文件:Angular Parameters of Elliptical Orbit.png

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Cī-siŏh-bĭh ùng-giông téng Wikimedia Commons lì, bĕng-chiā ô kō̤-nèng ké̤ṳk gì-tă cuŏng-áng sāi. Â-dā̤ sê cī-bĭh ùng-giông găk ùng-giông mièu-sŭk hiĕk-miêng gì mièu-sŭk nô̤i-ṳ̀ng.


Mièu-sŭk Raytraced image showing the concepts of inclination (i), longitude of the ascending node (Ω), argument of the periapsis (ω), and true anomaly (ν) for a "minor" object in an elliptic orbit around a larger object.
Nĭk-gĭ 2005年Sĕk-ék-nguŏk23日 (原始上傳日期)
Lài-nguòng No machine-readable source provided. Own work assumed (based on copyright claims).
Cáuk-ciā No machine-readable author provided. Peo~commonswiki assumed (based on copyright claims).
 
本圖形使用Persistence of Vision創作。

總結

Description (English)

Raytraced image showing the concepts of inclination (i), longitude of the ascending node (Ω), argument of the periapsis (ω), and true anomaly (ν) for a "minor" object in an elliptic orbit around a larger object.

Legend

Letters in the image denote:

  • A – Minor, orbiting body
  • B – Major body being orbited by A
  • C – Reference plane, e.g. the ecliptic
  • D – Orbital plane of A
  • E – Ascending node
  • F – Descending node
  • G – Periapsis
  • H – Apoapsis
  • i – Inclination
  • J – Reference direction; for orbits in or near the ecliptic, usually the vernal point
  • Ω – Longitude of the ascending node
  • ω – Argument of the periapsis
  • ν – True anomaly

The red line is the line of apsides; going through the periapsis (G) and apoapsis (H); this line coincides wíth the major axis in the elliptical shape of the orbit

The green line is the node line; going through the ascending (E) and descending node (F); this is where the reference plane (C) intersects the orbital plane (D).

Raytracing

This image was created using the Persistence of Vision Raytracer and the scene description code below: You can use this free raytracing package and the scene description below to re-render the image in new resolutions, or modify the description and thus the image being rendered.

A few notes of caution for those who want to do their own renditions of this image:

  • The "camera" (viewpoint) assumes that the image format is square (i.e. has the same number of pixels in width and height) - to achieve this, use the +w and +h command line options to set the same number of pixels in width and height, respectively.
  • This image comes complete with the letter annotations, and for this, the POV-Ray installation needs access to the TrueType fonts timesbi.ttf (Times new roman, bold and italic) and symbol.ttf (for greek letters). These come as standard on a Microsoft Windows installation, so this image should at least be able to render in POV-Ray for Windows.
  • A little "dirty trick" is used to put those annotations there; they are text objects placed right in front of the "camera" that "sees" the scenario. Because of this, if you modify the camera location and/or look_at-point in the code, you need to either delete the annotations or make sure they "move with" the camera.

Multiple images in one scene description

Rendering the POV-Ray scene description as shown below renders this image, showing all four angles of the orbital elements: the two remaining orbital elements not shown here are semimajor axis and eccentricity. Using this scene description, you can generate various views (isometric, normal to reference plane, normal to orbit plane) and display various features of the Keplerian orbit. You can also set the background color and whether to display the Cartesian coordinate axes.

The view variable declaration reads: 

#declare view=0;

view = 0 sets the camera to an isometric view

view = 1 sets the camera to a view normal to the reference plane

view = 2 sets the camera to a view normal to the orbit plane


The backgroundColor variable declaration reads: 

#declare backgroundColor = 0;

backgroundColor = 0 sets the background color as white

backgroundColor = 1 sets the background color as black


The featureCode variable declaration reads: 

#declare featureCode = 0;

featureCode = 0 displays all four Keplerian orbit angles (seen here)

featureCode = 1 displays the argument of the periapsis only (see Image:Argument of Periapsis in Elliptical Orbit.png)

featureCode = 2 displays the longitude of the ascending node only (see Image:Longitude of Ascending Node in Elliptical Orbit.png)

featureCode = 3 displays the orbit inclination only (see Image:Inclination in Elliptical Orbit.png)

featureCode = 4 displays the true anomaly only (ADD IMAGE HERE)

Beskrivelse (Dansk)

Raytracet billede der demonstrerer inklination, den opstigende knudes længde og periapsisargumentet for et mindre himmellegeme i elliptisk kredsløb om et større.

Nøgle

Bogstaverne i billedet angiver:

  • A – Det mindre himmellegeme
  • B – Det større himmellegeme
  • C – Referenceplan, f.eks. da:ekliptika
  • D – Baneplan for A's omløb
  • E – Nedadgående knude
  • F – Periapsis
  • G – Opstigende knude
  • H – Apoapsis
  • i – Inklination
  • J – Referenceretning; for baner i eller nær ekliptikas plan typisk forårspunktet i Vædderen
  • Ω – Opstigende knudes længde
  • ω – Periapsisargument

Raytracing

Billedet er lavet med raytracin-programmet Persistence of Vision Raytracer, samt den scenarie-beskrivelse der er vist nedenfor. Du kan bruge dette gratis raytracing-program og beskrivelsen nedenfor til at renderer billedet i nye opløsninger, eller lave ændringer i beskrivelsen og dermed også i det endelige billede.

Et par detaljer man skal være opmærksom på hvis man vil rendere billedet:

  • "Kameraet" (betragtningspunktet) i billedet går ud fra at det færdige billede får et kvadratisk format, dvs. har lige mange pixels i bredden og højden. Man bør derfor bruge kommandolinje-ordrerne +w og +h til at specificere det samme antal pixels i respektive bredden og højden.
  • Billedet leveres "komplet", inklusiv bogstav-annotationerne. For at lave disse, Persistence of Vision-programmet have adgang til Truetype-skrifttyperne timesbi.ttf (Times New Roman i fed og kursiv) og symbol.ttf (for græske bogstaver). Disse er standard i en Microsoft Windows-installation, så denne scenarie-beskrivelse skulle kunne køre fejlfrit med Persistence of Vision Raytracer for Windows.
  • Der er brugt et lille "sidegade-kneb" til at lave bogstav-annotationerne; de er text-objekter anbragt lige foran camera'et, så hvis man flytter på synsretningen mod motivet, skal man enten sørge for at annotationerne "flytter med" synsretningen, eller helt fjerne dem.

