Word problem help?

Question

A certain planet travels around its star in a nearly circular orbit with a radius of 108 million miles. If it takes 1.57 years for the planet to complete one orbit, estimate the orbital speed of the planet in miles per hour.

Answer 1

At first blush I thought this would was a physics problem about Newton's law of gravitation, but quickly realized it is a standard distance and time problem. First compute the circumference of the circular orbit. C = 2piR and R is 2pi*108,000,000 miles.So the speed is 2*pi*108,000,000/1.57 in miles per year. Now convert 1.57 years to hours. There are 8766 hours/year. So 1.57 years is 

1.57(8766) = 13763 hours

 

So the speed in mi/hr is 2*pi*108,000,000/13763 =7847*2*pi= 49,306 mi/hr

 

double check my math please