Question about Kepler's 1st law and barycentric orbits

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SUMMARY

Kepler's 1st law asserts that all planets orbit the sun in elliptical paths with the sun at one focus. However, the true center of mass, or barycenter, of a multi-planet system is not necessarily at the sun's focus, as it shifts based on the positions of the planets. In binary star systems, the orbits of the stars can overlap, resulting in a shared barycenter that may not coincide with either star. This discussion emphasizes the importance of understanding barycentric orbits in celestial mechanics.

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  • Understanding of Kepler's laws of planetary motion
  • Familiarity with barycentric coordinates in astronomy
  • Basic knowledge of elliptical orbits
  • Concept of center of mass in multi-body systems
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  • Research "Barycentric coordinates in astronomy" for detailed mathematical frameworks
  • Study "Kepler's laws of planetary motion" for foundational principles
  • Explore "Elliptical orbits and their properties" to understand orbital mechanics
  • Investigate "Center of mass in multi-body systems" for applications in astrophysics
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Astronomers, astrophysicists, and students of celestial mechanics will benefit from this discussion, particularly those interested in the dynamics of planetary and binary star systems.

RisingSun361
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Kepler's 1st law states, "All planets move about the sun in elliptical orbits, having the sun as one of the foci". But the orbit must also be barycentric. So, technically speaking, is the center of mass of the system actually at the focus, rather than the sun? And the sun itself orbits this focus in a small elliptical orbit?

And in a multi-planet solar system, would the focus/center of mass move as different planets change their positions?

And in a binary star system, do the two ellipses overlap each other in such a way that two foci overlap each other at one point, the center of mass?
 
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RisingSun361 said:
Kepler's 1st law states, "All planets move about the sun in elliptical orbits, having the sun as one of the foci". But the orbit must also be barycentric. So, technically speaking, is the center of mass of the system actually at the focus, rather than the sun? And the sun itself orbits this focus in a small elliptical orbit?

And in a multi-planet solar system, would the focus/center of mass move as different planets change their positions?

And in a binary star system, do the two ellipses overlap each other in such a way that two foci overlap each other at one point, the center of mass?
Have a read about barycentric coordinates:

http://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)
 

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