Fire billeder ud af én beskrivelse

Hvis man renderer scenariebeskrivelsen som den er vist nedenfor, får man dette billede der viser alle de tre parametre for en omløbsbane der er vinkler. Nogen synes at der er lidt for meget overvældende detaljemylder i billedet, så jeg ændrede beskrivelsen så den kan bruges til ikke blot hosstående billede, men også tre andre tilsvarende billeder, der blot kun beskriver én af vinklerne "ad gangen".

I linje 10 i beskrivelsen står der: 

#declare View=0;

Som beskrevet i de kommentarer der starter fra linje 11, giver 0'et i ovenstående linje det kombinerede billeder der viser alle tre vinkler. Erstatter man 0'et med enten 1, 2 eller 3, får man billeder der viser én vinkel:

  1. for periapsisargumentet (se Image:Argument of Periapsis in Elliptical Orbit.png)
  2. for den opstigende knudes længde (se Image:Longitude of Ascending Node in Elliptical Orbit.png)
  3. for banehældning (se Image:Inclination in Elliptical Orbit.png)

版權說明

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Nṳ̄ â̤-sāi cê̤ṳ-iù:
  • hŭng-hiōng – Hók-cié, huák-buó, diòng-bó̤ buōng cáuk-pīng
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Nâ diŏh áng ī-hâ gì dèu-giông:
  • biĕu-sê miàng-sáng – 您必須指名出正確的製作者，和提供授權條款的連結，以及表示是否有對內容上做出變更。您可以用任何合理的方式來行動，但不得以任何方式表明授權條款是對您許可或是由您所使用。
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已新增授權條款標題至此檔案，作為GFDL授權更新的一部份。
Nṳ̄ buóh dĭk sié-nó̤h sêu-guòng dèu-kuāng dŭ kō̤-ī gēng.

POV-Ray scene description

POV-ray image description: 

/*
ClassicalOrbitalElements.pov

Description:
    This scene shows the six classical orbital elements, namely:
    1) semimajor axis, a (implicit)
    2) eccentricity, e (implicit)
    3) orbit inclinaton, i
    4) argument of the ascending node, Omega
    5) argument of periapsis, omega
    6) true anomaly, nu 
    
Created by:
    Søren Peo Pedersen
    http://da.wikipedia.org/wiki/Bruger:Peo
    ~2005
    
Updated by:
    Bradley Canty
    https://commons.wikimedia.org/wiki/User:Aero_BSC
    2023/11/23

Updates:
    1. Added true anomaly, nu
    2. Added arrow preferences: ability for angles greater
       than 180 deg and options for arrow head visibility
    3. Added view selection (isometric, normal to reference plane,
       or normal to orbital plane)
    4. Added background color selection (black or white)
    5. Added axes (cartesian triad) display option   
    6. Set the 6 classical orbital elements as variables, which
       can be modified by the user
        
TO DO:
    -- Make ascending and descending nodes move when argument of 
       periapsis, omega_, changed
    -- Make yellow part of angle measurement thing stay in place when
       argument of periapsis, omega_, changed
    -- Fix aspect ratio of output image, see:  
       http://povray.tashcorp.net/tutorials/qd_aspect_ratio/
       https://www.povray.org/documentation/view/3.6.1/153/
    -- Mathematically determine vector normal to orbit plane, to 
       generalize the computation of the camera angle for the view 
       normal to the orbit plane (view 2)
    
================================================
*/

// VIEW PREFERENCES ----------------------------
#declare view = 0;
// 0 for isometric view
// 1 for view normal to reference plane
// 2 for view normal to orbit plane

#declare backgroundColor = 0;
// 0 for black background
// 1 for white background

#declare featureCode = 0;
// 0 for all four angles
// 1 for argument of the periapsis only 
// 2 for longitude of the ascending node only
// 3 for inclination only
// 4 for true anomaly only

#declare axesOn = 0;
// 0 for X, Y, Z axes off
// 1 for X, Y, Z axes on

//---------------------------------------------
   
// Classical Orbital Elements (NOTICE: if these are changed, then the labels must be replaced since it changes the scene!!!)
#declare Sma=20;        // Semimajor axis
#declare ecc=0.6;       // Eccentricity
#declare Omega = 60;    // Longitude of the ascending node, deg
#declare Incl= 60;      // Inclination, deg
#declare omega_ = 140;  // Argument of the periapsis, deg
#declare nu = 250;      // True anomaly, deg, must be in [0,360]

// Derived variables
#declare Smi=sqrt(Sma*Sma*(1-ecc*ecc));  // Semiminor axis
#declare r = Sma*(1-ecc*ecc)/(1+ecc*cos(nu*pi/180)); // distance between major body and minor body


// Texture for latitude and longitude lines on planet
#declare txtLatLonGrid=texture { 
  pigment {color rgb <.4,.7,1>}
  finish {ambient .6}            
  }

// Texture for planet  
#declare txtPlanet=texture {   
  pigment {color rgb <0,.5,1>}
  finish {ambient .6}
  }

// Texture with latitudes only
#local txtLatitudes=texture { 
  gradient y
  texture_map {
    [0 txtPlanet]
    #local Cnt=-9;
    #while (Cnt<9)
      [.5+sin(Cnt*.174533-.02)/2 txtPlanet]
      [.5+sin(Cnt*.174533-.02)/2 txtLatLonGrid]
      [.5+sin(Cnt*.174533+.02)/2 txtLatLonGrid]
      [.5+sin(Cnt*.174533+.02)/2 txtPlanet]
      #local Cnt=Cnt+3;
    #end
    [1 txtPlanet]
    }
  translate <0,-.5,0>
  scale 10    
  }

