Bode.txt

This document was meant to be a reply to a Wikipedia talk page post but took months to compile that I lost track of when it should be completed:


Titus -> Titius
it's -> its
where -> were
Saturn -> Saturn,
Learn how to spell.

Bode's law merely finds where a lone heavier body—thus planèt, planètoid (Ceres, Vesta), comètoid (Pluto, Eris, Haumea), comèt (Orcus, Halley's), or a set of these—in 1:2 harmonic equilibrium may last in a solar sýstem of infinite span, infinite mass, and smooth thickness.  It is a /model/ or toy theory good for the range wherein it applies, and is not "refuted" by outside findings.  Neither are Madelung's rule http://en.wikipedia.org/wiki/Electronic_configuration#Aufbau_principle_and_Madelung_rule (good in infinite room and celerity) or Golden Ratio refuted as "pseudo-science" if a few elements are off stead.  It was you who presume it's a relationship between all planèts; Titius wrote of his law to tell the ranges whereat roomhead was /not empty/.  And below is the full list of Titius-Bode ranges and the Sun's heaviest bodies, where you can see every stow fits very well into something!

By the way they, and you, forgot to put in the error or spread every time the range is twifolded: ·4±·05 + ·3±·05 2^m:

(law's range AU) body: range AU, weiht kg, length yr
(0) next Orion-Cygnus Arm Sun: ·0046492, 1·989E30,
(·4±·05) Mercury: ·387098, 3·3011E23, ·240846
(·7±·1) Venus: ·723332, 4·8675E24, ·615198
(1·0±·15) Earth: 1·00000102, 5·97237E24, 1·00001748096
          (3200 Phaethon: 1·271205253, <, 1·43)
(1·6±·25) Mars: 1·523679, 6·4171E23, 1·8808
          (2 comèts)
(2·8±·45) Vesta: 2·36179, 2·5907E20, 3·63
(2·8±·45) Ceres: 2·7675, 9·39E20, 4·60
(2·8±·45) Pallas: 2·77160611, 2E20, 4·614296176
(2·8±·45) (55+32 comèts)
          (202+45 comèts)
(5·2±·85) (84+56 comèts)
(5·2±·85) Jupiter: 5·2044, 1·8982E27, 11·862
          (26+35+60 comèts)
(10·0±1·65) Saturn: 9·5826, 5·6834E26, 29·4571
(10·0±1·65) (4+26+2 comèts)
            (3+26+1 comèts)
(19·6±3·25) Bienor: 16·480, E20?, 66·90
(19·6±3·25) Uranus: 19·2184, 8·68E25, 84·0205
(19·6±3·25) (6+32+1 comèts)
            1995 SN55: 23·565, E20, 114·39
            (3+23 comèts)
            Neptune: 30·110387, 1·0243E26, 164·8
(38·8±6·45) 2002 XW93: 37·425, E20?, 228·96
(38·8±6·45) 2004 TY364: 38·780, E20?, 241·50
(38·8±6·45) (27+1+3 comèts)
(38·8±6·45) 2003 UZ413: 39·146, E20, 244·93
(38·8±6·45) Orcus: 39·398, 6·41E20, 247·29
(38·8±6·45) 2002 XV93: 39·416, 1·7E20, 247·47
(38·8±6·45) 2003 VS2: 39·435, E20?, 247·64
(38·8±6·45) Pluto: 39·48, 1·30E22, 248·00
(38·8±6·45) 2003 AZ84: 39·560, E20, 248·83
(38·8±6·45) 2007 JH43: 39·589, E20, 249·10
(38·8±6·45) Ixion: 39·664, 3E20, 249·80
(38·8±6·45) 2011 FW62: 39·826, E20, 251·34
(38·8±6·45) 2005 RN43: 41·359, E20, 265·99
(38·8±6·45) 2002 MS4: 41·717, E20, 269·45
(38·8±6·45) Salacia: 41·947, 4·7E20, 271·68
(38·8±6·45) 2002 MS4: 42·01, E20, 272·29
(38·8±6·45) 2004 GV9: 42·173, E20, 273·88
(38·8±6·45) 2002 UX25: 42·488, 1·25E20, 276·95
(38·8±6·45) 2014 UM33: 42·897, E20, 280·96
(38·8±6·45) 2010 VK201: 43·113, E20, 283·08
(38·8±6·45) Varuna: 43·123, 3·7E20, 283·19
(38·8±6·45) 2005 UQ513: 43·201, E20, 283·95
(38·8±6·45) Haumea: 43·218, 4·0E21, 284·12
(38·8±6·45) 2004 NT33: 43·426, E20, 286·18
(38·8±6·45) Quaoar: 43·563, 1·4E21, 287·53
            2010 KZ39: 45·395, E20, 305·86
            Makemake: 45·715, 4E21, 309·09
            Chaos: 45·796, E20, 309·92
            Varda: 45·993, 2·4E20, 311·92
            2010 FX86: 47·015, E20, 322·38
            2004 XA192: 47·216, E19?E20?, 324·44
            2002 AW197: 47·526, 4·1E20, 327·65
            2007 JJ43: 47·82, E20, 330·74
            2013 FZ27: 48·418, E20, 336·91
            2010 RF43: 49·290, E20, 346·05
            2003 QX113: 49·448, E20, 347·72
            2014 WK509: 50·838184, E20, 362·49
            (40+1 comèts)
            2001 UR163: 51·351, E20, 367·98
            2014 EZ51: 52·445, E20, 379·81
            2002 TC302: 55·265, E20, 410·86
