Kepler's Law, focal points - Heliocentric or Barycentric? It is known that all the mass in the Solar system moves around the Barycenter.
For the two focal points in Kepler's law; is the first focal point $F_1$ a Heliocenter? Or is it actually a Barycenter?
If the $F_1$ is a Heliocenter, then, can the same exact ellipse and eccentricity of orbit be maintained by adjusting the second focal point $F_2$ and taking Barycenter as $F_1$ instead of Heliocenter?
Planetary orbits are normally described as heliocentric, but it is possible to describe them from a barycentric point of view. JPL Horizons (https://ssd.jpl.nasa.gov/horizons.cgi) provides for both possibilities.