#local Arrowhead=difference {
  box {<-5,-.002,0>,<0,.002,5> rotate <0,45,0> scale <1,1,3>}
  plane {<0,0,-1>,-1.5}    
  }      
#local AxesArrowhead=difference {
  box {<-6,-.0009,0>,<0,.0009,6> rotate <0,45,0> scale <1,1,3>}
  plane {<0,0,-1>,-2}    
  }  

#macro AngleArc(DegreeNumber,Radius,ArrowheadState,rgbVec)
    #if (DegreeNumber <= 180)  
        #if (ArrowheadState = 0) //Have both arrow heads
          merge {
            difference {
              cylinder {<0,-.002,0>,<0,.002,0>,Radius+.1}
              cylinder {<0,-1,0>,<0,1,0>,Radius-.1}
              plane {<0,0,1>,0 rotate <0,degrees(asin(1/Radius)),0>}
              plane {<0,0,-1>,0 rotate <0,DegreeNumber-degrees(asin(1/Radius)),0>}
              }
            #object {Arrowhead rotate <0,-6,0> translate <Radius,0,0> rotate <0,DegreeNumber-180,0>}
            #object {Arrowhead rotate <0,6,0> translate <-Radius,0,0>}
            
            pigment {color rgb rgbVec}
            finish {ambient 1}
            }   
        #elseif (ArrowheadState = 1) //Have starting arrow head only
          merge {
            difference {
              cylinder {<0,-.002,0>,<0,.002,0>,Radius+.1}
              cylinder {<0,-1,0>,<0,1,0>,Radius-.1}
              plane {<0,0,1>,0 rotate <0,degrees(asin(1/Radius)),0>} 
              plane {<0,0,-1>,0 rotate <0,DegreeNumber,0>}
              }
            #object {Arrowhead rotate <0,6,0> translate <-Radius,0,0>}
            
            pigment {color rgb rgbVec}
            finish {ambient 1}
            }
        #elseif (ArrowheadState = 2) //Have ending arrow head only
          merge {
            difference {
              cylinder {<0,-.002,0>,<0,.002,0>,Radius+.1}
              cylinder {<0,-1,0>,<0,1,0>,Radius-.1}
              plane {<0,0,1>,0 rotate <0,0,0>}
              plane {<0,0,-1>,0 rotate <0,DegreeNumber-degrees(asin(1/Radius)),0>}
              }
            #object {Arrowhead rotate <0,-6,0> translate <Radius,0,0> rotate <0,DegreeNumber-180,0>}
            
            pigment {color rgb rgbVec}
            finish {ambient 1}
            no_shadow
            }
        #end
    #else //DegreeNumber > 180
       #if (ArrowheadState = 0) //Have both arrow heads
          merge {
            difference {
              cylinder {<0,-.002,0>,<0,.002,0>,Radius+.1}
              cylinder {<0,-1,0>,<0,1,0>,Radius-.1}
              plane {<0,0,-1>,0 rotate <0,DegreeNumber-degrees(asin(1/Radius)),0>}   
              plane {<0,0,-1>,0 rotate <0,DegreeNumber,0>}
              }
            difference {
              cylinder {<0,-.002,0>,<0,.002,0>,Radius+.1}
              cylinder {<0,-1,0>,<0,1,0>,Radius-.1}
              plane {<0,0,1>,0 rotate <0,degrees(asin(1/Radius)),0>}
              }
            #object {Arrowhead rotate <0,-6,0> translate <Radius,0,0> rotate <0,DegreeNumber-180,0>}
            #object {Arrowhead rotate <0,6,0> translate <-Radius,0,0>}
            
            pigment {color rgb rgbVec}
            finish {ambient 1}
            no_shadow
            }
        #elseif (ArrowheadState = 1) //Have starting arrow head only
          merge {
            difference {
              cylinder {<0,-.002,0>,<0,.002,0>,Radius+.1}
              cylinder {<0,-1,0>,<0,1,0>,Radius-.1}  
              plane {<0,0,-1>,0 rotate <0,DegreeNumber,0>}
              }
            difference {
              cylinder {<0,-.002,0>,<0,.002,0>,Radius+.1}
              cylinder {<0,-1,0>,<0,1,0>,Radius-.1}
              plane {<0,0,1>,0 rotate <0,degrees(asin(1/Radius)),0>}
              }
            #object {Arrowhead rotate <0,6,0> translate <-Radius,0,0>}
            
            pigment {color rgb rgbVec}
            finish {ambient 1}
            no_shadow
            }
        #elseif (ArrowheadState = 2) //Have ending arrow head only      
          merge {
            difference {
              cylinder {<0,-.002,0>,<0,.002,0>,Radius+.1}
              cylinder {<0,-1,0>,<0,1,0>,Radius-.1}
              plane {<0,0,-1>,0 rotate <0,DegreeNumber-degrees(asin(1/Radius)),0>}   
              plane {<0,0,-1>,0 rotate <0,DegreeNumber,0>}
              }
            difference {
              cylinder {<0,-.002,0>,<0,.002,0>,Radius+.1}
              cylinder {<0,-1,0>,<0,1,0>,Radius-.1}
              plane {<0,0,1>,0 rotate <0,0,0>}
              }
            #object {Arrowhead rotate <0,-6,0> translate <Radius,0,0> rotate <0,DegreeNumber-180,0>}
            
            pigment {color rgb rgbVec}
            finish {ambient 1}
            no_shadow
            }
        #end
    #end    
#end  

#if (backgroundColor = 0)
   background {color rgb <0,0,0>}
   #declare arcRgbVec = <1,1,1>;
   #declare nodeRgbVec = <0.7,0.7,0.7>;

#else
   background {color rgb <1,1,1>}
   #declare arcRgbVec = <0,0,0>;
   #declare nodeRgbVec = <0.8,0.8,0.8>;
#end    

