Calculating the position of the 'other' focus point of an orbit

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SUMMARY

The discussion centers on calculating the position of the second focus point of an elliptical orbit, specifically in the context of developing a 2D space game. The user seeks a mathematical formula to determine this position relative to the origin (0,0), similar to the barycenter calculation referenced in a Wikipedia image. The user expresses difficulty in finding a formula that provides the actual vector representation of the focus point, rather than just the lengths of the vectors associated with periapsis and apoapsis.

PREREQUISITES
  • Understanding of elliptical orbits and their properties
  • Familiarity with barycentric coordinates
  • Basic knowledge of vector mathematics
  • Experience with 2D game development concepts
NEXT STEPS
  • Research the mathematical properties of ellipses, focusing on the foci and their coordinates
  • Learn about barycentric coordinates and their application in orbital mechanics
  • Explore vector mathematics, specifically how to calculate vectors from given points
  • Investigate existing algorithms for simulating orbits in game development
USEFUL FOR

Game developers, mathematicians, and physics enthusiasts interested in orbital mechanics and simulation techniques for 2D environments.

Chetic
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You know how orbits are made of ellipses and ellipses are made out of two foci?
I'm trying to find a formula where I can extract the position of the other focus point, relative to (0,0).
By the other focus point I mean the one that's generally out in space.

Very much like how the barycenter's position, R, is calculated in this Wikipedia page:
http://en.wikipedia.org/wiki/File:Two-body_Jacobi_coordinates.JPG"

I'm coding a 2d space game and want to predict my orbits using proper math, instead of running the simulation ahead.

P.S: Does this 'other' focus point have a name by the way?
 
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Actually, I think the best way might be to solve for vectors representing periapsis and apoapsis (the highest and the lowest points of orbit).

I have wiki'd myself crazy trying to find some formula for this. Can anybody give me a hint?

Edit: Forgot to mention my problem; I can only find formulas that give the lengths of what would be these two vectors, not any for an actual vector.
 
Last edited:

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