From doppler shifts of the spectral lines in the light coming from the east and west edges of the sun, astronomers find that the radial velocities of the two edges differ by about 4 km/s, meaning that the sun’s rotation rate is 2 km/s. find the approximate period of rotation of the sun in days. the circumference of a sphere is given by 2πr, where r is the radius of the sphere

T= 37 day

Explanation:

To solve this exercise we will use the definition of angular velocity as the angular distance, which for a full period is 2pi between time.

    w = T / t

The relationship between angular and linear velocity is

    v = w r

    w = v / r

We substitute everything in the first equation

    v / r = 2π / t

    t = 2π r / v

Let's reduce to the SI system

    V = 2 km / s (1000m / 1km) = 2 10³ m / s

    r= R = 6.96 10⁸ m

Let's calculate

    t = 2π 6.96 10⁸/2 10³

    t = 3.2 10⁶ s

    T = t = 3.2 10⁶ s ( 1h/3600s) (1 day/24 h)

    T= 37 day