Problems modelling astrometric orbits
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Problems modelling astrometric orbits
I've been working on a way to model astrometric orbits, essentially representing 3D orbits on a 2D plane for the purposes of this conversation. I've been having a hard time figuring out the math behind it. I've found what I thought was the proper formulation but it is producing results that are not particularly intuitive.
I will post some screenshots.
A simple, faceon configuration.
As expected, changing LongPeri for an inclined circular orbit does not produce a physical change.
But adding eccentricity seems to tilt the orbit.
Only changing e produces an unexpected result.
Here's my math.
I used my same formulation for the eccentric anomaly as used for these diagrams so I do not think it is a problem there.
Also, for eccentric orbits, the x and y coordinates of the orbit are not mapping them to positions that place the barycentre in the image centre.
I'll have to hack at it when I get home from work, but for now I can't figure out what's wrong. Any assistance would be appreciated.
I will post some screenshots.
A simple, faceon configuration.
As expected, changing LongPeri for an inclined circular orbit does not produce a physical change.
But adding eccentricity seems to tilt the orbit.
Only changing e produces an unexpected result.
Here's my math.
 Code:
//TheileInnes constants.
double A = a * (Math.Cos(omega) * Math.Cos(Node)  Math.Sin(omega) * Math.Sin(Node) * Math.Cos(inc));
double B = a * (Math.Cos(omega) * Math.Sin(Node) + Math.Sin(omega) * Math.Cos(Node) * Math.Cos(inc));
double F = a * (1 * Math.Sin(omega) * Math.Cos(Node)  Math.Cos(omega) * Math.Sin(Node) * Math.Cos(inc));
double G = a * (1 * Math.Sin(omega) * Math.Sin(Node) + Math.Cos(omega) * Math.Cos(Node) * Math.Cos(inc));
 Code:
double x_coord = A * (Math.Cos(E  ecc)) + F * Math.Sqrt(1  (ecc * ecc)) * Math.Sin(E);
double y_coord = B * (Math.Cos(E  ecc)) + G * Math.Sqrt(1  (ecc * ecc)) * Math.Sin(E);
I used my same formulation for the eccentric anomaly as used for these diagrams so I do not think it is a problem there.
Also, for eccentric orbits, the x and y coordinates of the orbit are not mapping them to positions that place the barycentre in the image centre.
I'll have to hack at it when I get home from work, but for now I can't figure out what's wrong. Any assistance would be appreciated.
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Sirius_Alpha Admin
 Number of posts : 3840
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Re: Problems modelling astrometric orbits
Followup. I've managed to get it working right. The orbit diagrams now match observations for known binary stars, etc.
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Caps Lock: Cruise control for 'Cool'!
Sirius_Alpha Admin
 Number of posts : 3840
Location : Earth
Registration date : 20080406
Re: Problems modelling astrometric orbits
Checked out Upsilon Andromedae yet? When I tried to do this a few years back I was unable to match all the data/figures in McArthur et al. (2010) simultaneously.
Lazarus dF star
 Number of posts : 3079
Registration date : 20080612
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