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File:Hyperbolic orbit.gif

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Hyperbolic_orbit.gif ‎(300 × 300 pixels, file size: 12 KB, MIME type: image/gif, looped, 90 frames, 4.2 s)

 
This image was created with POV-Ray.
a Semimajor axis
rp Periapsis' Radius
υ∞ Divergence angle

Summary

Description Animation showing the motion of a small body (green) in an hyperbolic orbit around a much more massive body (blue).
Date
Source Own work. Rendered with PovRay-3.0, animated with gifsicle.
Author Brandir
Permission
(Reusing this file)		 Brandir put it under the GFCL and the CC-BY-SA

Licensing

I, the copyright holder of this work, hereby publish it under the following licenses:
GNU head 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.
w:en:Creative Commons
attribution share alike 		This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
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.
This licensing tag was added to this file as part of the GFDL licensing update.
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 2.5 Spain license.
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.
You may select the license of your choice.

POV-Ray Scene description

POV-ray image description: 

 /*
 --------------------------
 Hyperbolic Orbit Animation
 --------------------------
 Created 7 Mar. 2006
 */
     
 #include "colors.inc"
 
 //Orbit Definition
 #declare OrbitA=30;
 #declare OrbitE=1.38;
 
 //Scene Constants
 #declare EarthRadius=6.356;
 #declare SatRadius=1.2;
 #declare OrbitWidth=0.5;
 #declare LineWidth=0.5/3;
 #declare Crosslength=1.5;
 #declare Textscale=9;
 #declare TextColor=rgb<0,0,0>;
 #declare xinit=-35;
 
 //Variables
 #declare Minit=OrbitE*sinh(acosh(-(xinit/OrbitA-OrbitE)))-acosh(-(xinit/OrbitA-OrbitE));
 #declare M=Minit-2*clock*Minit;
 #declare PI=3.14159265359;
 #declare Angleinf=180-acos(-1/OrbitE)*(180/PI);
 
 //Anomaly Determination - Solves the equation M=e*sinh(H)-H by the iterative method
 #declare Index=0;
 #declare prevAnomaly=0;
 #declare Anomaly=0;
 #while (Index<30)
     #declare Anomaly=asinh((M+prevAnomaly)/OrbitE);
     #declare prevAnomaly=Anomaly;
     #declare Index=Index+1;
 #end
 
 //General settings
 global_settings{
     ambient_light 1
     }
 
 light_source { <-50, 0, -70> color White }
 
 camera {
   orthographic
   location <-10, 0, -10>
   look_at  <-10, 0,  0>
   up <0,100,0>
   right <100,0,0>
 }
 
 
 plane { <0, 0, 1>, 8
     pigment {White}
     finish{ambient 1 brilliance 0}
 }
 
 
 //Earth
 sphere {
     <0, 0, 0>, EarthRadius
     pigment { Blue }
     finish{ ambient 0.3 brilliance 1.2 diffuse 0.8}
 }
 
 
 //Orbit
 intersection{
     box{
         <-100,-100,-OrbitWidth>, <100,100,OrbitWidth> 
     }
     quadric{
         <1/(OrbitA*OrbitA),-1/(OrbitA*OrbitA*(OrbitE*OrbitE-1)),0>,<0,0,0>,<2*OrbitE/OrbitA,0,0>,OrbitE*OrbitE-1
         translate x*OrbitWidth/2
     }
     quadric{
         <-1/(OrbitA*OrbitA),1/(OrbitA*OrbitA*(OrbitE*OrbitE-1)),0>,<0,0,0>,<-2*OrbitE/OrbitA,0,0>,1-OrbitE*OrbitE
         translate -x*OrbitWidth/2
     }
     pigment{ rgb<0.8,0,0> }
     finish{ ambient 1 brilliance 0 diffuse 0}
     rotate 2.2*y
     no_shadow
 }
 
 
 //Satellite
 sphere {
     <0, 0, -10>, SatRadius
     pigment { SeaGreen }
     finish{ ambient 1 brilliance 0 diffuse 0}
     no_shadow
     translate <-OrbitA*(OrbitE-cosh(Anomaly)),OrbitA*sqrt(OrbitE*OrbitE-1)*sinh(Anomaly),0>
 }
 