#if (axesOn = 1)
  //Red arrow along x-axis of inertial frame 
  merge {   
    box {<-.3,-.001,0>,<.3,.001,-9>}    
    #object {AxesArrowhead translate <0,0,-10>} 
    pigment {color rgb <.8,0,0>}
    finish {ambient 1 diffuse 0}           
    rotate <0,0,0>
    no_shadow}
  
  //Green arrow along y-axis of inertial frame   
  merge {     
    box {<0,-.001,-.2>,<9,.001,.2>}    
    #object {AxesArrowhead rotate <0,-90,0> translate <10,0,0>}
    pigment {color rgb <0,.8,0>}
    finish {ambient 1 diffuse 0}           
    rotate <0,0,0>
    no_shadow}
  
  //Blue arrow along z-axis of inertial frame
  merge {    
    box {<-.2,0,-.001>,<.2,9,.001>}    
    #object {AxesArrowhead rotate <90,0,0> translate <0,10,0>}
    pigment {color rgb <0,0,1>}       
    finish {ambient 1 diffuse 0}           
    rotate <0,0,0>
    no_shadow}
#end

// Major body ("blue sphere")
sphere {<0,0,0>,5
  texture {
    object {
      union {
        #local Cnt=0;
        #while (Cnt<18)
          box {<-.1,-8,-8>,<.1,8,8> rotate <0,10*Cnt+11,0>}
          #local Cnt=Cnt+3;
        #end
        }
      texture {txtLatitudes}
      texture {txtLatLonGrid}      
      }
    }
  }

#if (featureCode = 0 | featureCode = 2)
  merge {
    //Arrow for reference direction (typically the vernal point)
    box {<-.2,-.0021,0>,<.2,.0021,-23>}      
    #object {Arrowhead translate <0,0,-24>}  
    
    pigment {color rgb<1,0,1>}             
    finish {ambient 1 diffuse 0}           
    rotate <0,0,0>                         
    }
#end

// Longitude of ascending node arc
#if (featureCode=0 | featureCode=2)
  #object { 
    #if (featureCode=2)
     AngleArc(Omega,18,1,arcRgbVec)
    #else
     AngleArc(Omega,5.75,1,arcRgbVec)  
    #end
    rotate <0,270-Omega,0>}  
#end

// Orbit plane texture   
#local txtOrbitPlane=texture {    
  pigment {color rgbt<1,.9,0,0.5>}
  finish {ambient .6}            
  }

// Texture for markings on orbit plane
#local txtOrbitMarking=texture {
  pigment {color rgb<1,.9,0>} 
  finish {ambient 1 diffuse 0}
  }

union {
  //Cylinder to graphically find normal to orbital plane
  //cylinder {<sqrt(Sma*Sma-Smi*Smi),-60,0>,<sqrt(Sma*Sma-Smi*Smi),60,0>,.1 
  //  pigment {color rgb<1,1,0>} 
  //  finish {ambient 1 diffuse 0}}

  // Elliptic "disk" indicating the area inside the orbit
  disc {0,<0,1,0>,1,0
    scale <Sma,1,Smi>
    translate <sqrt(Sma*Sma-Smi*Smi),0,0>
    texture {
      #if (featureCode=0|featureCode=3)
        object {
          difference {
            box {<-1,-1,#if (featureCode=0) -9 #else -18 #end>,<1,1,0>}
            box {<-.8,-2,-1.8>,<.6,2,1>}
            box {<-2,-2,-99>,<.6,2,-2>}        
            #if (featureCode=0)
              translate <16,0,0>
            #else
              translate <7,0,0>
            #end
            rotate <0,-40,0>
            }
          texture {txtOrbitPlane}
          texture {txtOrbitMarking}
          }
      #else
        txtOrbitPlane
      #end
      }
    }
  
  difference {  
    // Orbit edge outline
    cylinder {<0,-.001,0>,<0,.001,0>,1
      scale <Sma+.15,1,Smi+.15>
      }
    cylinder {<0,-1,0>,<0,1,0>,1
      scale <Sma-.15,1,Smi-.15>
      }
    translate <sqrt(Sma*Sma-Smi*Smi),0,0>
    pigment {
      radial
      color_map{
        [0 color rgbt <1,1,0,0>]
        [0.1 color rgbt <1,1,.2,0>]
        [0.3 color rgbt <1,1,.3,0>]
        [0.7 color rgbt <1,1,.4,.5>]
        [.9 color rgbt <1,1,.5,1>]
        [1 color rgbt <1,1,.6,1>]
        }  
      
      rotate <0,180-nu,0>
      }
    finish {ambient 1 diffuse 0}
    }
  
  // Argument of periapsis arc
  #if (featureCode=0)
    #object {AngleArc(omega_,6.5,1,arcRgbVec)} 
  #end
  #if (featureCode=1)
    #object {AngleArc(omega_,9,1,arcRgbVec)}   // Larger arc for argument of periapsis only
  #end
  
  // Minor body ("yellow moon")
  #declare minorBodyPosVec = <0,0,0>;

  #if (nu < 90)
    #declare minorBodyXpos = -r*cos(nu*pi/180);
    #declare minorBodyZpos = -r*sin(nu*pi/180);
  #else
    #declare minorBodyXpos = r*cos(nu*pi/180 - pi);
    #declare minorBodyZpos = r*sin(nu*pi/180 - pi);
  #end  
  
  #declare minorBodyPosVec = <minorBodyXpos,0,minorBodyZpos>;
  
  sphere {
  minorBodyPosVec,1
  pigment {color rgb <1,.8,0>}
  finish {ambient .6}
  }     
  
  #if (featureCode = 0 | featureCode = 4)
      // Line from major body to minor body
      cylinder {
      <0,0,0>,
      minorBodyPosVec,.1
      pigment {color rgb<0,1,1>}
      finish {ambient 1 diffuse 0}
      }   
      // True anomaly arc
      #object {AngleArc(nu,7.25,1,arcRgbVec) rotate <0,360-nu,0>}  
  #end
  
