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

 

[paranormal]

I would approach this problem by first converting the given information into units that are more commonly used in astronomical calculations. The distance from the centre of the galaxy, 26,000 light years, can be converted to kilometers by using the fact that 1 light year is equal to approximately 9.461 trillion kilometers. Therefore, 26,000 light years is equal to 2.455 trillion kilometers.

Next, I would use the given speed of 220 km/sec to calculate the distance traveled in one year. This can be done by multiplying 220 km/sec by the number of seconds in a year (which is equal to 31,536,000 seconds). This gives us a distance of approximately 6.939 trillion kilometers traveled in one year.

Now, we can use the formula for circumference (2 pi r) to calculate the distance traveled in one orbit. The radius of the orbit can be calculated by dividing the distance from the centre of the galaxy (2.455 trillion km) by 2, since the orbit is a circle. This gives us a radius of approximately 1.2275 trillion km.

Plugging this value into our formula, we get a circumference of approximately 7.716 trillion km traveled in one orbit.

Finally, to calculate the time required for one orbit, we can divide the circumference by the distance traveled in one year (6.939 trillion km) and then convert the result to millions of years. This gives us a time of approximately 1.11 million years for one orbit around the centre of the galaxy.

Therefore, it would take approximately 1.11 million years for our solar system to complete one orbit around the centre of the Milky Way.