Final answer:
The center of mass of the Sun and Jupiter system is calculated using the masses of the Sun and Jupiter and their radii from the center of mass. It is then compared with the radius of the Sun to determine if it lies inside or outside of it.
Step-by-step explanation:
The position of the center of mass of the Sun and Jupiter system is determined by the formula:
RCM = (mSun * RSun + mJupiter * RJupiter) / (mSun + mJupiter)
Where mSun and mJupiter are the masses of the Sun and Jupiter, respectively, and RSun and RJupiter are the radii from the Sun to the center of mass and from Jupiter to the center of mass, respectively. Considering the Sun as the origin (RSun= 0) and using the values provided:
RCM = (1.989 × 10³⁰ kg * 0 + 1.9 × 10²⁷ kg * RJupiter) / (1.989 × 10³⁰ kg + 1.9 × 10²⁷ kg)
To determine if the center of mass lies inside or outside the Sun, we would compare the result to the radius of the Sun (6.96×10⁸ m). If RCM is less than the radius of the Sun, the center of mass is inside the Sun, otherwise, it is outside.
Given the significant mass of the Sun compared to Jupiter, the center of mass of the system will most likely be within or very close to the surface of the Sun, albeit it is a detailed calculation beyond the scope of this answer.