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) = √(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 (xk ‒ 1) / (2k ‒ 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
‒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⁻ + ve + 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 Kβ1 (3p → 1s) emitted by 74W x-ray tube electron target anode
681112312213'70 111'65 ⬤ 6.08 (17)
6412 ⬤ photon Kα1 (2p → 1s) of 74W anode
62'11 11111'44 111531812115 ⬤ 6.16 (21)
79 ⬤ 6.25 ‒ (2)
71321'19 ⬤ 6.21 (6)
8122 ⬤ photon Kβ1 of 47Ag anode
8172 ⬤ 2 AU × solar constant = 407 TW/m, ∛(hc² / (2 AU × solar const.)) = 52.7 pm
9'21 ⬤ photon Kα1 of 47Ag anode
93113194'87'12 ⬤ 6.22 (10)
922 ⬤ photon Kβ1 of 42Mo anode
912 ⬤ photon Kα1 of 42Mo anode
'10 6218111''302 1211215 ⬤ 6.06 (16)
'10 11233'10 1731222312 ⬤ 6.01 (17)
'11 12 ⬤ photon Kβ1 of 29Cu anode
'11 16112414212221'10 21215 ⬤ 6.20 (21)
'11 1'50 ⬤ photon Kα1 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 ⬤ Psun/(4π c rsun²) = 210 mPa, ⁴√(4π h c² rsun² / Psun) = 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
'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 (T1/2 of 92U 235)³) = 15 752 mm ⬤ (704 Mio. years)
'88 3'10 ⬤ ⁵√(2 G h (T1/2 of 92U 238)³) = 47 738 mm ⬤ (4 467 904 570 years)
'88 18 ⬤ 6.19 \ (3)
'90 33'70 ⬤ ⁵√(2 G h (T1/2 of 90Th 232)³) = 94 727 mm ⬤ (14 000 Mio. years)
'95 1811325 ⬤ T1/2 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 = me 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 (T1/2 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)