*Question E3A01:
What is the approximate maximum separation measured along the surface of the Earth between two stations communicating by EME?*  

*Correct Answer is  D: 12,000 miles, if the moon is “visible” by both stations*  

### AI Response: (may contain errors)  

To understand the maximum separation between two stations communicating via Earth-Moon-Earth (EME) communication, we need to consider the geometry of the Earth and the Moon.

### Correct Answer: D - 12,000 miles, if the moon is “visible” by both stations

- **Explanation**: The maximum distance between two stations on Earth that can communicate via EME is approximately the diameter of the Earth, which is about 12,742 kilometers or roughly 7,918 miles. However, since we are considering the maximum separation along the surface of the Earth, we can approximate this to about 12,000 miles. This distance assumes that both stations have a clear line of sight to the Moon, which is essential for EME communication.

### Why the Other Choices are Incorrect:

- **Choice A: 2,000 miles, if the moon is at perigee**  
  - **Reason**: While the Moon's distance at perigee (closest point to Earth) is about 225,623 miles, the maximum separation for EME communication is not limited by the Moon's distance but rather by the Earth's diameter. Thus, 2,000 miles is too small.

- **Choice B: 2,000 miles, if the moon is at apogee**  
  - **Reason**: At apogee, the Moon is about 252,088 miles away. Again, the maximum separation is not determined by the Moon's distance but by the Earth's diameter. Therefore, 2,000 miles is still too small.

- **Choice C: 5,000 miles, if the moon is at perigee**  
  - **Reason**: Similar to the previous choices, 5,000 miles is still less than the maximum possible separation. The distance is not constrained by the Moon's position but by the Earth's size.

### Useful Formulas or Rules of Thumb:

- **Maximum Separation**: The maximum distance for EME communication is approximately the Earth's diameter, which is about 12,000 miles when considering surface distance.
- **Visibility**: For EME communication, both stations must have a clear line of sight to the Moon, which is crucial for successful communication.

In summary, the correct answer reflects the maximum possible separation based on the Earth's dimensions, while the other choices underestimate this distance.