In recent years, scientists have discovered hundreds of planets orbiting other s

Question

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 ( M_sun= 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.

Part A

HD 10180g 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? (M_star/M_sun)Express your answer using two significant figures

Explanation / Answer

Mass of sun,

Msun = 1.99*10^30 kg

Period of planet,

T = 600 days = 51840000 s

Orbital radius of planet,

R = 1.4 au = 2.1*10^11 m

Mass of star,

Mstar = 4*pi^2*R^3 / GT^2

Mstar = [4*pi^2*(2.1*10^11)^2] / [6.67*10^(-11)*(51840000)^2]

Mstar = 2.04*10^30 kg

What is the ratio of the star's mass to our sun's mass,

Mstar / Msun = 2.04*10^30 / 1.99*10^30

Mstar / Msun = 1.024

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