The equatorial diameter of the earth is approximately 8,000 miles. A communications satellite makes a circular orbitals around the earth. If the satellite completes one orbit every 5 hours, how many miles does the satellite travel in 1 hour?

Options

A. `1,120pi`
B. `1,940pi`
C. `2,240pi`
D. `2,560pi`

Answer

To solve the problem step by step, we will calculate the distance the satellite travels in one hour based on the given information.

### Step 1: Determine the equatorial diameter of the Earth
The equatorial diameter of the Earth is given as approximately 8,000 miles.

### Step 2: Calculate the orbital diameter of the satellite
The satellite orbits at a height of 1,600 miles above the Earth's surface. Therefore, the orbital diameter can be calculated as follows:

\[ \text{Orbital Diameter} = \text{Equatorial Diameter} + 2 \times \text{Height of Satellite} \]

Substituting the values:

\[ \text{Orbital Diameter} = 8,000 + 2 \times 1,600 = 8,000 + 3,200 = 11,200 \text{ miles} \]

### Step 3: Calculate the circumference of the satellite's orbit
The circumference \(C\) of a circle is given by the formula:

\[ C = \pi \times \text{Diameter} \]

Using the orbital diameter we calculated:

\[ C = \pi \times 11,200 \text{ miles} \]

### Step 4: Determine the distance traveled in 5 hours
The satellite completes one orbit (which is the circumference we calculated) in 5 hours. Therefore, the distance traveled in 5 hours is:

\[ \text{Distance in 5 hours} = 11,200 \pi \text{ miles} \]

### Step 5: Calculate the distance traveled in 1 hour
To find the distance traveled in 1 hour, we divide the total distance traveled in 5 hours by 5:

\[ \text{Distance in 1 hour} = \frac{11,200 \pi}{5} \text{ miles} \]

Calculating this gives:

\[ \text{Distance in 1 hour} = 2,240 \pi \text{ miles} \]

### Conclusion
Thus, the satellite travels \(2,240 \pi\) miles in one hour.