  // Line of apsides    
  #if (featureCode = 0 | featureCode = 1 | featureCode = 4)
    cylinder {
      <sqrt(Sma*Sma-Smi*Smi)-Sma-50,0,0>,
      <sqrt(Sma*Sma-Smi*Smi)+Sma+50,0,0>,.1
      pigment {color rgb<1,0,0>}
      finish {ambient 1 diffuse 0}
      }
  #end
  
  #if (featureCode = 0 | featureCode = 1 | featureCode = 4)
    // Periapsis node
    sphere {<sqrt(Sma*Sma-Smi*Smi)-Sma,0,0>,.5 pigment {color rgb nodeRgbVec} finish {ambient 1 diffuse 0}}
  #end
  
  #if (featureCode = 0 | featureCode = 1 | featureCode = 4)
    // Apoapsis node
    sphere {<sqrt(Sma*Sma-Smi*Smi)+Sma,0,0>,.5 pigment {color rgb nodeRgbVec} finish {ambient 1 diffuse 0}}
  #end
    
  no_shadow
  // Order of elements in rotation tuple DOES MATTER: in rotate function, rotation occurs about x-axis first, then y-axis, then z-axis
  // Order of applying rotations to orient the ellipse DOES MATTER: 
  //    1) rotate about z-axis by argument of the periapsis, omega
  //    2) rotate about x-axis by inclination, inc
  //    3) rotate about z-axis by longitude of the ascending node, Omega   
  // Note: Coordinate frame is screwed up: it is (y,z,x)... SHOULD FIX THIS
  rotate <0,-90,0> // this rotations is needed because the ellipse was not intially oriented correctly... SHOULD FIX THIS
  rotate <0,-omega_,0>  //130 deg rotation about z-axis (but actually the screwed up y axis) 
  rotate <0,0,Incl>  //then 60 deg rotation about x-axis (but actuall the screwed up z axis)
  rotate <0,-Omega,0>  //then 60 deg rotation about z-axis (but actually the screwed up y axis)
}

union {
  #if (featureCode != 4)
    // Line of nodes
    cylinder {<-60,0,0>,<60,0,0>,.1 pigment {color rgb<0,1,0>} finish {ambient 1 diffuse 0}}
  
    // Ascending node
    sphere {<23.6,0,0>,.5 pigment {color rgb nodeRgbVec} finish {ambient 1 diffuse 0}}
    
    // Descending node
    sphere {<-8.8,0,0>,.5 pigment {color rgb nodeRgbVec} finish {ambient 1 diffuse 0}}
  #end
  
  #if (featureCode=0)
    // Measure of inclination
    #object {AngleArc(Incl,8,2,arcRgbVec)  
      rotate <90,-90,0> translate <16.8,0,0>}
      no_shadow
  #end
  #if (featureCode=3)
    // Measure of inclination
    #object {AngleArc(Incl,17,0,arcRgbVec) 
      rotate <90,-90,0> translate <7.8,0,0>}
      no_shadow
  #end

  rotate <0,90-Omega,0> 
}    

//Texture for reference plane
#local RefPlaneChecker=texture {  // Texture for 
  pigment {checker                // reference
    color rgbt<.6,.7,1,.5>        // plane
    color rgbt<.48,.56,.8,.5>
    scale 3
    }
  finish {ambient .4}
  }

//Texture for markings on reference plane
#local RefPlaneMark=texture {     // Texture for
  pigment {checker                // markings on
    color rgbt<.6,.7,1,0>         // reference
    color rgbt<.48,.56,.8,0>      // plane
    scale 3
    }
  finish {ambient 1 diffuse 0}
  }


merge { // The reference plane
  triangle {<-9,0,-21>,<21,0,-21>,<-9,0,9>}
  triangle {<21,0,9>,<21,0,-21>,<-9,0,9>}
  texture {
    #if (featureCode=0|featureCode=3)
      object {
        difference {
          box {<-1,-1,#if (featureCode=0) -9 #else -18 #end>,<1,1,0>}
          box {<-.8,-2,-1.8>,<.6,2,1>}
          box {<-2,-2,-99>,<.6,2,-2>}        
          #if (featureCode=0)
            translate <16,0,0>
          #else
            translate <7,0,0>
          #end
          rotate <0,90-Omega,0>
          }
        texture {RefPlaneChecker}
        texture {RefPlaneMark}
        }
    #else
      RefPlaneChecker
    #end
    }
  }           
  
#switch (view)
    #case (0) // Isometric view
    union { // A, B, C, and D are common for all four images...
    
      // A: Orbiting body
      text {ttf "timesbi.ttf","A",.001,0         
        scale 0.0035 translate <.0135,.014,0>} 
      
      // B: Body being orbited
      text {ttf "timesbi.ttf","B",.001,0         
        scale .0035 translate <-.0045,.0092,0>}
      
      // C: Reference plane
      text {ttf "timesbi.ttf","C",.001,0         
        scale .0035 translate <-.016,-.002,0>}
      
      // D: Orbital plane of A
      text {ttf "timesbi.ttf","D",-.001,0        
        scale .0035 translate <-.002,-.013,0>}
      
      // Deal with "special cases" in each of the four images:
      #switch (featureCode) 
      #case (0) // Letter markings for viewing all four angles
      
        // "Upper-case" Omega at the longitude of ascending node
        text {ttf "symbol.ttf","W",.001,0            
          scale .0035 translate <-.002,0.0038,0>}
        
        // "Lower-case" nu at the true anomaly
        text {ttf "symbol.ttf","\u006E",.001,0      
          scale .0035 translate <.0034,0.007,0>}
        
        // "Lower-case" omega at the argument of the periapsis 
        text {ttf "symbol.ttf","w",.001,0          
          scale .0035 translate <-0.001,.017,0>}
        