 //Lines
 #declare crossBars=
 object{
     union{
         box{
             <-LineWidth,-Crosslength,-LineWidth-7>, <LineWidth,Crosslength,LineWidth-7> 
         }
         box{
             <-Crosslength,-LineWidth,-LineWidth-7>, <Crosslength,LineWidth,LineWidth-7>
         }
         rotate z*45
         pigment{ TextColor }
         finish{ ambient 1 brilliance 0 diffuse 0}
         no_shadow
     }
 }
 
 box{
     <-OrbitA*OrbitE-3,-LineWidth,-LineWidth-7>, <0,LineWidth,LineWidth-7> 
     pigment{ TextColor }
     finish{ ambient 1 brilliance 0 diffuse 0}
     no_shadow
 }
 
 box{
     <0,-LineWidth,-LineWidth-7>, <300,LineWidth,LineWidth-7> 
     pigment{ TextColor }
     finish{ ambient 1 brilliance 0 diffuse 0}
     rotate z*Angleinf
     translate -x*OrbitA*OrbitE
     no_shadow
 }
 
 box{
     <0,-LineWidth,-LineWidth-7>, <300,LineWidth,LineWidth-7> 
     pigment{ TextColor }
     finish{ ambient 1 brilliance 0 diffuse 0}
     rotate -z*Angleinf
     translate -x*OrbitA*OrbitE
     no_shadow
 }
 
 difference{
     torus{
         4,LineWidth
         rotate x*90
     }
     box {
         <-5,0,-5>,<5,5,5>
     }
     box {
         <-5,-5,-5>,<5,0,5>
         rotate -z*Angleinf
     }
     pigment{ TextColor }
     finish{ ambient 1 brilliance 0 diffuse 0}
     translate -z*7
     translate -x*OrbitA*OrbitE
     no_shadow
 }
 
 object{
     crossBars
 }
 
 object{
     crossBars
     translate -x*OrbitA*(OrbitE-1)
 }
 
 object{
     crossBars
     translate -x*OrbitA*OrbitE
 }
 
 //Text
 text {
     ttf "timesi.ttf" "a" 1, 0
     pigment{ TextColor }
     finish{ ambient 1 brilliance 0 diffuse 0}
     scale Textscale
     translate <OrbitA*(0.5-OrbitE)-Textscale/4,Textscale/4,-7>
     no_shadow
 }
 
 union{
     text {
         ttf "timesi.ttf" "r" 1, 0
     }
     text {
         ttf "timesi.ttf" "p" 1, 0
         scale 0.5
         translate 0.2*x
     }
     pigment{ TextColor }
     finish{ ambient 1 brilliance 0 diffuse 0}
     scale Textscale
     translate <-(EarthRadius+0.3*(OrbitA*(OrbitE-1)-EarthRadius))-Textscale/4,Textscale/4,-7>
     no_shadow
 }
 
 union{
     text {
         ttf "symbol.ttf" "u" 1, 0
         matrix 
             < 1, 0, 0,
             0.3, 1, 0,
             0, 0, 1,
             0, 0, 0 >
     }
     text {
         ttf "symbol.ttf" chr(165) 1, 0
         scale 0.5
         translate <0.6,-0.1,0>
     }
     pigment{ TextColor }
     finish{ ambient 1 brilliance 0 diffuse 0}
     scale Textscale
     translate <-OrbitA*OrbitE-Textscale/4+9,-0.6*Textscale,-7>
     no_shadow
 }

Captions

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depicts

inception

7 March 2006

MIME type

image/gif

File history

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Date/TimeThumbnailDimensionsUserComment
current00:01, 8 March 2006Thumbnail for version as of 00:01, 8 March 2006300 × 300 (12 KB)Brandir~commonswiki{{Information| |Description = Animation showing the motion of a small body (green) in an hyperbolic orbit around a much more massive body (blue). |Source = Own work. Rendered with ''PovRay-3.0'', animated with ''gifsicle''. |Date = Created 7. Mar. 2006.

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