quality:corruption, linguistic:translation
Example with the Sun

If m ≫ m —which is true for the Sun and any planet—then the ratio r / R approximates to:

Hence, the barycenter of the Sun–planet system will lie outside the Sun only if:

—that is, where the planet is massive and far from the Sun.

If Jupiter had Mercury 's orbit (57,900,000 km, 0.387 AU), the Sun–Jupiter barycenter would be approximately 55,000 km from the center of the Sun (r / R ≈ 0.08). But even if the Earth had Eris 's orbit (1.02 × 10 km, 68 AU), the Sun–Earth barycenter would still be within the Sun (just over 30,000 km from the center).

To calculate the actual motion of the Sun, only the motions of the four giant planets (Jupiter, Saturn, Uranus, Neptune) need to be considered. The contributions of all other planets, dwarf planets, etc. are negligible. If the four giant planets were on a straight line on the same side of the Sun, the combined center of mass would lie at about 1.17 solar radii, or just over 810,000 km, above the Sun's surface.

The calculations above are based on the mean distance between the bodies and yield the mean value r. But all celestial orbits are elliptical, and the distance between the bodies varies between the apses, depending on the eccentricity, e. Hence, the position of the barycenter varies too, and it is possible in some systems for the barycenter to be sometimes inside and sometimes outside the more massive body. This occurs where:

The Sun–Jupiter system, with e = 0.0484, just fails to qualify: 1.05 < 1.07 > 0.954.