Question

A star has a mass of 1.36 x 1030 kg and is moving in a circular orbit about the center of its galaxy. the radius of the orbit is 2.1 x 104 light-years (1 light-year = 9.5 x 1015 m), and the angular speed of the star is 1.1 x 10-15 rad/s. (a) determine the tangential speed of the star. (b) what is the magnitude of the net force that acts on the star to keep it moving around the center of the galaxy?

Answer 1

a) We can use the equation for tangential speed: TangentalSpeed = AngularSpeed * radius = 1.1 x 10-15 rad/s * 2.1*10^4 light years * 9.5 x 10^15 m TangentalSpeed = 219,450 m/s b) Then we can use the equation relating force to mass and velocity: Force = mass * velocity^2/radius = 1.36 x 10^30 kg * (219,450 m/s )^2/ (2.1*10^4 light years * 9.5 x 10^15 m) Force = 3.28 * 10^20 N