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 m_sun² / v⁴ = c⁴/a² = h²/(m²c²) = √(h / rho c) = hc²/P = h²c²/E² = hc/F = √(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→±0 (x^k ‒ 1) / (2^k ‒ 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.

‒''150 3'28 ⬤ E = 963.0733 kWh of a photon whose wavelength = √(2 G h / c³) which is the Schwarzschild radius of the mass E/c² = √(hc / (2 G)) = √(pi) × Planck mass = 38 576 ng
‒'86 1'17 1'30 ⬤ (E = 1 Joule, SI unit of energy)
‒'65'27 ⬤ P_sun = 4 π AU² × solar constant = (503 600 nJ)² / h
‒'37 211124543 ⬤ m (of a) ₉₀Th 232 (atom)
‒'37'12 1219 ⬤ m ₈₃Bi 209
‒'36 1914 ⬤ m ₇₉Au 197
‒'28''129 ⬤ m ₄Be 9
‒'25 111''143 1'26 ⬤ m ₂He 4
‒'24 1511136 ⬤ m ₁H 3 tritium
‒'24 151113'26 ⬤ m ₂He 3
‒'23 1251'32 5 ⬤ m ₁H 2 deuterium
‒'23 118 ⬤ m tauon
‒'21 124111'18 63 ⬤ m neutron, ↓ ∛(h^4 / (2 G c² m^5)) = 10 682 μm
‒'21 1253134'16 ⬤ m ₁H 1 protium
‒'21 125121'19 16 ⬤ m proton, ↓ ∛(h^4 / (2 G c² m^5)) = 10 707 μm
‒'15 21111664 ⬤ m muon
‒418'32 113 ⬤ (F = 1 Newton, SI unit of force, and: E = √(hc × 1 Newton), P = c × 1 Newton)
‒324 ⬤ 5.09 ‒ (13)

‒3224 ⬤ 6.28 ‒ (16)
‒2133 ⬤ E of γ photon at ₂₈Ni 60* → ₂₈Ni 60 + γ
‒21282114 ⬤ m_neutron ‒ m_proton
‒2211'20 ⬤ E of photon at ₂₇Co 60 → ₂₈Ni 60* + e⁻ + v_e + γ
‒276 ⬤ 6.27 | (17)

‒274 ⬤ 6.26 (6)

‒2'15 3 ⬤ 6.25 ‒ (2)

‒118 ⬤ 5.08 \ (12)

‒1173 ⬤ 6.24 (5)

‒11312 ⬤ 6.23 ‒ (16)

‒1134 ⬤ 6.22 (10)

‒1118 ⬤ 6.21 (6)

‒13'15 ⬤ 6.20 (21)

‒138 ⬤ 6.19 \ (3)

‒137 ⬤ 5.07 \ (10)

‒1363 ⬤ 6.18 (16)

‒134 ⬤ 5.06 (1)

‒1332 ⬤ 6.17 ‒ (8)

‒13223 ⬤ 6.16 (21)

‒1323 ⬤ 5.05 (14)

‒1324 ⬤ 6.15 (15)

‒1327 ⬤ 6.14 (18)

‒132 ⬤ 4.02 ‒ (10)

‒13112 ⬤ 6.13 (9)

‒1312 ⬤ 5.04 (4)

‒1314 ⬤ 6.12 (4)

‒14 ⬤ 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 |, /, ‒ or \. This rational number becomes either greater or less than 1 by mirroring or rotating.)
‒158 ⬤ 6.11 (16)

‒177 ⬤ 6.10 (17)

‒176 ⬤ 6.09 (16)

‒1745 ⬤ 6.08 (17)

‒174 ⬤ 6.07 (17)

‒173 ⬤ 5.03 (13)

‒1723 ⬤ 6.06 (16)

‒172 ⬤ 5.02 ‒ (8)

‒1712 ⬤ 6.05 (13)

‒18 ⬤ 4.01 (5)

‒1'15 5 ⬤ 6.04 (12)

‒1'15 3 ⬤ 6.03 (18)

‒1'15 2 ⬤ 6.02 ‒ (1)

‒1'16 ⬤ 5.01 (9)

‒1'32 ⬤ 6.01 (17)

0 ⬤ 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, ↓ volume with this rho and whose Schwarzschild radius is h/(mc): ∛(hc/(2 G m rho)) = ∛(h^4 / (2 G c² m^5)) = 2948 m

0''''13309 ⬤ m of ₁H 1 ‒ m of proton
01'14 1'10 1'15 2'19 26114117 ⬤ 6.27 | (17)

1'13 141116'10 111'11 12632 ⬤ 6.03 (18)

