Sun's motion around the barycentre of the solar system

[lidocorc]

Which planets' gravitational effects are included in computing the sun's motion around the solar system barycentre? Only Jupiter and Saturn, or Neptune and Uranus as well?

[MKruer]

EDIT: I think its just Jupiter. The other planets are either not massive enough or are to far away to have any real effect.

[Hungry4info]

Only Jupiter and Saturn. Venus would have the third most dominant effect on the sun's wobble. Uranus and Neptune are very low-mass and very distant to make that much of an effect. Thus, from an extrasolar observer, Venus would probably be the third planet detected in our solar system. I'm guessing the fourth would either be Earth or Uranus.

[lidocorc]

EDIT: I think its just Jupiter. The other planets are either not massive enough or are to far away to have any real effect.

You can easily see the sun travelling on a rosetta-like trajectory around the barycentre. (Watch the variing radius of the rotation.) This means, there are at least two gravitational influences considered by Celestia.

Which ones among the planets have the most influence can be understood by a dynamical kind of the 'law of the lever':

Two masses, which are tied together by gravitation (or any other force), rotate around their centre of mass. This is just the 'Law of conservation of Momentum' in other words. As a consequence, their distances from this centre are inverse proportional their masses. Example: The Sun has 1050 times the mass of Jupiter. Since the radius of Jupiter's orbit is 5.2 AU, the radius of the Sun's orbit is 0.0052 AU = 780'000 km, a little more then the Sun's own radius.

On the basis of this theory, the inner planets don't have any significant impact on the Sun's motion. Reasoning from gravitational force (~ m/r^2) alone is wrong, because a centripetal force involves the angular velocity, too.

The product of their mass and orbit radius is what is needed for a ranking of the planets' influence:
Jupiter 1653, Saturn 908, Neptune 517, Uranus 280, Venus 0.589 (multiples of the Earth's influence)

[chris]

EDIT: I think its just Jupiter. The other planets are either not massive enough or are to far away to have any real effect.

You can easily see the sun travelling on a rosetta-like trajectory around the barycentre. (Watch the variing radius of the rotation.) This means, there are at least two gravitational influences considered by Celestia.

Which ones among the planets have the most influence can be understood by a dynamical kind of the 'law of the lever':

Two masses, which are tied together by gravitation (or any other force), rotate around their centre of mass. This is just the 'Law of conservation of Momentum' in other words. As a consequence, their distances from this centre are inverse proportional their masses. Example: The Sun has 1050 times the mass of Jupiter. Since the radius of Jupiter's orbit is 5.2 AU, the radius of the Sun's orbit is 0.0052 AU = 780'000 km, a little more then the Sun's own radius.

On the basis of this theory, the inner planets don't have any significant impact on the Sun's motion. Reasoning from gravitational force (~ m/r^2) alone is wrong, because a centripetal force involves the angular velocity, too.

The product of their mass and orbit radius is what is needed for a ranking of the planets' influence:
Jupiter 1653, Saturn 908, Neptune 517, Uranus 280, Venus 0.589 (multiples of the Earth's influence)

Celestia uses the VSOP87 theory for the orbit of the planets from Mercury to Neptune and for the path of the Sun around the solar system barycenter. The gravitational effects of all these bodies on each other should be accounted for.

--Chris