I just watched a PBS show on planetary motion and Kepler's Laws and had a couple of questions. According to Kepler's first law, the planets travel on an elliptical path with the Sun located at one of the two foci. Is there any significance to the other focus? I would think the gravitional pull of the Sun would contribute to the elliptical path, and that some other gravitional pull from the second focus would result in the elliptical orbit.
Actually, both the Sun and the planets move around each other with their center of mass lying at the focus of the elliptical orbits. However, since the Sun contains 99.9% of the mass of the solar system, the center of mass is located almost at the Sun and so it looks like the planets are going around the Sun.
There is no real significance to the second (empty) foci of the elliptical orbits. The same laws that govern the orbits of planets around the Sun also govern the motion of binary stars and in that case since the masses of the two stars may be roughly equal, the foci of the elliptical orbits may not correspond physically to any object. As I explained earlier, the Sun appears at one focus ony because it is so much more massive than any of the planets and so its center lies close to the focus (which is the actual location of the center of mass).
Are each of the planetary orbits on a different plane? I would guess so, yet they each share a common focus (the Sun) in their elliptical orbits, a single point of intersection for each planer orbit, right?
Strictly speaking, you are correct and each orbit is in a different plane. However, because of the physics of planetary formation, all the planets are roughly in the same plane. There are of course slight differences, but to within about ten degrees, all the planets are in the same plane. This is the reason why the planets appear to line up in the sky (when you can see many of them at the same time), and is also the reason why the planets are always found in one of the zodiac constellations.
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