The radius of Earth is 3,959 miles. A spacecraft orbits 6 miles above the surface of Earth. The spacecraft completes 220° of a revolution around Earth in one day. What is the average speed of the spacecraft?
This is a neat trick, as Earth is not spherical, the difference in radius at the poles compared to the Equator is 31miles.
Ignoring that bit of fact, assuming the Earth is spherical, and there is no atmospheric drag,then
period=1day=24hrs*3600sec/hr
speed=distancearund/tperiod=2PI(3959+6)/periodabove.
oops, I missed the 220 degrees, so period=2PI(3965)*360/22O
Hi Bob - I have 4 possible answers and cannot arrive at any of them by the above. My choices are (a)634mph (b)1038mph (c)761mph (d)113mph
To determine the average speed of the spacecraft, we need to calculate the distance it travels in one day.
First, we calculate the circumference of Earth's orbit by adding the radius of Earth to the spacecraft's altitude:
Circumference = 2 * π * (radius of Earth + altitude)
Circumference = 2 * 3.1416 * (3,959 + 6) = 49,898.9456 miles
Next, we need to find the fraction of the Earth's orbit the spacecraft completes in one day. Since the spacecraft completes 220° of a revolution, we can express this as a fraction of a full revolution:
Fraction of orbit completed = 220° / 360° = 11/18
Finally, we multiply the circumference of the orbit by the fraction of the orbit completed to find the distance traveled in one day:
Distance traveled = Circumference * Fraction of orbit completed
Distance traveled = 49,898.9456 * (11/18) = 30,921.85 miles
Therefore, the average speed of the spacecraft is 30,921.85 miles per day.