HR 8799 bcde and Beta Pictoris b

[ajtribick]

Neither the HR 8799 system nor Beta Pictoris b are currently included in the extrasolar planets data files.

Orbital elements for HR 8799 are available here. The convention used for the orbital elements is not specified and turns out to be different to that used in the binary star catalogues, I had to replace ? with 90°-? to reproduce the astrometric displacements before converting to the ecliptic plane.

Three cases are given for HR 8799. All have planets b, c and d in a 1:2:4 resonance.

1. coplanar, planet d eccentric, e and d in 5:2 resonance
2. non-coplanar, all orbits circular, e and d in 2:1 resonance
3. non-coplanar, all orbits circular, e and d in 5:2 resonance

The .ssc files for the 3 cases are as follows. For now I have given all planets a radius of 1.1 times Jupiter and a glowing texture.
Case A:

Code: Select all

"e" "HIP 114189"
{
   Radius 79000
   Texture "browndwarf.*"
   Emissive true
   EllipticalOrbit {
      Epoch 2446826
      Period 44.96
      SemiMajorAxis 14.66
      Inclination 141.9
      AscendingNode 259.0
      ArgOfPericenter 164.7
   }
   UniformRotation {
      Inclination 141.9
      AscendingNode 259.0
   }
}

"d" "HIP 114189"
{
   Radius 79000
   Texture "browndwarf.*"
   Emissive true
   EllipticalOrbit {
      Epoch 2448736
      Period 112.4
      SemiMajorAxis 27.01
      Eccentricity 0.1
      Inclination 141.9
      AscendingNode 259.0
      ArgOfPericenter 244.9
   }
   UniformRotation {
      Inclination 141.9
      AscendingNode 259.0
   }
}

"c" "HIP 114189"
{
   Radius 79000
   Texture "browndwarf.*"
   Emissive true
   EllipticalOrbit {
      Epoch 2394603
      Period 224.9
      SemiMajorAxis 42.89
      Inclination 141.9
      AscendingNode 259.0
      ArgOfPericenter 164.7
   }
   UniformRotation {
      Inclination 141.9
      AscendingNode 259.0
   }
}

"b" "HIP 114189"
{
   Radius 79000
   Texture "browndwarf.*"
   Emissive true
   EllipticalOrbit {
      Epoch 2450650
      Period 449.7
      SemiMajorAxis 68.08
      Inclination 141.9
      AscendingNode 259.0
      ArgOfPericenter 164.7
   }
   UniformRotation {
      Inclination 141.9
      AscendingNode 259.0
   }
}

Case B:

Code: Select all

"e" "HIP 114189"
{
   Radius 79000
   Texture "browndwarf.*"
   Emissive true
   EllipticalOrbit {
      Epoch 2450340
      Period 56.05
      SemiMajorAxis 16.99
      Inclination 111.82
      AscendingNode 300.60
      ArgOfPericenter 281.66
   }
   UniformRotation {
      Inclination 111.82
      AscendingNode 300.60
   }
}

"d" "HIP 114189"
{
   Radius 79000
   Texture "browndwarf.*"
   Emissive true
   EllipticalOrbit {
      Epoch 2438834
      Period 112.11
      SemiMajorAxis 27.01
      Inclination 153.38
      AscendingNode 249.93
      ArgOfPericenter 155.99
   }
   UniformRotation {
      Inclination 153.38
      AscendingNode 249.93
   }
}

"c" "HIP 114189"
{
   Radius 79000
   Texture "browndwarf.*"
   Emissive true
   EllipticalOrbit {
      Epoch 2392700
      Period 224.21
      SemiMajorAxis 42.80
      Inclination 139.82
      AscendingNode 252.02
      ArgOfPericenter 150.17
   }
   UniformRotation {
      Inclination 139.82
      AscendingNode 252.02
   }
}

"b" "HIP 114189"
{
   Radius 79000
   Texture "browndwarf.*"
   Emissive true
   EllipticalOrbit {
      Epoch 2457159
      Period 448.44
      SemiMajorAxis 67.94
      Inclination 134.57
      AscendingNode 268.08
      ArgOfPericenter 183.42
   }
   UniformRotation {
      Inclination 134.57
      AscendingNode 268.08
   }
}

Case C:

Code: Select all

"e" "HIP 114189"
{
   Radius 79000
   Texture "browndwarf.*"
   Emissive true
   EllipticalOrbit {
      Epoch 2446483
      Period 44.84
      SemiMajorAxis 14.64
      Inclination 133.37
      AscendingNode 258.31
      ArgOfPericenter 157.00
   }
   UniformRotation {
      Inclination 133.37
      AscendingNode 258.31
   }
}

"d" "HIP 114189"
{
   Radius 79000
   Texture "browndwarf.*"
   Emissive true
   EllipticalOrbit {
      Epoch 2438834
      Period 112.11
      SemiMajorAxis 27.01
      Inclination 153.38
      AscendingNode 249.93
      ArgOfPericenter 155.99
   }
   UniformRotation {
      Inclination 153.38
      AscendingNode 249.93
   }
}

"c" "HIP 114189"
{
   Radius 79000
   Texture "browndwarf.*"
   Emissive true
   EllipticalOrbit {
      Epoch 2392700
      Period 224.21
      SemiMajorAxis 42.80
      Inclination 139.82
      AscendingNode 252.02
      ArgOfPericenter 150.17
   }
   UniformRotation {
      Inclination 139.82
      AscendingNode 252.02
   }
}

"b" "HIP 114189"
{
   Radius 79000
   Texture "browndwarf.*"
   Emissive true
   EllipticalOrbit {
      Epoch 2457159
      Period 448.44
      SemiMajorAxis 67.94
      Inclination 134.57
      AscendingNode 268.07
      ArgOfPericenter 183.41
   }
   UniformRotation {
      Inclination 134.57
      AscendingNode 268.07
   }
}

[ajtribick]

For Beta Pictoris the orbital elements can be found here. This does seem to be in the Pourbaix convention if the planet is orbiting in the same direction as the disc.

Two cases are given, one with the planet at 11.2 AU and one at 8.8 AU.

Case 1: Least-squares Levenberg-Marquardt best fit:

Code: Select all

"b" "HIP 27321"
{
   Radius 79000
   Texture "browndwarf.*"
   Emissive true
   EllipticalOrbit {
      Epoch 2456402
      Period 28.3
      SemiMajorAxis 11.2
      Eccentricity 0.16
      Inclination 98.12
      AscendingNode 298.76
      ArgOfPericenter 351.49
   }
   UniformRotation {
      Inclination 98.12
      AscendingNode 298.76
   }
}

Case 2: Typical "highly probable" output of MCMC fit:

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"b" "HIP 27321"
{
   Radius 79000
   Texture "browndwarf.*"
   Emissive true
   EllipticalOrbit {
      Epoch 2453846
      Period 19.6
      SemiMajorAxis 8.8
      Eccentricity 0.021
      Inclination 97.72
      AscendingNode 298.33
      ArgOfPericenter 232.41
   }
   UniformRotation {
      Inclination 97.72
      AscendingNode 298.33
   }
}