Help with a Math Problem

Question

It takes 3x10^7 years for a particular star to make one orbit around it's galaxy. Assume that this star's orbit in it's galaxy is circular with a diameter of 10^4 light years. A light year is the distance that light travels in one year. There are about 5.859x10^12 miles in 1light year. Estimate how many miles this star travels in one year. The star travels about____________miles in one year.

 

Could someone please help me solve this problem and provide step by step on how to do so.

Answer 1

A circular orbit is easy to calculate: circumference of a circle is 2πr.

 

The star makes one orbit in a year, so that distance is exactly the circumference of its circular orbit.

 

However, we are given diameter, not radius. So we have to divide the diameter amount in half, or we could just leave off the 2 in the formula. So we have

 

πr = 3.14*10⁴ = 31,415.93

 

Now this is still in light years, so all that is left is to convert it to miles.

 

31,415.93 light years * 5.859 e 12 miles/light year

 

Let's change the exponents so they are closer together and thus easier to calculate:

 

3.1415 e 4 * 585,900,000 e 4 = 1.840659 e 13 miles / year