Question

A space shuttle 340 miles above the earth is orbiting the earth once every 11 hours. How far does the shuttle travel in 3 hours? (Assume the radius of the earth is 4,000 miles.)

Answer 1

The time period of rotation of space shuttle `T=11hr`

So the angular velocity of the space shuttle will be `omega=(2pi)/11` rad/hr

The radius of the orbit of the space shuttle from the center of the earth is `R=4000+340=4340` miles.

Hence speed of the space shuttle will be `V=omega*R`

So the distance traveled by the space shuttle in 3hr will be

`d=3*V=3*omega*R=3*(2pi)/11*4340`miles

`=3*2*22/7*1/11*4340=7440` miles