13'19 1163532122513 ⬤ 6.23 ‒ (16)

1215121621432 ⬤ 5.03 (13)

121211'20 12121'13 225'11 ⬤ 6.10 (17)

11112'24 1112 ⬤ 4.02 ‒ (10)

25115283''175 ⬤ 5.01 (9)

2111'13 22811411162 ⬤ 6.09 (16)

21'72 112'10 17 ⬤ 6.13 (9)
21''392 11'22 ⬤ rho 1 kg/l = 1 g/cm³
3'32 442'28 ⬤ 6.26 (6)

3111'10 ⬤ 4.01 (5)

3142217343 ⬤ 5.07 \ (10)

412324115411'17 ⬤ 5.09 ‒ (13)

5114 ⬤ 3.01 \ (4)
515 ⬤ x-ray photon K_β1 (3p → 1s) emitted by ₇₄W x-ray tube electron target anode
681112312213'70 111'65 ⬤ 6.08 (17)
6412 ⬤ photon K_α1 (2p → 1s) of ₇₄W anode
62'11 11111'44 111531812115 ⬤ 6.16 (21)

79 ⬤ 6.25 ‒ (2)

71321'19 ⬤ 6.21 (6)
8122 ⬤ photon K_β1 of ₄₇Ag anode
8172 ⬤ 2 AU × solar constant = 407 TW/m, ∛(hc² / (2 AU × solar const.)) = 52.7 pm
9'21 ⬤ photon K_α1 of ₄₇Ag anode
93113194'87'12 ⬤ 6.22 (10)
922 ⬤ photon K_β1 of ₄₂Mo anode
912 ⬤ photon K_α1 of ₄₂Mo anode
'10 6218111''302 1211215 ⬤ 6.06 (16)

'10 11233'10 1731222312 ⬤ 6.01 (17)
'11 12 ⬤ photon K_β1 of ₂₉Cu anode
'11 16112414212221'10 21215 ⬤ 6.20 (21)
'11 1'50 ⬤ photon K_α1 of ₂₉Cu anode
'12'32 1'44'15 ⬤ 6.24 (5)

'12 23112126212 ⬤ 6.04 (12)

'13 2'22 77334112'56 3122 ⬤ 6.28 ‒ (16)
'14 82 ⬤ ⁵√(2 G h V_earth / c³) = 324 pm
'15 322 ⬤ 5.04 (4)

'15 15221131113412'37 13 ⬤ 6.14 (18)

'16 211'12 5322233 ⬤ 5.08 \ (12)

'18 1111619312113 ⬤ 5.05 (14)

'19 6'20 3 ⬤ 6.12 (4)

'21 22'60 2113411111124 ⬤ 6.07 (17)
'23 3122144 ⬤ (P 1 Watt, SI unit of power, and: p = (1 Watt)² / (h c³) = 56 012 101 Pa)
'23 2132''270 42114'24 222 ⬤ 6.15 (15)

'23 2'11 415212221''103 ⬤ 6.05 (13)