        // "Lower-case" i at the inclination
        text {ttf "timesbi.ttf","i",.001,0         
          scale .0035 translate <.0045,-.0083,0>}
          
        // E: Ascending node  
        text {ttf "timesbi.ttf","E",.001,0
          scale .0035 translate <.0145,-.003,0>}         
          
        // F: Descending node
        text {ttf "timesbi.ttf","F",.001,0         
           scale .0035 translate <-.011,.013,0>} 
          
        // G: Periapsis
        text {ttf "timesbi.ttf","G",.001,0
          scale .0035 translate <-.008,.0175,0>}
          
        // H: Apoapsis
        text {ttf "timesbi.ttf","H",.001,0         
          scale .0035 translate <.006,-.0182,0>}
          
        // J: Reference direction, e.g. vernal point
        text {ttf "timesbi.ttf","J",.001,0         
          scale .0035 translate <-.0145,-.014,0>}  
        #break
     
      #case (1)  // Letter markings for viewing only argument of periapsis 
      
        // "lower-case" omega at argument of periapsis
        text {ttf "symbol.ttf","w",.001,0          
          scale .007 translate <.0053,.01,0>}
          
        // E: Ascending node     
        text {ttf "timesbi.ttf","E",.001,0         
          scale .0035 translate <.0149,-.003,0>}
        
        // F: Periapsis
        text {ttf "timesbi.ttf","F",-.001,0     
          scale .0035 translate <-.0085,.0167,0>}
        #break
        
      #case (2) // Letter markings for viewing only longitude of ascending node 
      
        // "Upper-case" Omega at longitude of ascending node 
        text {ttf "symbol.ttf","W",.001,0          
          scale .007 translate <0.0005,-.009,0>}
        
        // E: Ascending node  
        text {ttf "timesbi.ttf","E",.001,0
          scale .0035 translate <.0145,-.003,0>}         
          
        // F: Descending node
        text {ttf "timesbi.ttf","F",.001,0         
           scale .0035 translate <-.011,.013,0>} 
        #break
        
      #case (3) // Letter markings for viewing only the inclination
        
        // E: Ascending node  
        text {ttf "timesbi.ttf","E",.001,0
          scale .0035 translate <.0145,-.003,0>}         
          
        // F: Descending node
        text {ttf "timesbi.ttf","F",.001,0         
           scale .0035 translate <-.011,.013,0>}
        
        // "Lower-case" i at the inclination
        text {ttf "timesbi.ttf","i",.001,0         
          scale .007 translate <-.011,-.012,0>}
        #break       
        
      #case (4) // Letter markings for viewing only the true anomaly
      
        // "Lower-case" nu at the true anomaly
        text {ttf "symbol.ttf","\u006E",.001,0      
          scale .007 translate <.0015,0.002,0>}
          
        // G: Periapsis
        text {ttf "timesbi.ttf","G",.001,0
          scale .0035 translate <-.008,.0175,0>}
          
        // H: Apoapsis
        text {ttf "timesbi.ttf","H",.001,0         
          scale .0035 translate <.006,-.0182,0>}
        #break
      #end
      
      // Common settings for the letters in the image
      #if (backgroundColor = 0)
        pigment {color rgb<1,1,1>}
      #else
        pigment {color rgb<0,0,0>}
      #end
        
      finish {ambient 1 diffuse 0}
      no_shadow
                        
      translate <0,0,.04>
      rotate <51.3765,-13.62699,0>
      translate <11,26,-33>
      }
      
    #case(1) // View normal to the reference plane
    union { // A, B, C, and D are common for all four images...:
      
      // A: Orbiting body
      text {ttf "timesbi.ttf","A",.001,0         
        scale 0.0035 translate <.0095,.0038,0>} 
      
      // B: Body being orbited
      text {ttf "timesbi.ttf","B",.001,0         
        scale .0035 translate <-.009,.004,0>}
      
      // C: Reference plane
      text {ttf "timesbi.ttf","C",.001,0         
        scale .0035 translate <-.011,-.007,0>}
      
      // D: Orbital plane of A
      text {ttf "timesbi.ttf","D",-.001,0        
        scale .0035 translate <.0075,-.008,0>}
      
      // Deal with "special cases" in each of the four images:
      #switch (featureCode) 
      #case (0)  // Letter markings for viewing all four angles
      
        // "Upper-case" Omega at the longitude of ascending node
        text {ttf "symbol.ttf","W",.001,0            
          scale .0035 translate <-.004,-0.0022,0>}
        
        // "Lower-case" nu at the true anomaly
        text {ttf "symbol.ttf","\u006E",.001,0      
          scale .0035 translate <.0012,0.0018,0>}
        
        // "Lower-case" omega at the argument of the periapsis 
        text {ttf "symbol.ttf","w",.001,0          
          scale .0035 translate <-0.0035,.0085,0>}
        
        // "Lower-case" i at the inclination
        text {ttf "timesbi.ttf","i",.001,0         
          scale .0035 translate <.003,-.007,0>}
          
        // E: Ascending node  
        text {ttf "timesbi.ttf","E",.001,0         
          scale .0035 translate <.0135,-.005,0>}      
          
        // F: Descending node
        text {ttf "timesbi.ttf","F",.001,0         
           scale .0035 translate <-.0153,.0065,0>}
          
        // G: Periapsis
        text {ttf "timesbi.ttf","G",.001,0
          scale .0035 translate <-.01,.012,0>}
          
        // H: Apoapsis
        text {ttf "timesbi.ttf","H",.001,0         
          scale .0035 translate <.005,-.013,0>}
          
        // J: Reference direction, e.g. vernal point
        text {ttf "timesbi.ttf","J",.001,0         
          scale .0035 translate <-0.0051,-.0174,0>}  
        #break
     
      #case (1) // Letter markings for viewing only argument of periapsis 
      
        // "lower-case" omega at argument of periapsis
        text {ttf "symbol.ttf","w",.001,0          
          scale .007 translate <-.002,.01,0>}
          
