A planet named Zeta orbits a distant star, called Omicron, in the Andromeda Galaxy. Zeta follows an elliptical path with a period of 8.4 years and an eccentricity of 0.76. At its closest approach during 2015, Zeta was merely 90 AU from Omicron ($1\ AU=1.50\times 10^{11}$ m). Calculate the mass m of the star Omicron, assumed to be a typical massive star. Express m in kilograms and in terms of solar masses $m_{solar}$ . Use: Mass of the Sun = $1.989 \times 10^{30} \mathrm{~kg}$.

• A. $m\approx 1.5\times 10^{36}\mathrm{~kg};\ m_{\text{solar }}\approx 7.5\times 10^5$
• B. $m\approx 1.5\times 10^{36}\mathrm{~kg};\ m_{\text{solar }}\approx 3.8\times 10^5$
• C. $m\approx 2.5\times 10^{36}\mathrm{~kg};\ m_{\text{solar }}\approx 7.5\times 10^5$
• D. $m\approx 2.5\times 10^{36}\mathrm{~kg};\ m_{\text{solar }}\approx 3.8\times 10^5$

Answer: (A)