +39.3557999 ([aa]^3)[PM][Pf]/([Mp][2af]) +39.3546348 * +39.3557714 +39.3557998 is dimensionless $ [PC][a0][aa]/[Mp] +39.3546349 * +39.3552032 +39.3552173 in AmprkgrmMetr $$ [c^4][a0][k]/[Mp] +39.3546349 | +39.3546350 +39.3546349 $$ {[PC]^2}{[PL]^2}/{[aa][Me][Mp]} +39.3546351 | +39.3546351 +39.3546350 $$ {[PQ]^2}[c^2]/{[aa][Me][Mp]} +39.3546349 | +39.3546350 +39.3546349 in FradkgrmM4trs4nd = A2prk2rmM2tr = C2ulk2rmM2trs2nd [PM][PL] = {[PQ]^2}[d] -42.4537446 | -42.4537442 -42.4537446 [hB]/[c] = [Me][Re]/[aa] = [Me][a0][aa] -42.4537446 | -42.4537446 -42.4537446 [aa][4Pi][k]{[B0]^2}{[a0]^4} -42.4537446 | -42.4537446 -42.4537446 [aa][Ke]{[Me^2}/({[B0]^2}{[a0]^2}) -42.4537447 | -42.4537446 -42.4537446 ([Q0]^2)[d]/([aa][4Pi]) -42.4537445 | -42.4537446 -42.4537446 [Jf][aa]{[Me]^2}/{4[k][B0]} -42.4537447 | -42.4537446 -42.4537446 4[k][aa]{[w0]^2}/[Pi] = 2[hB][RK][k][aa] -42.4537447 | -42.4537446 -42.4537446 in KgrmMetr = C2ulHnrymetr = FradM3trT2la = FradJuulmetrOhmmScnd $ {[PL]^2}[PC]/[aa] -42.4537445 * -42.4543127 -42.4543270 $ [c][PL][PQ]/[aa] -42.4537446 * -42.4543128 -42.4543270 in AmprM2tr $$ [c^4]{[PL]^2}[k]/{[aa]^2} -42.4537445 * -42.4548810 -42.4549094 in FradM5tr [G][Me]/([a0]{[v0]^2}) -42.6185437 * -42.6196798 -42.6197084 [G]{[B0]^2}[4Pi][k]/{[2af]^2} -42.6185437 * -42.6196798 -42.6197084 ([Me][Fg])/([Fe][Mp]) = [Fge]/[Fe] -42.6185437 * -42.6196798 -42.6197084 ([Me]^2)[G][4Pi][k]/([Q0]^2) -42.6185439 * -42.6196798 -42.6197084 {[Me]^2}/([aa]{[PM]^2}) -42.6185437 * -42.6196809 -42.6197087 [Me][c^2]/({[aa]^2}[FBH][a0]) -42.6185436 * -42.6196801 -42.6197087 [Me][PL]/([a0][PM]([aa]^2)) -42.6185436 * -42.6196805 -42.6197087 [Me][2af]/([PM][Pf]{[aa]^3}) -42.6185436 * -42.6196802 -42.6197086 ([PL]^2)/{([a0]^2)([aa]^3)} -42.6185435 * -42.6196801 -42.6197086 4[PL][B0][k]/({[aa]^2}[PM][Jf]) -42.6185436 * -42.6196805 -42.6197087 [Pf]{[PL]^3}/({[aa]^2}{[a0]^3}[2af]) -42.6185435 * -42.6196804 -42.6197086 [FBH] = [hB][c]/{[PL]^2} +44.0817422 * +44.0828786 +44.0829072 [G]{[PM]^2}/{[PL]^2} +44.0817421 * +44.0828797 +44.0829075 [PM][PL]{[Pf]^2} +44.0817422 * +44.0828784 +44.0829072 [PM][c^2]/[PL] +44.0817422 * +44.0828790 +44.0829072 [c][PM][Pf] +44.0817422 * +44.0828787 +44.0829072 [c^4]/[G] +44.0817423 * +44.0828784 +44.0829070 {[PC^2]}[d] +44.0817423 * +44.0828787 +44.0829072 {[PQ]^2}/([k]{[PL]^2}) +44.0817421 * +44.0828786 +44.0829072 in Nwtn = KgrmMetrs2nd = A2prHnrymetr = C2ulfradmetr $ {[PM]^1.5}[aa]/({[k]^.5}{[PL]^1.5}) +44.0817422 * +44.0834474 +44.0834897 in f12dK32mmetr = KgrmTsla $$ [PC][c^2]/[aa] +44.0817423 * +44.0823105 +44.0823247 in AmprM2trs2nd [A0]/[PA] = [4Pi]([a0]^2)/{[4Pi]([PL]^2)} +49.0290476 * +49.0301841 -49.0302126 [PM][Pf]/{[Me][2af]} +49.0290477 * +49.0301842 -49.0302126 [a0][Pf][aa]/([PL][2af]) +49.0290476 * +49.0301838 -49.0302126 [PE][PM]/{[He][Me]} +49.0290477 * +49.0301849 -49.0302128 {[Pp]^2}/{[p0]^2} +49.0290476 * +49.0301843 -49.0302128 [PM]/[Pf] -50.9305653 | -50.9305646 -50.9305652 [hB]/[c^2] = [Me]{[aa]^2}/[2af] -50.9305653 | -50.9305653 -50.9305653 in KgrmScnd = Juulm2trS3nd $ [PL][PQ]/[aa] -50.9305653 * -50.9311335 -50.9311477 in CuulMetr $$ [c^3]{[PL]^2}[k]/{[aa]^2} -50.9305652 * -50.9317017 -50.9317302 in FradM4trs3nd =================================++================================= CODATA 2010 G : 6.67384(80) e-11 6.67384 e-11 -10.1756242 PM : 2.17651(13) e-8 2.17651 e-8 - 7.6622393 PL : 1.616199(97) e-35 1.616199 e-35 -34.7915052 PT : 5.39106(32) e-44 5.39106 e-44 -43.2683258 CODATA 2006 G : 6.67428(67)e-11 6.67428e-11 -10.1755956 PM : 2.17644(11)e-08 2.17644e-08 - 7.6622533 PL : 1.616252(81)e-35 1.616252e-35 -34.7914909 PT : 5.39124(27)e-44 5.39124e-44 -43.2683113 CODATA 2002 G: 6.6742(10)e-11 6.6742e-11 -10.1756008 PM : 2.17645(16)e-08 2.17645e-08 - 7.6622513 PL : 1.61624(12)e-35 1.61624e-35 -34.7914941 PT : 5.39121(40)e-44 5.39121e-44 -43.2683138 CODATA 1998 G: 6.673(10)e-11 6.673e-11 -10.1756789 PM : 2.1767(16)e-08 2.1767e-08 - 7.6622014 PL : 1.6160(12)e-35 1.6160e-35 -34.7915586 PT : 5.3906(40)e-44 5.3906e-44 -43.2683629 CODATA 1986 G: 6.67259(85)e-11 6.67259e-11 -10.1757056 PM : 2.17671(14)e-08 2.17671e-08 - 7.6621994 PL : 1.61605(10)e-35 1.61605e-35 -34.7915452 PT : 5.39056(34)e-44 5.39056e-44 -43.2683661 =================================++=================================