Also, Jupiter and Saturn make up most of the mass of the planets (1.8986×10^27 kg and 5.6846×10^26 = 2.46x10^27) where the total mass of the planets is 2.67×10^27 kg.
As long as Jupiter and Saturn are aligned with the sun the barometric center of the solar system will be outside of the sun, and they would align once every 12 years or so, so this does happen from time to time.
>>The center of mass of the solar system is often not inside the Sun.
That paper was just looking at one extreme combination where it's possible. Yes, most of the time it is inside the sun.
I don't think that 3 dimensions make much of a difference because the tilt off the solar plane for Jupiter and Saturn are much: http://en.wikipedia.org/wiki/Invariable_plane
Also, Jupiter and Saturn make up most of the mass of the planets (1.8986×10^27 kg and 5.6846×10^26 = 2.46x10^27) where the total mass of the planets is 2.67×10^27 kg.
As long as Jupiter and Saturn are aligned with the sun the barometric center of the solar system will be outside of the sun, and they would align once every 12 years or so, so this does happen from time to time.