From: gdpusch@NO.xnet.SPAM.com   
   Copy: ctoffline@yahoo.com   
      
   ctoffline@yahoo.com (I_am_on_Saturn) writes:   
      
   > Is Sun positioned at the center of the elliptical orbits of all the   
   > planets?   
      
   Depends on what you mean by "center." To a first approximation, if we can   
   neglect the mass of the planet compared to the Sun (see below), then the   
   Sun would be located at one of the two foci of the ellipse. Do a Google   
   search on the exact phrase "Kepler's laws" to find a huge number of references.   
      
      
   > If so, why would we have to define nearest and farthest points of planet   
   > from Sun?   
      
   Because the foci of an ellipse are "off ceneter" --- but note that since an   
   ellipse has both a "major" and a "minor" axis, even if the Sun _were_   
   located at the "center" (which it isn't!), one would _still_ have to   
   specify both axes (or equivalently and more commonly, the semimajor axis   
   and the eccentricity of the orbit).   
      
      
   > If not so, what is the relative position of Sun relative to all the   
   > planets?   
      
   Because of Newton's law of action and reaction (which gravity obeys),   
   it is located such that the Center of Mass of the Sun plus all the planets   
   and asteroids moves at a constant velocity. This means that, if we for the   
   moment neglect all the other planets in the solar system except Jupiter,   
   since Jupiter is about a thouasand times less massive than the Sun,   
   Jupiter and the Sun would both appear to execute elliptical orbit about   
   a point called the "barycenter" (a fancy word for "center of mass")   
   that is located a thousands times closer to the Sun than to Jupiter.   
   Since Jupiter's mean orbital radius is 776.5e6 km, while the Sun's   
   radius is about 6.96e5 km, the Sun-Jupiter "barycenter" is located   
   about 1/10 of a solar radius below the Sun's visible surface along   
   the line between the Sun and Jupiter --- but since the Sun is so small   
   compared to typical interplanetary distances, this "offset" would be hard   
   to obeserve without precision instruments.   
      
   The planet causing the next largest displacement of the Sun is Saturn.   
   Saturn is about 4,000 times less massive than the Sun, so the Sun-Saturn   
   barycenter is 4000 times closer to the Sun than to Saturn. Since Saturn's   
   mean orbital radius is about 1,434e6 km, so the Sun-Saturn barycenter is   
   about 1/2 a solar radius from the Sun's center. And so on.   
      
      
   > I am trying to get the above information because I am building a Java   
   > applet to show the Solar system and for the purpose of display, I need   
   > to know the relative position of the Sun with respect to the planets.   
      
   There is no simple formula for computing this; one woould need  to simulate   
   the gravitational forces between all the bodies in the solar system, which   
   is probably not practical unless your display consumes unreasonable amounts   
   of computing resources.   
      
   To a first approximation, you can compute the center of mass for the Sun   
   and all of the planets given the orbital elements and masses of the planets,   
   and then assume they all orbit a common barycenter to compute the relative   
   distance of the Sun from that barycenter.   
      
   However, in practice, the radius of the Sun is so small compared to the   
   radii of the planetary orbits that the displacement of the Sun from the   
   barycenter of the Solar System will be invisibly small unless the display   
   is zoomed in on the Sun.   
      
      
   -- Gordon D. Pusch   
      
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