Question

Given that the Sun moves in a circular orbit of radius 8.09 kpc around the center of the Milky Way, and its orbital speed is 216 km/sec, work out how long it takes the Sun to complete one orbit of the Galaxy. How many orbits has the Sun completed in the 4.5 billion years since it formed?

____ × 10⁸ years

_____ orbits

Answer 1

The radius of circular orbit is given to be 8.09 kPc.

Thus, to complete one circle, the Sun would have to travel along the circumference a distance of

d= 2*π*R=2*3.14*8.09 kPc = 50.8052 kPc

Now, we know 1 Pc = 3.086 x 10¹³ km

So, d = 50.8052 x 1000 x 3.086 x 10¹³ = 1.567 x 10¹⁸

Given the orbital speed = v = 216 km/s

The tiem taken to complete one orbit = d/v = 7.255 x 10¹⁵ s

                                                      = 2.3 x 10⁸ years

Assuming the sun was formed 4.5billion years ago, i.e. 4.5 x 10⁹

No. of orbits completed = 4.5 x 10⁹ / (2.3 x 10⁸) = 19.56

i.e. 19 complete orbits and more than a half the present one.