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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 43.3 km/s and 58.6 km/s. The slower planet's orbital period is 7.60 years. a) What is the mass of the star? b) What is the orbital period of the faster planet, in years?

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a)

We have

`V_1 =43.3 (km)/s` and `V_2 =58.6 (km)/s`

For the slower planet 1 the angular speed is

`omega_1 =(2*pi)/T =V_1/R_1`

`R1 = T_1*V_1/(2*pi) =7.6*365*24*3600*43300/(2*pi)=1.652*10^12 m`

The gravitational force between the star and the slower planet 1 is

`F_1 =G*(m1*M)/R_1^2`

This force needs to be...

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