Question

A star rotates in a circular orbit about the center of its galaxy. The radius of the orbit is 1.3 x 1020 m, and the angular speed of the star is 4.2 x 10-15 rad/s. How long (in years) does it take for the star to make one revolution around the center?

Answer 1

Given, Radius of orbit,r = 1.3 x 10²⁰ m

Angluar speed of star, = 4.2 x 10^-15 rad/sec

Since given the orbit is circular the total distance travelled in one revolution of star is equal to circumference of that circular orbit.

Therefore, total distance travelled by star,

  

We know that tangential velocity, v = angular velocity () x radius of orbit (r)

  

As we have got both tangential velocity v and distance d, total time taken for 1 revolution of star,

-----(1)

Now, we know there are 365 days in an year, each day has 24 hours, each hour consists of 60 minutes and each minutes has 60 seconds.

So in an year there is

----------(2)

Now to convert t into years we have to divide (1) by (2),

Therefore t in years,