Determine whether the center of mass of the solar system is inside or outside the sun, neglecting the masses

Determine whether the center of mass of the solar system is inside or outside the sun, neglecting the masses of all planets except Jupiter. The mass of the Sun M is 1050 times greater than the mass of Jupiter mю. It is known that the diameter of the Sun is 108 times less than the distance from the Earth to the Sun, and the distance from Jupiter to the Sun is Lю = 5.2. a.u.

If we neglect all the planets, except for Jupiter, then the center of mass of the Sun-Jupiter system, which is located from the center of the Sun at a distance of = 5.2 / 1051 = 4.2 * 10-3 AU. The radius of the Sun is half of its angular size as seen from the Earth, multiplied by the radius of the Earth’s orbit, i.e. Ro = 4.65 * 10-3 AU. We see that L is greater than Ro. Thus, within the framework of the assumptions made under the condition, the center of mass of the solar system is outside the sun.

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