File:Lagrange_points.svg
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![Lêer:Lagrange points.svg](http://upload.wikimedia.org/wikipedia/commons/thumb/d/d0/Lagrange_points.svg/600px-Lagrange_points.svg.png)
Oorspronklike lêer (SVG-lêer, normaalweg 600 × 480 piksels, lêergrootte: 191 KG)
Hierdie lêer kom vanaf Wikimedia Commons en kan ook in ander projekte gebruik word. Die beskrywing op die lêer se inligtingsblad word hieronder weergegee.
Opsomming
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
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Lêergeskiedenis
Klik op die datum/tyd om te sien hoe die lêer destyds gelyk het.
Datum/Tyd | Duimnael | Dimensies | Gebruiker | Opmerking | |
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huidig | 02:58, 7 Februarie 2007 | ![]() | 600 × 480 (191 KG) | EnEdC | Improved initial approximations. |
12:53, 6 Februarie 2007 | ![]() | 600 × 480 (191 KG) | EnEdC | Improved version | |
23:32, 4 Februarie 2007 | ![]() | 600 × 480 (346 KG) | 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 |
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