User:LKreissig

This list of natural constants and astronomic measuring sizes ordered by corresponding areas utilizing Planck units specifies continued fraction expansions of the binary logarithm of A / (electron's Compton wavelength)² each with area A obtained by A = l² = c²t² = G² msun² / v4 = c4/a² = h²/(m²c²) = &#8730;(h / rho c) = hc²/P = h²c²/E² = hc/F = &#8730;(hc / p) with speed of light c, Planck constant h, Gravitational constant G and with lengths l, times t, velocities v, accelerations a, masses m, densities rho, powers P, energies E, forces F and pressures p. The binary logarithm of x is lim k&rarr;±0 (xk &#8210; 1) / (2k &#8210; 1). From v the square of the sun distance of an object circling around sun that would have orbital v is calculated. The negative part contains the more ordered isotope masses which appears parallel to direct polyomino definitions, so for completeness the not rotational symmetric trominos till hexominos are added that way in red, the continued fraction terms (the amount of them in parenthesis) of the square of the distance between its centroid (arithmetic mean) and its harmonic mean when placed in a complex plane with its centroid at center each in the positive part.  
 * &#8210;&#39;'150 3&#39;28 &#11044; E = 963.0733 kWh of a photon whose wavelength = &#8730;(2 G h / c³) which is the Schwarzschild radius of the mass E/c² = &#8730;(hc / (2 G)) = &#8730;(pi) × Planck mass = 38 576 ng
 * &#8210;&#39;86 1&#39;17 1&#39;30 &#11044; (E = 1 Joule, SI unit of energy)
 * &#8210;&#39;65'27 &#11044; P_sun = 4 &pi; AU² × solar constant = (503 600 nJ)² / h
 * &#8210;&#39;37 211124543 &#11044; m (of a) 90Th 232 (atom)
 * &#8210;&#39;37'12 1219 &#11044; m 83Bi 209
 * &#8210;&#39;36 1914 &#11044; m 79Au 197
 * &#8210;&#39;28&#39;'129 &#11044; m 4Be 9
 * &#8210;&#39;25 111&#39;'143 1&#39;26 &#11044; m 2He 4
 * &#8210;&#39;24 1511136 &#11044; m 1H 3 tritium
 * &#8210;&#39;24 151113&#39;26 &#11044; m 2He 3
 * &#8210;&#39;23 1251&#39;32 5 &#11044; m 1H 2 deuterium
 * &#8210;&#39;23 118 &#11044; m tauon
 * &#8210;&#39;21 124111&#39;18 63 &#11044; m neutron, &darr; &#8731;(h^4 / (2 G c² m^5)) = 10 682 &mu;m
 * &#8210;&#39;21 1253134&#39;16 &#11044; m 1H 1 protium
 * &#8210;&#39;21 125121&#39;19 16 &#11044; m proton, &darr; &#8731;(h^4 / (2 G c² m^5)) = 10 707 &mu;m
 * &#8210;&#39;15 21111664 &#11044; m muon
 * &#8210;418&#39;32 113 &#11044; (F = 1 Newton, SI unit of force, and: E = &#8730;(hc × 1 Newton), P = c × 1 Newton)
 * &#8210;324 &#11044; 5.09 &#8210; (13)
 * &#8210;3224 &#11044; 6.28 &#8210; (16)
 * &#8210;2133 &#11044; E of &gamma; photon at 28Ni 60* &rarr; 28Ni 60 + &gamma;
 * &#8210;21282114 &#11044; m_neutron &#8210; m_proton
 * &#8210;2211&#39;20 &#11044; E of photon at 27Co 60 &rarr; 28Ni 60* + e&#8315; + ve + &gamma;
 * &#8210;276 &#11044; 6.27 | (17)
 * &#8210;274 &#11044; 6.26 (6)
 * &#8210;2&#39;15 3 &#11044; 6.25 &#8210; (2)
 * &#8210;118 &#11044; 5.08 \ (12)
 * &#8210;1173 &#11044; 6.24 (5)
 * &#8210;11312 &#11044; 6.23 &#8210; (16)
 * &#8210;1134 &#11044; 6.22 (10)
 * &#8210;1118 &#11044; 6.21 (6)
 * &#8210;13&#39;15 &#11044; 6.20 (21)
 * &#8210;138 &#11044; 6.19 \ (3)
 * &#8210;137 &#11044; 5.07 \ (10)
 * &#8210;1363 &#11044; 6.18 (16)
 * &#8210;134 &#11044; 5.06 (1)
 * &#8210;1332 &#11044; 6.17 &#8210; (8)
 * &#8210;13223 &#11044; 6.16 (21)
 * &#8210;1323 &#11044; 5.05 (14)
 * &#8210;1324 &#11044; 6.15 (15)
 * &#8210;1327 &#11044; 6.14 (18)
 * &#8210;132 &#11044; 4.02 &#8210; (10)
 * &#8210;13112 &#11044; 6.13 (9)
 * &#8210;1312 &#11044; 5.04 (4)
 * &#8210;1314 &#11044; 6.12 (4)
 * &#8210;14 &#11044; 3.01 \ (4) (The tromino #1 defined by the continued fraction terms' binary expansions, the last decreased by 1, written line by line, with possible symmetry axis |, /, &#8210; or \. This rational number becomes either greater or less than 1 by mirroring or rotating.)