        // E: Ascending node  
        text {ttf "timesbi.ttf","E",.001,0         
          scale .0035 translate <.0135,-.005,0>}      
          
        // F: Descending node
        text {ttf "timesbi.ttf","F",.001,0         
           scale .0035 translate <-.0153,.0065,0>}
          
        // G: Periapsis
        text {ttf "timesbi.ttf","G",.001,0
          scale .0035 translate <-.0125,.012,0>}
          
        // H: Apoapsis
        text {ttf "timesbi.ttf","H",.001,0         
          scale .0035 translate <.005,-.013,0>}
        #break
        
      #case (2) // Letter markings for viewing only longitude of ascending node 
      
        // "Upper-case" Omega at longitude of ascending node 
        text {ttf "symbol.ttf","W",.001,0          
          scale .007 translate <-0.0015,-.0075,0>}
        
        // E: Ascending node  
        text {ttf "timesbi.ttf","E",.001,0         
          scale .0035 translate <.0135,-.005,0>}      
          
        // F: Descending node
        text {ttf "timesbi.ttf","F",.001,0         
           scale .0035 translate <-.0153,.0065,0>}
        
        // J: Reference direction, e.g. vernal point
        text {ttf "timesbi.ttf","J",.001,0         
          scale .0035 translate <-0.0051,-.0174,0>}  
        #break
        
      #case (3) // Letter markings for viewing only the inclination
      
        // E: Ascending node  
        text {ttf "timesbi.ttf","E",.001,0         
          scale .0035 translate <.0135,-.005,0>}      
          
        // F: Descending node
        text {ttf "timesbi.ttf","F",.001,0         
           scale .0035 translate <-.0153,.0065,0>}
           
        // "Lower-case" i at the inclination
        text {ttf "timesbi.ttf","i",.001,0         
          scale .007 translate <-.005,-.012,0>}
        #break       
        
      #case (4) // Letter markings for viewing only the true anomaly
      
        // "Lower-case" nu at the true anomaly
        text {ttf "symbol.ttf","\u006E",.001,0      
          scale .007 translate <.0005,-0.0015,0>}
        
        // G: Periapsis
        text {ttf "timesbi.ttf","G",.001,0
          scale .0035 translate <-.01,.012,0>}
          
        // H: Apoapsis
        text {ttf "timesbi.ttf","H",.001,0         
          scale .0035 translate <.005,-.013,0>}
        #break
      #end
      
      // Common settings for the letters in the image
      #if (backgroundColor = 0)
        pigment {color rgb<1,1,1>}
      #else
        pigment {color rgb<0,0,0>}
      #end
        
      finish {ambient 1 diffuse 0}
      no_shadow
      
      rotate <90,0,0>
      translate <6,44.96,-6>
      }
      
    #case (2) // View normal to the orbital plane
    union { // A, B, C, and D are common for all four images...
      
      // A: Orbiting body
      text {ttf "timesbi.ttf","A",.001,0         
        scale 0.0025 translate <0.0034,.0533,0>} 
      
      // B: Body being orbited
      text {ttf "timesbi.ttf","B",.001,0         
        scale .0025 translate <-.007,.0475,0>}
      
      // C: Reference plane
      text {ttf "timesbi.ttf","C",.001,0         
        scale .0025 translate <0.01,0.0452,0>}
      
      // Deal with "special cases" in each of the four images:
      #switch (featureCode) 
      #case (0) // Letter markings for viewing all four angles
      
        // "Upper-case" Omega at the longitude of ascending node
        text {ttf "symbol.ttf","W",.001,0            
          scale .0025 translate <-0.0025,.0455,0>}
        
        // "Lower-case" nu at the true anomaly
        text {ttf "symbol.ttf","\u006E",.001,0      
          scale .0025 translate <-.00084,0.0484,0>}
        
        // "Lower-case" omega at the argument of the periapsis 
        text {ttf "symbol.ttf","w",.001,0          
          scale .0025 translate <-.005,0.052,0>}
        
        // "Lower-case" i at the inclination
        text {ttf "timesbi.ttf","i",.001,0         
          scale .0025 translate <.0053,0.043,0>}
          
        // E: Ascending node  
        text {ttf "timesbi.ttf","E",.001,0         
          scale .0025 translate <.0087,.0483,0>}          
          
        // F: Descending node
        text {ttf "timesbi.ttf","F",.001,0         
          scale .0025 translate <-0.0127,0.04692,0>}
          
        // G: Periapsis
        text {ttf "timesbi.ttf","G",.001,0         
          scale .0025 translate <-.0111,0.0505,0>}
          
        // H: Apoapsis
        text {ttf "timesbi.ttf","H",.001,0 
          scale .0025 translate <.0092,0.034,0>}        
          
        // J: Reference direction, e.g. vernal point
        text {ttf "timesbi.ttf","J",.001,0         
          scale .0025 translate <0.0025,0.039,0>}  
        #break
        
        // D: Orbital plane of A
        text {ttf "timesbi.ttf","D",-.001,0        
          scale .0025 translate <-.003,0.036,0>}
     
      #case (1) // Letter markings for viewing only argument of periapsis 
      
        // "lower-case" omega at argument of periapsis
        text {ttf "symbol.ttf","w",.001,0
          scale .005 translate <-.006,0.0535,0>} 
          
        // E: Ascending node     
        text {ttf "timesbi.ttf","E",.001,0         
          scale .0025 translate <0.0085,0.0483,0>}
          
        // F: Descending node
        text {ttf "timesbi.ttf","F",.001,0         
          scale .0025 translate <-0.0127,0.04692,0>}
        
        // G: Periapsis
        text {ttf "timesbi.ttf","G",.001,0         
          scale .0025 translate <-.0111,0.0505,0>}
          
        // H: Apoapsis
        text {ttf "timesbi.ttf","H",.001,0 
          scale .0025 translate <.0092,0.034,0>}
        
        // D: Orbital plane of A
        text {ttf "timesbi.ttf","D",-.001,0        
          scale .0025 translate <-.003,0.036,0>}
        