'23 191'19 11'37 11'40 11512 ⬤ 6.11 (16)
'27 1412 ⬤ p Earth surface = 1 bar
'30 11'18 ⬤ H5→1 (extreme UV spectral line of H)
'30 112 ⬤ H4→1
'30 1213 ⬤ H3→1 (UVC wavelength)
'31 42 ⬤ H2→1 (H spectral line at innermost orbit change)
'33 1114124'12 ⬤ √(Cs hyperfine structure × e⁻ Compton) (border between UVB and UVC wavelengths)
'34 1813'10 ⬤ H5→2 (H γ, blue)
'35 616 ⬤ blue light of a frequency doubled Nd-doped Y-Al-garnet laser (secondary line)
'35 425'10 ⬤ H4→2 (H β)
'35 2'15 ⬤ green light of a frequency doubled ₆₀Nd-doped ₃₉Y-₁₃Al-garnet laser
'35 132123 ⬤ ₂He (yellow)
'36'11'15 ⬤ H3→2 (H α, red)
'36 7622'10 ⬤ (p 1 Pascal = 1 N/m², SI unit of pressure)
'36 4 ⬤ ruby laser red
'36 314 ⬤ G m_ceres
'37 3133 ⬤ P_sun/(4π c r_sun²) = 210 mPa, ⁴√(4π h c² r_sun² / P_sun) = 986 nm
'37 2'15 ⬤ Nd doped Y-Al-garnet laser infrared
'38'44 ⬤ H5→3 infrared spectral line
'39 82 ⬤ H4→3 spectral line
'40 ⬤ 5.06 (1)
'44 114 ⬤ G m_Eris
'45'70 ⬤ p Solar constant at earth orbit / c = 4539 nPa
'47 11 ⬤ G m_(Jupiter moon Europa)
'48 152 ⬤ G m_moon
'50 55 ⬤ T_1/2 (mean lifetime) of a τ lepton
'51 11151122225111'21 ⬤ 6.18 (16)
'53 5115 ⬤ G m_mercury
'55'10 7 ⬤ G m_mars
'56 2'18 1611'15 ⬤ 5.02 ‒ (8)
'60 1'17 ⬤ G m_venus
'61 116 ⬤ G m_earth
'67 322186'40 ⬤ ₅₅Cs hyperfine structure wavelength
'72 1271612''118 ⬤ H main microwave line = 21.106114 cm = l, 6.33392 fW/m = h c² l⁻³
'74 128 ⬤ G m_saturn
'77 51'12 11913 ⬤ (1 m, SI basic unit of length)
'78 6313 ⬤ G m_jupiter
'85 8'11 ⬤ ⁵√(2 G h (T_1/2 of ₉₂U 235)³) = 15 752 mm ⬤ (704 Mio. years)
'88 3'10 ⬤ ⁵√(2 G h (T_1/2 of ₉₂U 238)³) = 47 738 mm ⬤ (4 467 904 570 years)
'88 18 ⬤ 6.19 \ (3)
'90 33'70 ⬤ ⁵√(2 G h (T_1/2 of ₉₀Th 232)³) = 94 727 mm ⬤ (14 000 Mio. years)
'95 1811325 ⬤ T_1/2 of a muon
'98 424 ⬤ G m_sun = 4 π² AU³ / year² = 1476 m × c²
''112 14124 ⬤ ‒AItov (electrons's magnetic moment A×I) = 23 884 389 m/s (← AItov = m_e c h⁻¹ × 1 Coulomb⁻¹ eV⁻¹ 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)
''118 11115312111'25 13112 ⬤ Pulse wavelength of PSR J0437-4715 ≈ 1726 km
''122 21114 ⬤ r_(earth at equator)
''126 14'12 ⬤ ⁵√(2 G h (T_1/2 of ₈₃Bi 209)³) = 29 560 km ⬤ (201 × 10¹⁷ years)
''133 2'19 116 ⬤ (1 s, SI basic unit of time, 299 792 458 m)
''135 1'11 ⬤ r_sun = 695 508 km
''138'14 1'16 ⬤ venus orbit ellipse focal points distance
''140 12112 ⬤ √(G m_sun / a_EarthSurface) = 3 678 000 km
''141 11115'25 ⬤ earth orbit (ellipse) foci dist. = 4 999 627 km
''146 81''343 ⬤ mercury orbit foci dist.
''147 1312 ⬤ mars orbit foci dist.
''148 12'13 ⬤ mean mercury‒sun distance
''149 233 ⬤ jupiter orbit foci dist.
''149 11'40 ⬤ neptun orbit foci dist.
''149 1951'14 ⬤ AItov (magnetic moment A×I of atomic nucleus of tritium, ₁H 3)
''150 31116 ⬤ AItov (proton's magnetic moment A×I) = 36 287 m/s
''150 2'11 32 ⬤ mean venus‒sun distance, v = 35 021 m/s
''151 222112'16 ⬤ 1 AU, large halfaxis of earth orbit around sun, v = 29 785 m/s
''151 152253 ⬤ ‒AItov (magnetic moment A×I of atomic nucleus of isotope ₂He 3) = 27 643 764 mm/s
''151 11'36 ⬤ saturn orbit foci dist.
''152 252123 ⬤ ‒AItov (neutron's magnetic moment A×I) = 24 855.7 m/s
''152 111245 ⬤ mean mars‒sun dist.
''153'20 ⬤ T_1/2 of free neutron
''153 71'14 ⬤ uranus orbit foci dist.
''156 51462 ⬤ mean jupiter‒sun dist.
''157'11 334 ⬤ AItov (magnetic moment A×I of deuterium, ₁H 2)
''157 1'11 1136 ⬤ mean saturn‒sun dist.
''158 4511112 ⬤ AItov (magnetic moment A×I of isotope ₆C 13)
''159 1'15 6254 ⬤ mean uranus‒sun dist.
''161 43112'10 ⬤ mean neptun‒sun dist.
''183 4 ⬤ a Earth surface
''187 11'12 ⬤ Sun‒Alpha centauri distance
''828'16 11'28 714 ⬤ 6.17 ‒ (8)

Category:Physics \| Category:Astronomy \| Category:Polyforms