This page is under development. Comments are welcome, but please load any comments in the comments section at the bottom of the page. Please include your wiki MONIKER and date in your comment with the same courtesy that I will give you. Aside from your courtesy, your wiki MONIKER and date as a signature and minimal good faith of any internet post are the rules of this TCL-WIKI. Its very hard to reply reasonably without some background of the correspondent on his WIKI bio page. Thanks, gold 20Aug2020
gold 20aug2020 Here are some calculations
Here are TCL calculations on the equation converting Note. This field is rapidly changing, one needs to check in at for the latest up to date info.
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This is not an intended use of calculator, but the calculator can work with other consistent units like days, months and distances, simply treating the Golden Ratio constants and Fibonacci sequence numbers as reals. This paragraph largely follows the book “Harmonic Trading” by Scott M. Carney. The planet Venus has a revolution period of 225 Earth days. Enter 225 Earth days in the TCL calculator and receive 364 Earth days, the revolution period of Planet Earth. Alternate hand calculations were expr { 225. * 1./ 0.618 }, 364.0 days. Alternate calculation using the later Fibonnaci sequence numbers as reals was expr { 225. * 1346269. / 832040. }, 364.0 days.
The Titius–Bode law estimated rough distances in Astronomical Units (AU) of Planets from the Sun by square laws, Johann Elert Bode, pub 1772. Although much more known in modern times, an examination of the original Titius–Bode results in AU gives some fodder for the theory of the TCL calculator. For example, Titius–Bode law rated Earth as 1 AU from the Sun and predicted Mars as 1.6 AU. The Bode estimate for Mars was short of the true value 1.676 AU by 4.77 percent error. Using hand calculations, a similar value can be ginned up from the golden ratio, expr { $golden_ratio_constant / 1. } returns 1.618 AU rounded. The golden ratio method is still short of the Mars true distance by 3.6 percent error. Numerous excellent papers have used both the Fibonacci and the golden ratio constants methods to estimate planetary distances from the Sun. The Lombardi paper found the best fit to the Fibonacci constants used the scaling constant < K1 = 55.88 > to get E6 km prediction. Both the Fibonacci and Bode sequences have unassigned slots or skips, due to the Asteriod belt(s) and possible undiscovered bodies. The Asteroid Ceres is representative of Asteroid belt here, but was not known to Bode. Also, both Neptune and Pluto not known to Bode in 1772.
Here is an example of how the Fibonacci method might be used with < K1 = 55.88 > . Astronomer Mary Blagg in 1913 conjectured that if the transplutonian Planet X existed, it might be at ~68 AU from the Sun. The nearest Fibonacci constants are 233 and 377, and unassigned at that. Perhaps, expr { 0.349 * 233. } ;# 81.317 AU for Planet X?Th e interest in Planet X and the region of 80 AU is not original or new by any means. Schuette suggested a family of comets in the region of 80 AU aphelia, circa 1949. The perihelion of the object Sedna is around 76 AU, reported in 2004. The perihelion of the object 2012 VP is around 80 AU, reported in 2012.
With additional scale factors loaded in the deck, the TCL calculator could use the Fibonacci sequence to output the planetary distances in kilometers and AU. The scale factor for kilometers is 55.88 (*E6). Sample calculation for Planet X was expr { 233. * 55.88 } ;# returns rounded 13000 X 1E6 km. The scale factor for AU is expr { 19.2 / 55. } ;# ratio of Uranus returns 0.349 AU/Fi
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What would be the range window(s) for the hypothetical transplutonian planet X ?
proportions 55 / 19.22 AU = X /68 au
X * 19.2 = 55* 68
x = 55.* 68./19.2
expr { 55.* 68./19.2} ;# returns 194.7 as F estimate
nearest Fibonacci constants are 233 and 377,
and unassigned at that.
expr { 233. * 55.88 } ;# returns rounded 13000 X 1E6 km
expr { 377. * 55.88 } ;# returns rounded 21000 X 1E6 km
expr { 19.2 / 55. } ;# ratio of Uranus returns 0.349 AU/Fi
expr { 0.349 * 233. } ;# 81.317 AU for planet X? ----
Here is an example of how the Fibonacci method might be used with ''' < K1 = 55.88 > '''. Astronomer Mary Blagg in 1913 conjectured that if transplutonian planet existed, it might be at ~68 AU from the Sun. The perihelion of Sedna is around 76 AU. The perihelion of 2012 VP is around 80 AU.