 * &#8210;158 &#11044; 6.11 (16)
 * &#8210;177 &#11044; 6.10 (17)
 * &#8210;176 &#11044; 6.09 (16)
 * &#8210;1745 &#11044; 6.08 (17)
 * &#8210;174 &#11044; 6.07 (17)
 * &#8210;173 &#11044; 5.03 (13)
 * &#8210;1723 &#11044; 6.06 (16)
 * &#8210;172 &#11044; 5.02 &#8210; (8)
 * &#8210;1712 &#11044; 6.05 (13)
 * &#8210;18 &#11044; 4.01 (5)
 * &#8210;1&#39;15 5 &#11044; 6.04 (12)
 * &#8210;1&#39;15 3 &#11044; 6.03 (18)
 * &#8210;1&#39;15 2 &#11044; 6.02 &#8210; (1)
 * &#8210;1&#39;16 &#11044; 5.01 (9)
 * &#8210;1&#39;32 &#11044; 6.01 (17)
 * 0 &#11044; m electron, one of the most precisely measured natural constants, this m c² / electron's Compton wavelength = m² c³/h = 33 743 029 nN, rho = m^4 c³ / h³ = 63 775 g/l, &darr; volume with this rho and whose Schwarzschild radius is h/(mc): &#8731;(hc/(2 G m rho)) = &#8731;(h^4 / (2 G c² m^5)) = 2948 m
 * 0&#39;'&#39;'13309 &#11044; m of 1H 1 &#8210; m of proton
 * 01&#39;14 1'10 1&#39;15 2&#39;19 26114117 &#11044; 6.27 | (17)
 * 1&#39;13 141116'10 111&#39;11 12632 &#11044; 6.03 (18)
 * 13&#39;19 1163532122513 &#11044; 6.23 &#8210; (16)
 * 1215121621432 &#11044; 5.03 (13)
 * 121211&#39;20 12121&#39;13 225&#39;11 &#11044; 6.10 (17)
 * 11112&#39;24 1112 &#11044; 4.02 &#8210; (10)
 * 25115283&#39;'175 &#11044; 5.01 (9)
 * 2111&#39;13 22811411162 &#11044; 6.09 (16)
 * 21&#39;72 112'10 17 &#11044; 6.13 (9)
 * 21&#39;'392 11&#39;22 &#11044; rho 1 kg/l = 1 g/cm³
 * 3&#39;32 442&#39;28 &#11044; 6.26 (6)
 * 3111'10 &#11044; 4.01 (5)
 * 3142217343 &#11044; 5.07 \ (10)
 * 412324115411'17 &#11044; 5.09 &#8210; (13)
 * 5114 &#11044; 3.01 \ (4)
 * 515 &#11044; x-ray photon K&beta;1 (3p &rarr; 1s) emitted by 74W x-ray tube electron target anode
 * 681112312213&#39;70 111&#39;65 &#11044; 6.08 (17)
 * 6412 &#11044; photon K&alpha;1 (2p &rarr; 1s) of 74W anode
 * 62&#39;11 11111&#39;44 111531812115 &#11044; 6.16 (21)
 * 79 &#11044; 6.25 &#8210; (2)
 * 71321&#39;19 &#11044; 6.21 (6)
 * 8122 &#11044; photon K&beta;1 of 47Ag anode
 * 8172 &#11044; 2 AU × solar constant = 407 TW/m, &#8731;(hc² / (2 AU × solar const.)) = 52.7 pm
 * 9&#39;21 &#11044; photon K&alpha;1 of 47Ag anode
 * 93113194&#39;87'12 &#11044; 6.22 (10)
 * 922 &#11044; photon K&beta;1 of 42Mo anode
 * 912 &#11044; photon K&alpha;1 of 42Mo anode
 * '10 6218111&#39;'302 1211215 &#11044; 6.06 (16)
 * '10 11233'10 1731222312 &#11044; 6.01 (17)
 * &#39;11 12 &#11044; photon K&beta;1 of 29Cu anode
 * &#39;11 16112414212221'10 21215 &#11044; 6.20 (21)
 * &#39;11 1&#39;50 &#11044; photon K&alpha;1 of 29Cu anode
 * &#39;12'32 1&#39;44'15 &#11044; 6.24 (5)
 * &#39;12 23112126212 &#11044; 6.04 (12)
 * &#39;13 2&#39;22 77334112&#39;56 3122 &#11044; 6.28 &#8210; (16)
 * &#39;14 82 &#11044; &#8309;&#8730;(2 G h V_earth / c³) = 324 pm
 * &#39;15 322 &#11044; 5.04 (4)
 * &#39;15 15221131113412&#39;37 13 &#11044; 6.14 (18)
