HD \(10180 \mathrm{~g}\) orbits with a period of 600 days at a distance of 1.4 au from its star. What is the ratio of the star's mass to our sun's mass?

In recent years, scientists have discovered hundreds of planets orbiting other stars. Some of these planets are in orbits that are similar to that of earth, which orbits the sun \(\left(M_{\text {sun }}=1.99 \times 10^{30} \mathrm{~kg}\right)\) at a distance of \(1.50 \times 10^{11} \mathrm{~m}\), called 1 astronomical unit \((1 \mathrm{au})\). Others have extreme orbits that are much different from anything in our solar system. Problems 47-49 relate to some of these planets that follow circular orbits around other stars.