Question

Two newly discovered planets follow circular orbits around a star in a distant part of the galaxy. The orbital speeds of the planets are determined to be 45.7 km/s and 64.2 km/s. The slower planet's orbital period is 8.58 years. (a) What is the mass of the star? (b) What is the orbital period of the faster planet, in years?

Answer 1

a)

orbital velocity

vo = 2 pi R / t

45.7* 10^3 = 2* 3.14* R / (8.58* 365* 24*3600)

R = 1.969* 10^12 m

as we know from kepler's law

T^2 = 4 pi^2 R^3 / (GM)

(8.58* 365* 24* 3600)^2 = 4* 3.14^2* ( 1.969* 10^12)^2 / ( 6.67* 10^-11* M)

M = 6.165* 10^31 kg

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b)

again

as we know

V^2 = GM / r

r = 6.67* 10^-11* 6.165* 10^31 / ( 64.2* 1000)^2

r = 9.98* 10^11 m

now

t = 2 pi t / v

t = 3.095 years

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