Question

A density wave made up of two spiral arms is moving through the Galactic disk. At the 8-kpc radius of the Sun’s orbit around the Galactic center, the wave’s speed is 120 km/s and the Galactic rotation speed is 220 km/s. Calculate how many times the Sun has passed through a spiral arm since forming 4.6 billion years ago.

Answer 1

Relative speed of moving = 220 -120 = 100km/s = 100*10³ m/s
Distance covered in one revolution = 2r
where r is radius of sun orbit = 8 kpc = 8*3.086*10¹⁹ m
Distance covered = 2*( 8*3.086*10¹⁹ ) = 155.12*10¹⁹ m
time taken to complete one revolution = 155.12*10¹⁹/ 10⁵
= 155.12*10¹⁴ s
Revolution takes place in 4.6 billion years
4.6 billion years = 4.6*3.1536*10¹⁶
= 14.506*10¹⁶ s
No . of revolution = total time/ time in one revolution
= 14.506*10¹⁶ /155.12*10¹⁴
= 9.35 revolution
In one revolution sun has passed twice the spiral arm , therefore
18 times sun will passed through a spiral arm.