Answer
The center of mass is a distance of $7.42\times 10^{8}~m$ from the center of the sun. Since the sun's radius is $6.96\times 10^8~m$, the center of mass lies outside the sun.
Work Step by Step
Let the center of the sun be at the origin.
$x_{cm} = \frac{m_1x_1+m_2x_2}{m_1+m_2}$
$x_{cm} = \frac{0+(1.9\times 10^{27}~kg)(7.78\times 10^{11}~m)}{1.99\times 10^{30}~kg+1.9\times 10^{27}~kg}$
$x_{cm} = 7.42\times 10^{8}~m$
The center of mass is a distance of $7.42\times 10^{8}~m$ from the center of the sun. Since the sun's radius is $6.96\times 10^8~m$, the center of mass lies outside the sun.
