Question

The Sun travels in a circular orbit at a velocity of 220 km/second at a distance of 8.5 kiloparsecs from the center of the Galaxy (note that these numbers are slightly different from those in your book). Calculate the number of years it takes the Sun to complete an orbit (i.e., the circumference of a circle with an 8.5 kiloparsec radius) around the center of the Galaxy. (There are 3.1 x 1013 kilometers/parsec and 3.2 x 107 seconds/year.)

Answer 1

2.353 × 10⁵ years

Step-by-step explanation:

Since speed, v = distance/time

time, t = distance/speed

The distance, d = circumference of orbit = 2πr where r = radius of orbit = 8.5 kiloparsecs = 8.5 kiloparsecs × 3.1 × 10¹³ kilometers/parsec = ‭26.35‬ × 10¹³ kilometers and velocity of sun, v = 220 km/s

So, the time it takes to complete one orbit, T is

T = 2πr/v

= 2π × 26.35‬ × 10¹³ km/220 km/s

= 165.562 × 10¹³ km ÷ 220 km/s

= 0.753 × 10¹³ s

= 7.53 × 10¹² s

We now convert T to years

T = 7.53 × 10¹² s ÷ 3.2 × 10⁷ seconds/year

T = 2.353 × 10⁵ years