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 (Msun = 1.99 x 1030 kg) at a distance of 1.50 x 1011 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 ratio of the star's mass to our sun's mass?

Explanation / Answer

applyKeplers third law as T^2 = 4pi^2 R^3/*GM

T = 365* 24* 60*60 3 = 31536000 secs

so mass of the star

M = 4*3.14^2 * (1.4*1.5e11)^3/(6.67e-11*(31530000)^2

M = 5.508 *10^30

so mass of the star/mass of sun   = 5.508e30/1.99 e30 = 2.76

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