            2010 DN93: 55·67, E20, 415
            2004 XR190: 57·458, E20, 435·54
            2013 FY27: 58·789, E20, 452·65
            2017 FO161 61·515, E19?E20?, 482·48
            2013 AT183 61·611, E19?E20?, 483·61
            2014 SV349 61·996, E19?E20?, 488·15
            2015 KH162: 62·282, E20, 491·53
            2010 TJ: 62·395, E20, 492·87
(77·2±12·85) 2010 RE64: 65·438, E20, 529·37
(77·2±12·85) 2008 OG19: 66·290, E20, 539·73
(77·2±12·85) 2007 OR10: 67·059, 1·3E21, 549·16
(77·2±12·85) 2006 QH181: 67·235, E20, 551·31
(77·2±12·85) Eris: 67·781, 1·66E22, 558·04
(77·2±12·85) Dziewanna: 70·544, E20, 592·51
(77·2±12·85) 2014 FC69: 72·135, E20, 612·67
(77·2±12·85) Gǃkúnǁʼhòmdímà: 72·722, E20, 620·17
(77·2±12·85) 2005 TB190: 75·166, E19?E20?, 651·69
(77·2±12·85) 2014 FC72: 76·114, E20, 664·06
(77·2±12·85) (36 comèts)
(77·2±12·85) 2015 RR245: 81·373, E20, 734·05
(77·2±12·85) 2005 RM43: 89·610, E20, 848·28
             2008 ST291: 99·885, E20, 998·30
             "Farout": 100?, E20?E21?, 1000?
             2014 UZ224: 108·2, E20, 1125·24
             2005 QU182: 110·51, E20, 1161·74
             (15+18 comèts)
(154·0±25·65) "FarFarOut": 150?, E20?, 1800?
(154·0±25·65) 2010 VZ98: 150·48, E20, 1846·03
(154·0±25·65) (48 comèts)
              2013 FS28: 197·37, E20, 2773
              (43 comèts)
              |next Hubble ST range: 220, E20, |
(307·6±51·25) 2012 VP113: 257·67, E20, 4136·24
(307·6±51·25) (35 comèts)
(307·6±51·25) 2013 FT28: 312, E19?E20?, 5460
              (41 comèts)
              |farthest Hubble ST range: 450, E20, |
              |next Hubble ST range; 470, E21, |
(614·8±102·45) Sedna: 506·8, 1·6E21, 11400
(614·8±102·45) (38 comèts)
(614·8±102·45) *Planet Nine: 654, 6E25, 18000
               (32 comèts)
               |farthest Hubble ST range: 970, E21, |
               |next Hubble ST range: 1000, E22, |
(1229·2±204·85) (38 comèts)
                (2014 FE72: 1550, E19, 60900)
                (38 comèts)
(2458·0±409·65) Hills cloud
(2458·0±409·65) |farthest Hubble ST range: 2100, E22, |
(2458·0±409·65) |next Hubble ST range: 2100, E23, |
(2458·0±409·65) (23 comèts)
                (23 comèts)
                |farthest Hubble ST range: 4400, E23, |
(4915·6±819·25) Hills cloud
(4915·6±819·25) |next Hubble ST range: 4600, E24, |
(4915·6±819·25) (17 comèts)
                (17 comèts)
                |farthest Hubble ST range: 9500, E24, |
(9830·8±1638·45) Hills cloud
(9830·8±1638·45) (17 comèts)
                 |next Hubble ST range: 9800, E25, |
                 (17 comèts)
(19661·2±3276·85) Oort cloud
(19661·2±3276·85) |farthest Hubble ST range: 20000, E25, |
(19661·2±3276·85) (C/2005 G1: 20300, <, 2890000)
(39322·0±6553·65) Oort cloud
(39322·0±6553·65) (Comet West, 35000, <, 6550000)
                  (C/2001 C1_−1: 49000, <, 11000000)
                  Oort cloud
                  (C/2005 G1_−1: 55000, <, 12900000)
(78643·6±13107·25) Oort cloud
                   Oort cloud
(157286·8±26214·45) Oort cloud
                    Oort cloud
                    Sun's Hill sfær: 230000, <<, >)
)314573·2±52428·85( ]Proxima Centauri: 268400, 2·429E29, >[
)314573·2±52428·85( ]Alpha Centauri AB: 276000, 3·992E30, >[
)630k±100k(
)1·3M±210k(
)2·5M±420k(
)5·0M±840k(
)10M±1·7M(
)20M±3·3M(
)40M±6·7M(
)81M±13M(
)160M±27M(
)320M±54M( ]next Carina-Sagittarius Arm: 3·2E8, , [
           ]next Perseus Arm: 3·8E8, , [
)640M±110M( ]next Scutum-Centaurus Arm: 6·4E8, , [
            ]next Outer Arm: 9·5E8, , [
)1·3G±210M( ]farthest Orion-Cygnus Arm: 1·3E9, , [
            ]Canis Major Overdensity: 1·6E9, , [
            Milky Way: 1·67E9±6·3E6, 1·8E41 net–2·57E42 gross, 2·4E8
)2·6G±430M( ]farthest Perseus Arm: 3·0E9, , [
            ]Sagittarius Dwarf Spheroidal Galaxy: 4E9, , [
)5·2G±860M( ]farthest Scutum-Centaurus Arm: 4·6E9, , [
)5·2G±860M( ]farthest Carina-Sagittarius Arm: 4·7E9, , [
            ]farthest Outer Arm? 99kly cepheid: 6·3E9, , [
            ]apogalactic Sagittarius Dwarf Spheroidal Galaxy: 6·8E9, , [