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;# Pseudocode & Equations
What would be the range window(s) for the hypothetical transplutonian planet X ?
proportions 55 / 19.22 AU = X /68 au
X * 19.2 = 55* 68
X = 55.* 68./19.2
expr { 55.* 68./19.2} ;# returns 194.7 as F estimate
nearest Fibonacci constants are 233 and 377,
and unassigned at that.
expr { 233. * 55.88 } ;# returns rounded 13000 X 1E6 km
expr { 377. * 55.88 } ;# returns rounded 21000 X 1E6 km
;# scale Fibonacci to AU in outer reaches of solar system
expr { 19.2 / 55. } ;# ratio of Uranus returns 0.349 AU/Fi
expr { 0.349 * 233. } ;# 81.317 AU for Planet X? | Table : Est. Distance of Planets from Fibonacci and Bode Rules | printed in tcl wiki format | |||||||
|---|---|---|---|---|---|---|---|---|
| sources >> | JPL | JPL | Fibonacci constants | Lombardi Paper | Lombardi Paper | Wikipedia | Wikipedia | comments |
| quantity | real measured AU, semi_major axis | real measured 10E6 km, semi_major axis | Fibonacci constants | Fibonacci * 55.88, 10E6 km Prediction | Titius-Bode number | Titius-Bode AU Prediction | Real Measured AU , semi_major axis | comments, if any |
| Sun | 0 | 0 | Sun not assigned value in Fibonacci and Bode Rules | |||||
| Mercury | 0.39 | 57.9 | 1 | 55.8 | 4 | 0.4 | 0.39 | |
| Venus | 0.723 | 108.2 | 2 | 111.6 | 7 | 0.7 | 0.72 | |
| Earth | 1 | 149.6 | 3 | 167.4 | 10 | 1 | 1 | Earth assigned unit 1 AU in Bode Rules |
| Mars | 1.524 | 227.9 | 5 | 279 | 16 | 1.6 | 1.52 | |
| Ceres | 8 | 446.4 | 28 | 2.8 | 2.77 | Asteroid belt | ||
| Jupiter | 5.203 | 778.3 | 13 | 725.4 | 52 | 5.2 | 5.2 | |
| Jupiter clearance belt | 21 | 1171.8 | Jupiter clearance belt | |||||
| Saturn | 9.539 | 1427 | 34 | 1897.2 | 100 | 10 | 9.55 | |
| Uranus | 19.18 | 2871 | 55 | 3069 | 196 | 19.6 | 19.22 | |
| Neptune | 30.07 | 4497.1 | 89? | 4966.2 | 388? | 38.8? | 30.11 | Bodes Law breaks down for Neptune and Pluto. Confusing references. |
| Pluto (avg) | 39.482 | 5906.38 | 144? | 8035.2? | 772? | 77.20? | 39.54 | Pluto is not considered a planet, currently. Bodes Law breaks down for Neptune and Pluto. Confusing references. |
| Note | several sources | Wikipedia | Jpl | Lombardi Paper | ||||
| Note | Neptune, Pluto, & Ceres were not known to Bode | |||||||
| Note | Ceres representative of Asteroid belt here | |||||||
| Note | Bodes Law breaks down for Neptune and Pluto, confusing references | Opinion: Bode Number assignment for N&P uncertain here. |
;# pretty print from autoindent and ased editor occurrence
;# Planetary Distances Using Titius-Bodes Law V2 calculator
;# written on Windows 10
;# working under TCL version 8.6
;# gold on TCL Club, 10jul2021
package require Tk
package require math::numtheory
namespace path {::tcl::mathop ::tcl::mathfunc math::numtheory }
set tcl_precision 17
frame .frame -relief flat -bg aquamarine4
pack .frame -side top -fill y -anchor center
set names {{} { method number, 1 = Bode :} }
lappend names {reference year CE: }
lappend names {answers: Mercury : }
lappend names { Venus : }
lappend names { Earth : }
lappend names { Mars : }
lappend names { Jupiter : }
lappend names { Saturn : }
lappend names { Uranus : }
foreach i {1 2 3 4 5 6 7 8 9} {
label .frame.label$i -text [lindex $names $i] -anchor e
entry .frame.entry$i -width 35 -textvariable side$i
grid .frame.label$i .frame.entry$i -sticky ew -pady 2 -padx 1 }
proc about {} {
set msg "Calculator for Planetary Distances Using Titius-Bodes Law V2
from TCL WIKI,
written on TCL 8.6 "
tk_messageBox -title "About" -message $msg }
proc self_help {} {
set msg "Calculator for Planetary Distances Using Titius-Bodes Law V2
from TCL ,
;# self help listing
;# 1 given follow.
