Empty focus for Locus

[eburacum45]

Hi!
I've got a little request for help; it may or may not be straightforward enough, but I can't quite figure out how to do it.
Recently I've created a world for Orion's Arm which is both tidally locked and high;ly eccentric. Among other things this means the planet receives sunlight all over its surface to varying degrees, as the sunward hemisphere points more-or-less directly at the empty focus of the orbit. (This is a phenomenon mentioned over at Bautforum a year or two ago).

I've made a reasonably successful texture for this world, and it can be seen on the OA site here
http://www.orionsarm.com/eg-article/4eb9314768886
but I wonder if anyone can figure out how to align this planet so that it faces the empty focus of its orbit.

Code: Select all

"locus" "JD 9044191"
{
Texture "locus3.*"
SpecularTexture "locus3spec.*"
BumpMap "locus3bump.*"
BumpHeight 3
NightTexture "locusnight.*"
Radius 5832

Color [ 0.85 0.85 1.0 ]
SpecularColor [ 0.5 0.5 0.55 ]
   SpecularPower 25.0


   

   Atmosphere {
      Height 60
      Lower [ 0.43 0.52 0.65 ]
      Upper [ 0.26 0.47 0.84 ]
      Sky [ 0.40 0.6 1.0 ]
      Sunset [ 1.0 0.6 0.2 ]
      CloudHeight 7
      CloudSpeed 65
      CloudMap   "locusclouds.png"

      Mie 0.01
      MieAsymmetry -0.25
      Rayleigh [ 0.002 0.004 0.01 ]
      MieScaleHeight 12
   }
EllipticalOrbit
   {
   Period         0.199
   SemiMajorAxis  0.271
Inclination 0.04
Eccentricity 0.75
ArgOfPericenter 320
MeanAnomaly     100
   
   }


RotationPeriod   0.0
   Obliquity        19
Albedo 0.37
}


Any help would be appreciated...

[selden]

Well, you could force it: place an invisible, unmoving object at the secondary focus and use a two-vector frame which points its primary axis at the unmoving object for the BodyFrame for the orbiting object.

[eburacum45]

That is more-or-less the method I was thinking of, except how do I define the location of the invisible object?

[selden]

Here's what I came up with, after reviewing the definition of the position of a focus in the Wikipedia article on ellipses.

Code: Select all

"locus" "JD 9044191"
{
   Texture "locus3.*"
   SpecularTexture "locus3spec.*"
   BumpMap "locus3bump.*"
   BumpHeight 3
   NightTexture "locusnight.*"
   Radius 5832

   Color [ 0.85 0.85 1.0 ]
   SpecularColor [ 0.5 0.5 0.55 ]
   SpecularPower 25.0

   Atmosphere {
      Height 60
      Lower [ 0.43 0.52 0.65 ]
      Upper [ 0.26 0.47 0.84 ]
      Sky [ 0.40 0.6 1.0 ]
      Sunset [ 1.0 0.6 0.2 ]
      CloudHeight 7
      CloudSpeed 65
      CloudMap   "locusclouds.png"

      Mie 0.01
      MieAsymmetry -0.25
      Rayleigh [ 0.002 0.004 0.01 ]
      MieScaleHeight 12
   }
   EllipticalOrbit
     {
       Period         0.199
       SemiMajorAxis  0.271
       Inclination 0.04
       Eccentricity 0.75
       ArgOfPericenter 320
       MeanAnomaly     100
     }

   BodyFrame { EclipticJ2000 {Center "JD 9044191"} }  # gets replaced
   FixedRotation {} # required to prevent locus from pointing toward the star

Albedo 0.37
}


"focus" "JD 9044191"
{
  Radius 1000000
  EllipticalOrbit
   {
     Period         1e32  #close enough to infinity to prevent focus from moving much
     SemiMajorAxis  0.4065 # 2ae = 2.0*0.271*0.75 = 0.4065
     Inclination 0.04        # same as locus
     ArgOfPericenter 320  # same as locus
     MeanAnomaly     180  # at apocenter
     Eccentricity 0              # perfect circle: a distance
   }
}

Modify "locus" "JD 9044191"
{
  BodyFrame {
    TwoVector {
        Center "JD 9044191/locus" 
        Primary {
            Axis "y"
            RelativePosition { Target "JD 9044191/focus" }
        }
        Secondary {
            Axis "x"
            RelativeVelocity { Target "JD 9044191"}
        }
    }
  }

}


I made the focus object large enough to see from a distance, and selected wireframes (Ctrl-W) and body axes (RMB --> Reference Marks --> Show Body Axes) to see where Locus was pointing.

insert
Class "invisible"
in the definition of focus when you've convinced yourself the BodyFrame is doing the right thing.

[selden]

Here's the diagram that I devised to help determine what to do. I added comments afterward.

[eburacum45]

Thank you very much. I still need to align the texture correctly- the Warm Pole seems to be misaligned by 90 degrees, for some reason- but I feet confident that I can work that out for myself.

[eburacum45]

Now that the texture is properly aligned, the peculiar characteristics of these system can be clearly seen; the short season of Hotness at Periaston is followed by the longer season of Falling, the long, slow, cold season of Coolness and the increasingly warm season of Rising. As seen from the surface at the Warm Pole the sun goes across the sky from horizon to horizon without actually setting. Nearly as confusing as the seasons on Mercury.

[Tegmine]

Looks good! Now that it's aligned properly, will it be available?

-M-

[ajtribick]

If the planet's orbit is highly eccentric then it may end up in either pseudo-synchronisation (for planets without a permanent asymmetry, e.g. gas/ice giants) or higher-order spin:orbit resonances (for solid planets, e.g. Mercury), rather than a 1:1 lock.

[eburacum45]

That is another option I intend to explore; thanks!

Here's Locus, by the way
http://www.orionsarm.com/fm_store/Locus.zip

the extremes of hot and cold on this planet would make it uninhabitable by humans, so (as mentioned in the write-up) I've decided to use J Storrs Hall's concept of the 'weather machine' to ameliorate the climate. Tiny airborne diamonoid spheres, filled with hydrogen and helium, each have a mirror inside which can be oriented to reflect light back into space, or back toward the ground. They make quite good weapons, too.