.96: 732->750km; .8: 698->700km; .5: 547->550km; .32: 317->300km; .23: 392->400km; .17: 457->450km; .14: 381->400km; .13: 450km; .11: 469->450km; .044: 413->400km; .04: 367->350km
63.9*2.51^(32-20.8)^.25*(3)^.25*((100000^.33)^2)^.5

Each pair of ranges, Bode and nonBode, has as many hèliocentric comèts yet the Bode ranges only reach 2/3 of the next nonBode range or 4/9 of the area.

There's another trend above between Jupiter and Uranus: If Sun were cold and still, its heat and solar wind wouldn't hav ripped the atmosfærs off the inner planèts, and they'd likely be even heavier than Jupiter, all the way towards Sun—wherefore a protoplanètary disc is heaviest and thickest attwards.  However, I'd expect to see density waves or ripples—thus Neptune and Eris—how galactic spiral arms and lava flows also show them.

>= Ceres kg:

(law's range AU) body: range AU, weiht kg, length yr
(·4±·05) Mercury: ·387098, 3·3011E23, ·240846
(·7±·1) Venus: ·723332, 4·8675E24, ·615198
(1·0±·15) Earth: 1·00000102, 5·97237E24, 1·00001748096
(1·6±·25) Mars: 1·523679, 6·4171E23, 1·8808
(2·8±·45) Ceres: 2·7675, 9·39E20, 4·60
(5·2±·85) Jupiter: 5·2044, 1·8982E27, 11·862
(10·0±1·65) Saturn: 9·5826, 5·6834E26, 29·4571
(19·6±3·25) Uranus: 19·2184, 8·68E25, 84·0205
            Neptune: 30·110387, 1·0243E26, 164·8
(38·8±6·45) Pluto: 39·48, 1·30E22, 248·00
(38·8±6·45) Haumea: 43·218, 4·0E21, 284·12
(38·8±6·45) Quaoar: 43·563, 1·4E21, 287·53
            Makemake: 45·715, 4E21, 309·09
            2007 OR10: 67·059, 1·3E21, 549·16
(77·2±12·85) Eris: 67·781, 1·66E22, 558·04
(154·0±25·65) 2015 TH367: , ,
(307·6±51·25)
(614·8±102·45) Sedna: 506·8, 1·6E21, 11400
(614·8±102·45) *Planet Nine: 654, 6E25, 18000
(1229·2±204·85)
(2458·0±409·65) Hills cloud
(4915·6±819·25) Hills cloud
(9830·8±1638·45) Hills cloud
(19661·2±3276·85) Oort cloud
(39322·0±6553·65) Oort cloud
(78643·6±13107·25)
(157286·8±26214·45)
Sun's Hill sfær
)314573·2±52428·85(