a space shuttle 240 miles above the earth orbits the earth every 5 hours. How far does the space shuttle travel in 1 hour?

Question

I am in basic Trigonometry and we are learning about radians and the length of an arc. 

Answer 1

Earth's equatorial diameter is 7,926 miles (12,756 kilometers), but from pole to pole, the diameter is 7,900 miles (12,720 km) — a difference of only 40 miles (64 km).

 

Let's say that the shuttle is orbiting the equator, so the diameter is 7,926 miles and the radius is 3,963 miles.

Since the space shuttle is 240 miles above the earth, the radius of its orbit is 3,963 + 240 = 4,203 miles.

 

The circumference of the circular orbit is 2 x π x r = 2 x 3.1415 x 4203 = 26408.2278 miles

 

Since the shuttle makes a complete orbit every 5 hours, we can compute how far it goes in 1 hour by the equation:

 

26408.2278 miles / 5 hours = x miles / 1 hour

 

so x = 5281.6456 miles

Answer 2

Olivia:

 

If the earth is 7,918 miles, then the radius would be 7,918/2 = 3,959 miles.  So if you add the 240 to the radius of 3,959, you end up with a total distance of 4,199 miles from the center of the earth to the shuttle's location in space.  The circumference of a circle is 2 times pi times the radius = 26,383 miles.  If that is traveled in 5 hours, divide by 5 to end up with 5,277 miles in an hour.

 

But, putting that in a Trig formula is beyond me.  This will at least get you the right answer, even if not in the correct form.  Good luck.

 

Larry