Step-by-step explanation:
The distance around the Earth can be calculated as the circumference of a circle with radius equal to the sum of the Earth's radius and the height of the space shuttle orbit. Since the shuttle's height above Earth is negligible compared to the Earth's radius, we can use the Earth's radius for the radius of the orbit.
Radius of orbit = Earth's radius = 6.36 x 10^6 m
Circumference of orbit = 2π(6.36 x 10^6 m) = 4.00 x 10^7 m
To convert the speed of the shuttle from miles per hour to meters per second, we use the conversion factor 1.00 m/s = 2.24 mi/h:
Speed of shuttle = 17600 mi/h × 1.00 m/s ÷ 2.24 mi/h = 7857.14 m/s
The time for a complete orbit is equal to the distance around the orbit divided by the speed of the shuttle:
Time for orbit = Circumference of orbit ÷ Speed of shuttle = (4.00 x 10^7 m) ÷ (7857.14 m/s) = 5091.02 seconds
Converting to hours:
Time for orbit = 5091.02 s ÷ (60 s/min × 60 min/h) = 1.41 hours
Therefore, the time for a complete orbit about Earth at an average speed of 17600 miles per hour is approximately 1.41 hours.