Question

A satellite orbits around the Earth at a height of 400 miles and makes 3 revolutions around the Earth per day. The radius of the Earth is 3985 miles. What angle (in degrees) does the satellite rotate through in one day?

A) 360 degrees
B) 400 degrees
C) 720 degrees
D) 1080 degrees
E) 1440 degrees

Answer 1

The satellite rotates through an angle of 360 degrees in one day.

Step-by-step explanation:

To find the angle the satellite rotates through in one day, we need to determine the arc length of its path. The distance traveled by the satellite can be found by multiplying the circumference of its orbit by the number of revolutions it makes in a day. The circumference of the orbit is equal to the sum of the radius of the Earth and the height of the satellite, which is 3985 miles + 400 miles. The number of revolutions in a day is given as 3. Multiplying these values, we get: (3985 + 400) x 3 = 13,155 miles.

Since the satellite makes a complete revolution around the Earth in one day, the angle it rotates through is equal to 360 degrees. Therefore, the correct answer is (A) 360 degrees.