1) method N1
2) Reference year
;# This calculator uses the Titius-Bodes Law
;# to predict Planetary Distances in AU.
;# For comparison, TCL code may include redundant paths & formulas.
;# The TCL calculator normally uses modern
;# units for convenience to modern users and textbooks.
;# Any convenient and consistent in/output units might be used
;# like inches, feet, nindas, cubits, or dollars to donuts.
;# Recommended procedure is push testcase and fill frame,
;# change first three entries etc, push solve,
;# and then push report. Report allows copy and paste
;# from console to conventional texteditor. For testcases
;# testcase number is internal to the calculator and
;# will not be printed until the report button is pushed
;# for the current result numbers.
;# Use one line errorx proc to estimate percent errors.
;# errorx proc is used in the report window (console).
;# Additional significant figures are used to check
;# the TCL program, not to infer the accuracy
;# of inputs and product reports.
Conventional text editor formulas or grabbed from internet
screens can be pasted into green report console.
Try copy and paste following into green screen console
set answer \[* 1. 2. 3. 4. 5. \]
returns 120
;# gold on TCL Club, 10jul2021 "
tk_messageBox -title "self_help" -message $msg }
proc precisionx {precision float} {
;# tcl:wiki:Floating-point formatting, <AM>
;# select numbers only, not used on every number.
set x [ expr {round( 10 ** $precision * $float) / (10.0 ** $precision)} ]
;# rounded or clipped to nearest 5ird significant figure
set x [ format "%#.3g" $x ]
return $x
}
;# Use one line errorx proc to estimate percent errors
;# errorx proc is used in the report window (console)
proc errorx {aa bb} {expr { $aa > $bb ? (($aa*1.)/$bb -1.)*100. : (($bb*1.)/$aa -1.)*100.}}
proc titius_bode_law {aa } {expr { (4. + 3 * 2**$aa)*.1 } }
proc calculate { } {
global answer2
global side1 side2 side3 side4 side5
global side6 side7 side8 side9 k1
global side10 side11 side12 side13
global testcase_number
incr testcase_number
;# scaling constant K1
set k1 55.8
set side3 [precisionx 2 [ titius_bode_law -1]]
set side4 [precisionx 2 [ titius_bode_law 0]]
set side5 [precisionx 2 [ titius_bode_law 1]]
set side6 [precisionx 2 [ titius_bode_law 2]]
set side7 [precisionx 2 [ titius_bode_law 4]]
set side8 [precisionx 2 [ titius_bode_law 5]]
set side9 [precisionx 2 [ titius_bode_law 6]]
set side10 [precisionx 2 [ titius_bode_law 7]] ;# Neptune
set side11 [precisionx 2 [ titius_bode_law 8]] ;# Pluto
set side12 [precisionx 2 [ titius_bode_law 9]] ;# extra Bode slot, unk planet?