      #case (2) // Letter markings for viewing only longitude of ascending node 
      
        // "Upper-case" Omega at the longitude of ascending node
        text {ttf "symbol.ttf","W",.001,0            
          scale .0045 translate <0.0042,.0425,0>}
        
        // E: Ascending node  
        text {ttf "timesbi.ttf","E",.001,0         
          scale .0025 translate <.0087,.0483,0>}          
          
        // F: Descending node
        text {ttf "timesbi.ttf","F",.001,0         
          scale .0025 translate <-0.0127,0.04692,0>}   
          
        // J: Reference direction, e.g. vernal point
        text {ttf "timesbi.ttf","J",.001,0         
          scale .0025 translate <0.0025,0.039,0>}
        
        // D: Orbital plane of A
        text {ttf "timesbi.ttf","D",-.001,0        
          scale .0025 translate <-.003,0.036,0>}  
        
        #break
        
      #case (3) // Letter markings for viewing only the inclination
        
        // "Lower-case" i at the inclination
        text {ttf "timesbi.ttf","i",.001,0         
          scale .005 translate <-.003,0.038,0>}
        
        // E: Ascending node  
        text {ttf "timesbi.ttf","E",.001,0         
          scale .0025 translate <.0087,.0483,0>}          
          
        // F: Descending node
        text {ttf "timesbi.ttf","F",.001,0         
          scale .0025 translate <-0.0127,0.04692,0>}
          
        // "Lower-case" i at the inclination
        text {ttf "timesbi.ttf","i",.001,0         
          scale .007 translate <-.011,-.012,0>}
          
        // D: Orbital plane of A
        text {ttf "timesbi.ttf","D",-.001,0        
          scale .0025 translate <0.0025,0.036,0>}
        #break       
        
      #case (4) // Letter markings for viewing only the true anomaly 
      
        // "Lower-case" nu at the true anomaly
        text {ttf "symbol.ttf","\u006E",.001,0      
          scale .005 translate <-.0011,0.0445,0>}
          
        // D: Orbital plane of A
        text {ttf "timesbi.ttf","D",-.001,0        
          scale .0025 translate <-.003,0.036,0>}
          
        // G: Periapsis
        text {ttf "timesbi.ttf","G",.001,0         
          scale .0025 translate <-.0111,0.0505,0>}
          
        // H: Apoapsis
        text {ttf "timesbi.ttf","H",.001,0 
          scale .0025 translate <.0092,0.034,0>} 
        #break
      #end
      
      // Common settings for the letters in the image
      #if (backgroundColor = 0)
        pigment {color rgb<1,1,1>}
      #else
        pigment {color rgb<0,0,0>}
      #end
        
      finish {ambient 1 diffuse 0}
      no_shadow
      
      rotate <30,30,0>
      translate <-12.45,14.65,-40>
      }
    #end


// Viewpoint - DO NOT CHANGE without recalculating the translate and rotate above,
// which align the letter markings in the image with the camera's viewing angle
#if (view = 0)
    camera {                    
        right <1,0,0> up <0,1,0>
        //right <1.33,0,0> up <0,1,0> 
        location <11,26,-33>     
        look_at <3,-16.5,0>
        angle 58                                                                             
        }
#elseif (view = 1)
    camera {
        right <1,0,0> up <0,1,0>
        location <6,45,-6>
        look_at <6,0,-6>
        angle 54
        }

#elseif (view = 2) 
    camera {
        right <1,0,0> up <0,1,0>
        location <-12.45,14.7,-40>
        look_at <6.032,-6.680,-7.936>
        angle 58
        } 
#end

light_source {<10000,5000,-5000> color rgb 1}

說明

添加單行說明來描述出檔案所代表的內容
Raytraced image showing the concepts of inclination (i), longitude of the ascending node (Ω), argument of the periapsis (ω), and true anomaly (ν) for a "minor" object in an elliptic orbit around a larger object.

在此檔案描寫的項目

描繪內容 繁體中文

Kúi-tō kheng-siâ-kak 閩南語

kīn-kióng-tiám 閩南語

著作權狀態 繁體中文

有著作權 繁體中文

多媒體型式 繁體中文

image/png

校驗和 繁體中文

f9096656ca785422e44d9238afe828549de4b8a5

斷定方法 繁體中文: SHA-1 中文 (已轉換拼寫)

資料大小 繁體中文

202,025 Byte

高度 繁體中文

1,200 ōe-sò͘

寬度 繁體中文

1,200 ōe-sò͘

Ùng-giông lĭk-sṳ̄

Sōng-dĕk siŏh bĭk nĭk-gĭ/sì-găng lì káng hiā sèng-hâiu gì ùng-giông.

Nĭk-gĭ/Sì-găngSáuk-liŏk-dùChióh-cháungÊ̤ṳng-hôSuók-mìng
hiêng-káik-sì2023 nièng 11 nguŏk 29 hô̤ (B3) 16:522023 nièng 11 nguŏk 29 hô̤ (B3) 16:52 bēng-buōng gì sáuk-liŏk-dù1,200 × 1,200（268 KB）Aero BSCAdded true anomaly angle, line from major body to minor body, and directionality of arrows
2005 nièng 11 nguŏk 27 hô̤ (LB) 15:492005 nièng 11 nguŏk 27 hô̤ (LB) 15:49 bēng-buōng gì sáuk-liŏk-dù1,200 × 1,200（197 KB）Peo~commonswikiReordered letter annotations. Scene description modified to render several images.
2005 nièng 11 nguŏk 23 hô̤ (B3) 20:582005 nièng 11 nguŏk 23 hô̤ (B3) 20:58 bēng-buōng gì sáuk-liŏk-dù1,200 × 1,200（198 KB）Peo~commonswiki== Beskrivelse == Raytraced image showing the concepts of inclination, longitude of the ascending node, and argument of the periapsis for a "minor" object in an elliptic orbit around a larger object. Raytraced using the Persistence of Vision Raytracer an

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