Earth orbits once around the sun every 365.25 days at an average radius of 1.5x10^11 m. earth's mass is 6x10^24 kg. what distance does the earth travel in a year? what is earth's average centripetal acceleration?

(a) The distance the Earth travels every year is the perimeter of the orbit; since we have the average radius of the orbit, we can calculate the perimeter:


(b) The average centripetal acceleration is given by

where v is the average speed of the Earth, that we can find by dividing the distance covered by the Earth in one year (=the perimeter of the orbit) by the the time corresponding to 1 year:
t=1 year=365.25 days=3.2 \cdot 10^7 s
So the velocity is: 

And so the centripetal acceleration is: