College Physics Problem 1.10

a) The average distance between the Earth and the Sun is  10^{8} km. Calculate the average speed of the Earth in its orbit in kilometers per second. 
b) What is this is meters per second?

SOLUTIONS:

a) We assume that the earth revolves around the sun in a circular manner. Therefore, the distance between the earth and the sun will be the radius of its orbit.

The total distance traveled the earth in full revolution is 

d=2pi r

d=2 pi (10)^{8} km

d=pi times 2.0 times 10^{8} km

The total time of travel is

t=365.25 d times frac {24 hours}{1 day} times frac{3600 s}{ 1 hour}=3.15576 times 10^{7} sec

Therefore, the average speed is 

v=frac{distance}{time}=frac{d}{t}

v=frac{pi times 2.0 times 10^{8} km }{3.15576 times 10^{7} sec}

v=19.91 km/s

Therefore, the average velocity of the earth is 19.91 km/s.

 

b) Convert 19.91 km/s to m/s.

v=frac{19.91 km}{s} times frac{1000 m}{1 km}

v=19910 m/s

Therefore, the velocity is 19910 m/s. 

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