 * &#39;16 211&#39;12 5322233 &#11044; 5.08 \ (12)
 * &#39;18 1111619312113 &#11044; 5.05 (14)
 * &#39;19 6&#39;20 3 &#11044; 6.12 (4)
 * &#39;21 22&#39;60 2113411111124 &#11044; 6.07 (17)
 * &#39;23 3122144 &#11044; (P 1 Watt, SI unit of power, and: p = (1 Watt)² / (h c³) = 56 012 101 Pa)
 * &#39;23 2132&#39;'270 42114&#39;24 222 &#11044; 6.15 (15)
 * &#39;23 2&#39;11 415212221&#39;'103 &#11044; 6.05 (13)
 * &#39;23 191&#39;19 11&#39;37 11&#39;40 11512 &#11044; 6.11 (16)
 * &#39;27 1412 &#11044; p Earth surface = 1 bar
 * &#39;30 11&#39;18 &#11044; H5&rarr;1 (extreme UV spectral line of H)
 * &#39;30 112 &#11044; H4&rarr;1
 * &#39;30 1213 &#11044; H3&rarr;1 (UVC wavelength)
 * &#39;31 42 &#11044; H2&rarr;1 (H spectral line at innermost orbit change)
 * &#39;33 1114124&#39;12 &#11044; &#8730;(Cs hyperfine structure × e&#8315; Compton) (border between UVB and UVC wavelengths)
 * &#39;34 1813'10 &#11044; H5&rarr;2 (H &gamma;, blue)
 * &#39;35 616 &#11044; blue light of a frequency doubled Nd-doped Y-Al-garnet laser (secondary line)
 * &#39;35 425'10 &#11044; H4&rarr;2 (H &beta;)
 * &#39;35 2&#39;15 &#11044; green light of a frequency doubled 60Nd-doped 39Y-13Al-garnet laser
 * &#39;35 132123 &#11044; 2He (yellow)
 * &#39;36'11'15 &#11044; H3&rarr;2 (H &alpha;, red)
 * &#39;36 7622'10 &#11044; (p 1 Pascal = 1 N/m², SI unit of pressure)
 * &#39;36 4 &#11044; ruby laser red
 * &#39;36 314 &#11044; G m_ceres
 * &#39;37 3133 &#11044; Psun/(4&pi; c rsun²) = 210 mPa, &#8308;&#8730;(4&pi; h c² rsun² / Psun) = 986 nm
 * &#39;37 2&#39;15 &#11044; Nd doped Y-Al-garnet laser infrared
 * &#39;38'44 &#11044; H5&rarr;3 infrared spectral line
 * &#39;39 82 &#11044; H4&rarr;3 spectral line
 * &#39;40 &#11044; 5.06 (1)
 * &#39;44 114 &#11044; G m_Eris
 * &#39;45'70 &#11044; p Solar constant at earth orbit / c = 4539 nPa
 * &#39;47 11 &#11044; G m_(Jupiter moon Europa)
 * &#39;48 152 &#11044; G m_moon
 * &#39;50 55 &#11044; T1/2 (mean lifetime) of a &tau; lepton
 * &#39;51 11151122225111&#39;21 &#11044; 6.18 (16)
 * &#39;53 5115 &#11044; G m_mercury
 * &#39;55&#39;10 7 &#11044; G m_mars
 * &#39;56 2&#39;18 1611&#39;15 &#11044; 5.02 &#8210; (8)
 * &#39;60 1&#39;17 &#11044; G m_venus
 * &#39;61 116 &#11044; G m_earth
 * &#39;67 322186&#39;40 &#11044; 55Cs hyperfine structure wavelength
 * &#39;72 1271612&#39;'118 &#11044; H main microwave line = 21.106114 cm = l, 6.33392 fW/m = h c² l&#8315;³
 * &#39;74 128 &#11044; G m_saturn
 * &#39;77 51&#39;12 11913 &#11044; (1 m, SI basic unit of length)
 * &#39;78 6313 &#11044; G m_jupiter
 * &#39;85 8&#39;11 &#11044; &#8309;&#8730;(2 G h (T1/2 of 92U 235)³) = 15 752 mm &#11044; (704 Mio. years)
 * &#39;88 3'10 &#11044; &#8309;&#8730;(2 G h (T1/2 of 92U 238)³) = 47 738 mm &#11044; (4 467 904 570 years)
 * &#39;88 18 &#11044; 6.19 \ (3)
