File:Lagrange points.svg
Original file (SVG file, nominally 600 × 480 pixels, file size: 191 KB)
This is a file from the Wikimedia Commons. Information from its description page there is shown below. Commons is a freely licensed media file repository. You can help. |
Summary
A contour plot of the effective potential of a two-body system. (the Sun and Earth here), showing the 5 Lagrange points. An object in free-fall would trace out a contour (such as the Moon, shown).
SVG replacement for Image:Lagrange points.jpg. Not complete yet.
Diagram of w:Lagrange points for a system where the ratio of masses (primary:secondary) is 25:1. Contour lines plot effective potential in rotating frame.
Self-made in w:Gnuplot:
# Ratio of masses (primary:secondary) R=25 left=-R*1.25 right=R*1.5 bottom=-R*1.25 top=R*1.25 set isosamples 200 unset surface set cntrparam levels 30 set cntrparam levels incremental 1.4,0.019 set view 0,0 set contour base set table 'lpoints.dat' # Perturbatory force (vector) # centrifugal primary secondary lperturb(z) = z/(R+1)**2 - R*(z+1)/abs(z+1)**3 - (z-R)/abs(z-R)**3 # Effective potential (negative) lpotential(z) = abs(z)**2/2/(R+1)**2 + R/abs(z+1) + 1/abs(z-R) set parametric splot [0:2*pi][0:right][left:right][bottom:top][1:3] v*sin(u),v*cos(u),lpotential(v*sin(u)*{1,0}+v*cos(u)*{0,1}) unset table set term svg set out 'lagrange.svg' unset object unset label set size square set multiplot unset key unset xtics unset ytics set parametric # Space set style line 6 lt 1 lw 2 lc rgb "black" set samples 5 plot [0:4] [left:right][bottom:top] t<1?left+0.001:t<2?(t-1)*(right-left-0.002)+left+0.001:t<3?right+0.001:(t-3)*(left-right+0.002)+right-0.001,t<1?t*(top-bottom-0.002)+bottom+0.001:t<2?top-0.001:t<3?(t-2)*(bottom-top+0.002)+top-0.001:bottom linestyle 6 with filledcurves closed set samples 100 unset parametric # Contours set style line 1 lt 1 lw 1 lc rgb "white" plot [left:right][bottom:top] 'lpoints.dat' smooth bezier with lines linestyle 1 # Newton-Raphson method to calculate L1-L3 dlperturb(z) = 1.0/(R+1)**2 + 2.0*R/abs(z+1)**3 + 2.0/abs(z-R)**3 newtonraphson(x, m) = m<0 ? x : newtonraphson(x - lperturb(x)/dlperturb(x), m-1) #set label 1 "Primary" at -1,0 offset -1,2 textcolor rgb "red" #set label 2 "Secondary" at R,0 offset 1,1 textcolor rgb "red" # Barycentre set label 3 "" at 0,0 offset 1,0 point pointtype 1 pointsize 1 set label 4 "L1" at newtonraphson(R - (R+1)/(3*R)**(1.0/3), 10),0 right offset -1,-1 point pointtype 7 pointsize 1 linetype 1 lc rgb "green" textcolor rgb "green" font "Sans,14" set label 5 "L2" at newtonraphson(R + (R+1)/(3*R)**(1.0/3), 10),0 offset 1,-1 point pointtype 7 pointsize 1 linetype 1 lc rgb "green" textcolor rgb "green" font "Sans,14" set label 6 "L3" at newtonraphson((7.0*R+7)/(12.0*R-5)-(R+2), 10),0 offset 1,-1 point pointtype 7 pointsize 1 linetype 1 lc rgb "green" textcolor rgb "green" font "Sans,14" set label 7 "L4" at (R-1)/2,sqrt(3)*(R+1)/2 offset 1,1 point pointtype 7 pointsize 1 linetype 1 lc rgb "green" textcolor rgb "green" font "Sans,14" set label 8 "L5" at (R-1)/2,-sqrt(3)*(R+1)/2 offset 1,-1 point pointtype 7 pointsize 1 linetype 1 lc rgb "green" textcolor rgb "green" font "Sans,14" set parametric # Primary set style line 4 lt 1 lw 1 lc rgb "white" plot [0:2*pi] [left:right][bottom:top] 4*sin(t)-1,4*cos(t) linestyle 4 with filledcurves closed set style line 3 lt 1 lw 1 lc rgb "blue" plot [0:2*pi] [left:right][bottom:top] sin(t),cos(t) linestyle 3 # Secondary plot [0:2*pi] [left:right][bottom:top] R*sin(t),R*cos(t) linestyle 3 set style line 6 lt 1 lw 1 lc rgb "black" plot [0:2*pi] [left:right][bottom:top] 2.2*sin(t)+R,2.2*cos(t) linestyle 6 with filledcurves closed set style line 5 lt 1 lw 1 lc rgb "#80C0FF" plot [pi:2*pi] [left:right][bottom:top] 1.2*sin(t)+R,1.2*cos(t) linestyle 5 with filledcurves closed set style line 8 lt 1 lw 1 lc rgb "#406080" plot [0:pi] [left:right][bottom:top] 1.2*sin(t)+R,1.2*cos(t) linestyle 8 with filledcurves closed # Moon plot [0:2*pi] [left:right][bottom:top] 2.2*sin(t)+R,2.2*cos(t) linestyle 3 set style line 2 lt 1 lw 1 lc rgb "#DDDDDD" plot [pi:2*pi] [left:right][bottom:top] 0.4*sin(t)+R+2.2*sqrt(0.5),0.4*cos(t)+2.2*sqrt(0.5) linestyle 2 with filledcurves closed set style line 7 lt 1 lw 1 lc rgb "#222222" plot [0:pi] [left:right][bottom:top] 0.4*sin(t)+R+2.2*sqrt(0.5),0.4*cos(t)+2.2*sqrt(0.5) linestyle 7 with filledcurves closed unset parametric unset multiplot
Licensing
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license. | ||
| ||
This licensing tag was added to this file as part of the GFDL licensing update.http://creativecommons.org/licenses/by-sa/3.0/CC BY-SA 3.0Creative Commons Attribution-Share Alike 3.0truetrue |
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
Items portrayed in this file
depicts
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 02:58, 7 February 2007 | 600 × 480 (191 KB) | EnEdC | Improved initial approximations. | |
12:53, 6 February 2007 | 600 × 480 (191 KB) | EnEdC | Improved version | ||
23:32, 4 February 2007 | 600 × 480 (346 KB) | EnEdC | Self-made in w:Gnuplot: <nowiki> n=25 left=-n*1.25 right=n*1.5 bottom=-n*1.25 top=n*1.25 set isosamples 200 unset polar unset surface set cntrparam levels 30 set cntrparam levels incremental 1.4,0.019 set zrange [0:2] set view 0,0 set contour base |
File usage
The following page uses this file:
Global file usage
The following other wikis use this file:
- Usage on en.wikibooks.org
- Usage on en.wikiversity.org
- Usage on ru.wikinews.org
Metadata
This file contains additional information, probably added from the digital camera or scanner used to create or digitize it.
If the file has been modified from its original state, some details may not fully reflect the modified file.
Image title | Produced by GNUPLOT 4.2 patchlevel rc1 |
---|