The ratio of the star's mass to the sun's mass can be calculated using the equation Mstar/Msun = (2πr)^2/G(P^2), where r is the distance of the planet from the star, P is the orbital period of the planet, and G is the gravitational constant.
In this case, r = 1.4 au, P = 600 days, and G = 6.67 x 10^-11 m^3 kg^-1 s^-2.
Plugging these values into the equation gives us Mstar/Msun = (2π(1.4 au))^2/6.67 x 10^-11 m^3 kg^-1 s^-2 (600 days)^2 = 0.945 Msun.
Therefore, the ratio of the star's mass to the sun's mass is 0.945.
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 (Msun = 1.99 × 10^(30) kg) at a distance of 1.50 × 10^(11) m, called 1 astronomical unit (1 au). Others have extreme orbits that are much different from anything in our solar system. The following problem relates to one of these planets that follows circular orbit around its star. Assume the orbital period of earth is 365 days.
HD 10180g orbits with a period of 600 days at a distance of 1.4au from its star. What is the RATIOof the star's mass to our sun's mass?
So i know that Msun=1.99*10^(30).
And that Mstar/Msun gives me my answer. However I am having trouble getting the Mstar. I believe the distance of the Mstar is 6x10^11m and i got this by multiplying 1.5*10^(11) times (.4). After that I am not really sure what to do to get the mass? Please help!
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