 * &#39;90 33&#39;70 &#11044; &#8309;&#8730;(2 G h (T1/2 of 90Th 232)³) = 94 727 mm &#11044; (14 000 Mio. years)
 * &#39;95 1811325 &#11044; T1/2 of a muon
 * &#39;98 424 &#11044; G m_sun = 4 &pi;² AU³ / year² = 1476 m × c²
 * &#39;'112 14124 &#11044; &#8210; AItov  (electrons's magnetic moment A×I ) = 23 884 389 m/s (&larr; AItov = me c h&#8315;&#185; × 1 Coulomb&#8315;&#185; eV&#8315;&#185; J = 2 572 428 / (pm × Picocoulomb), multiplying with a magnetic moment yields its basic velocity when viewing its defining electric charge as electrons' mass energy)
 * &#39;'118 11115312111&#39;25 13112 &#11044; Pulse wavelength of PSR J0437-4715 &#8776; 1726 km
 * &#39;'122 21114 &#11044; r_(earth at equator)
 * &#39;'126 14&#39;12 &#11044; &#8309;&#8730;(2 G h (T1/2 of 83Bi 209)³) = 29 560 km &#11044; (201 × 1017 years)
 * &#39;'133 2&#39;19 116 &#11044; (1 s, SI basic unit of time, 299 792 458 m)
 * &#39;'135 1&#39;11 &#11044; r_sun = 695 508 km
 * &#39;'138'14 1&#39;16 &#11044; venus orbit ellipse focal points distance
 * &#39;'140 12112 &#11044; &#8730;(G m_sun / a_EarthSurface) = 3 678 000 km
 * &#39;'141 11115&#39;25 &#11044; earth orbit (ellipse) foci dist. = 4 999 627 km
 * &#39;'146 81&#39;'343 &#11044; mercury orbit foci dist.
 * &#39;'147 1312 &#11044; mars orbit foci dist.
 * &#39;'148 12&#39;13 &#11044; mean mercury&#8210;sun distance
 * &#39;'149 233 &#11044; jupiter orbit foci dist.
 * &#39;'149 11&#39;40 &#11044; neptun orbit foci dist.
 * &#39;'149 1951&#39;14 &#11044;  AItov  (magnetic moment A×I of atomic nucleus of tritium, 1H 3)
 * &#39;'150 31116 &#11044;  AItov  (proton's magnetic moment A×I ) = 36 287 m/s
 * &#39;'150 2&#39;11 32 &#11044; mean venus&#8210;sun distance, v = 35 021 m/s
 * &#39;'151 222112&#39;16 &#11044; 1 AU, large halfaxis of earth orbit around sun, v = 29 785 m/s
 * &#39;'151 152253 &#11044; &#8210; AItov  (magnetic moment A×I of atomic nucleus of isotope 2He 3) = 27 643 764 mm/s
 * &#39;'151 11&#39;36 &#11044; saturn orbit foci dist.
 * &#39;'152 252123 &#11044; &#8210; AItov  (neutron's magnetic moment A×I ) = 24 855.7 m/s
 * &#39;'152 111245 &#11044; mean mars&#8210;sun dist.
 * &#39;'153'20 &#11044; T1/2 of free neutron
 * &#39;'153 71&#39;14 &#11044; uranus orbit foci dist.
 * &#39;'156 51462 &#11044; mean jupiter&#8210;sun dist.
 * &#39;'157'11 334 &#11044;  AItov  (magnetic moment A×I of deuterium, 1H 2)
 * &#39;'157 1&#39;11 1136 &#11044; mean saturn&#8210;sun dist.
 * &#39;'158 4511112 &#11044;  AItov  (magnetic moment A×I of isotope 6C 13)
 * &#39;'159 1&#39;15 6254 &#11044; mean uranus&#8210;sun dist.
 * &#39;'161 43112'10 &#11044; mean neptun&#8210;sun dist.
 * &#39;'183 4 &#11044; a Earth surface
 * &#39;'187 11&#39;12 &#11044; Sun&#8210;Alpha centauri distance
 * &#39;'828'16 11&#39;28 714 &#11044; 6.17 &#8210; (8)