Chris wrote:
It wouldn't change Kepler's laws in the slightest. Keep in mind that Kepler's laws are a special case of Newtonian gravity, applied to two bodies. Even in a simple system they are an approximation, although a very good one.
Depending on the dynamics of the multiple star system, Kepler's laws would either continue to be a reasonable approximation of reality, or they would not (the latter in most cases, I think). So you would need to analyze such a system by numerical integration, just like you need to do with our solar system if you want the most accurate results.
More digging and I found the answer to my query in the description of the way Kepler and Spitzer spacecrafts orbit the Sun;
Heliocentric.
From Wikipedia:
A heliocentric orbit (also called circumsolar orbit) is an orbit around the Sun. All planets, comets, and asteroids in our Solar System are in such orbits, as are many artificial probes and pieces of debris. The moons of planets in the Solar System, by contrast, are not in heliocentric orbits as they orbit their respective planet.
While it is convenient to think of orbits around the Sun, bodies in the Solar System do not actually orbit the Sun. Instead, all bodies in the Solar System (including the Sun) actually orbit the barycenter of the Solar System. A similar phenomenon allows the detection of extrasolar planets by way of the radial velocity method.
.....
While in geometry the term barycenter is a synonym for "centroid", in physics "barycenter" may also mean the physical center of mass or the center of gravity, depending on the context. The center of mass (and center of gravity in a uniform gravitational field) is the arithmetic mean of all points weighted by the local density or specific weight. If a physical object has uniform density, then its center of mass is the same as the centroid of its shape.
Kepler's Laws, though only approximation, indeed paved the way to proving the existence of extra solar planets.
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