Calculate the time required in millions of years for one orbit.

[quah13579]

Homework Statement

The solar system is situated 26,000 light years from the centre of our galaxy, the Milky Way, and it orbits the centre at a speed of 220 km/sec.

Calculate the time required in millions of years for one orbit.
(NOTE: The circumference of a circle = 2 pi r where r is its radius.)

Homework Equations

The Attempt at a Solution

I am not really sure how to do it, please help thanks

 

[tiny-tim]

welcome to pf!

hi quah13579! welcome to pf!

(have a pi: π )

find how to convert light years into km, and then calculate the length of the circumference of the orbit …

what do you get? ​

 

[quah13579]

hi quah13579! welcome to pf!

(have a pi: π )

find how to convert light years into km, and then calculate the length of the circumference of the orbit …

what do you get? ​

9,460,730,472,580.8(light-year in km) * 26000(of light-years around) * 2 * 3.1415926535 = 1545531590213152572.8104183193436(km) / 220(km/sec) / 60(sec/min) / 60 (min/hrs) / 24 (hrs/days) / 365.25(days/years) = 222613367.04559 years
is it right?

 

[tiny-tim]

9,460,730,472,580.8(light-year in km) * 26000(of light-years around) * 2 * 3.1415926535 = 1545531590213152572.8104183193436(km) / 220(km/sec) / 60(sec/min) / 60 (min/hrs) / 24 (hrs/days) / 365.25(days/years) = 222613367.04559 years
is it right?

hmmm … never never never use all those figures (you'll lose marks in the exam if you do) … 3 sig figs should usually be more than enough

and the question asked for the answer in millions of years

but apart from that (and i haven't checked your lightyear/km figure), that looks fine