set side13 [precisionx 2 [ titius_bode_law 3]] ;# Ceres
set scaled_results [list 0.000001 $side1 $side3 $side4 $side5 $side6 $side7 $side8 $side9 $side10]
puts " scaled_results $scaled_results "
}
proc fillup {aa bb cc dd ee ff gg hh ii} {
.frame.entry1 insert 0 "$aa"
.frame.entry2 insert 0 "$bb"
.frame.entry3 insert 0 "$cc"
.frame.entry4 insert 0 "$dd"
.frame.entry5 insert 0 "$ee"
.frame.entry6 insert 0 "$ff"
.frame.entry7 insert 0 "$gg"
.frame.entry8 insert 0 "$hh"
.frame.entry9 insert 0 "$ii"
}
proc clearx {} {
foreach i {1 2 3 4 5 6 7 8 9 } {
.frame.entry$i delete 0 end } }
proc reportx {} {
global side1 side2 side3 side4 side5
global side6 side7 side8 side9 k1
global side10 side11 side12 side13
global testcase_number
console show;
puts "%|table $testcase_number| || printed in tcl wiki format|% "
puts "&| $testcase_number:|testcase_number || |&"
puts "&| $side1 :|method number, 1 = Bode | | |&"
puts "&| $side2 :|reference year CE : | | |& "
puts "&| value AU |quantity |distance E6 km | comment, if any|& "
puts "&| $side3 :| Mercury : |[* $side3 $k1 ] | |& "
puts "&| $side4 :| Venus : |[* $side4 $k1 ] | |& "
puts "&| $side5 :| Earth : |[* $side5 $k1 ] | |&"
puts "&| $side6 :| Mars : |[* $side6 $k1 ] | |&"
puts "&| $side7 :| Jupiter : : |[* $side7 $k1 ] | |&"
puts "&| $side8 :| Saturn : | [* $side8 $k1 ]| |&"
puts "&| $side9 :| Uranus : | [* $side9 $k1 ] | |&"
puts "&| $side10 :| Neptune : | [* $side10 $k1 ] | |&"
puts "&| $side11 :| PLuto : | [* $side11 $k1 ] | |&"
puts "&| $side12 :| extra slot, unk planet? : | [* $side12 $k1 ] | |&"
puts "&| $side13 :| Ceres : | [* $side13 $k1 ] | |&"
}
frame .buttons -bg aquamarine4
::ttk::button .calculator -text "Solve" -command { calculate }
::ttk::button .test2 -text "Testcase1" -command {clearx;fillup 1. 1772. 0.40 0.70 1.0 1.6 5.2 10. 19.6}
::ttk::button .test3 -text "Testcase2" -command {clearx;fillup 1. 1772. 0.40 0.70 1.0 1.6 5.2 10. 19.6}
::ttk::button .test4 -text "Testcase3" -command {clearx;fillup 1. 1772. 0.40 0.70 1.0 1.6 5.2 10. 19.6}
::ttk::button .clearallx -text clear -command {clearx }
::ttk::button .about -text about -command {about}
::ttk::button .self_help -text self_help -command {self_help }
::ttk::button .cons -text report -command { reportx }
::ttk::button .exit -text exit -command {exit}
pack .calculator -in .buttons -side top -padx 10 -pady 5
pack .clearallx .cons .self_help .about .exit .test4 .test3 .test2 -side bottom -in .buttons
grid .frame .buttons -sticky ns -pady {0 10}
. configure -background aquamarine4 -highlightcolor brown -relief raised -border 30
wm title . " Planetary Distances Using Titius-Bodes Law V2"
# end of working deck
# add cosmetics below to bottom of file
console eval {.console config -bg palegreen}
console eval {.console config -font {fixed 20 bold}}
console eval {wm geometry . 40x20}
console eval {wm title . " Report for Planetary Distances Using Titius-Bodes Law V2 "}
console eval {. configure -background orange -highlightcolor brown -relief raised -border 30}
puts " Console wrapper for solution proc"
puts " ***************************"
puts " ***************************"Please include your wiki MONIKER and date in your comment with the same courtesy that I will give you. Thanks, gold 20Jul2021
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