To find the diameter of Mercury based on the distance halfway around the planet (which is the circumference divided by 2), we can use the relationship between the circumference and diameter of a circle, which is given by the formula:
\[ C = \pi \times d \]
where \(C\) is the circumference and \(d\) is the diameter. Since we have the distance halfway around Mercury (4,761 miles), we can first calculate the full circumference by multiplying this distance by 2:
\[ C = 2 \times 4,761 \text{ mi} = 9,522 \text{ mi} \]
Now, we can rearrange the circumference formula to find the diameter:
\[ d = \frac{C}{\pi} \]
Substituting the value we found for \(C\):
\[ d = \frac{9,522 \text{ mi}}{\pi} \approx \frac{9,522 \text{ mi}}{3.14159} \approx 3,031 \text{ mi} \]
Thus, the length of the diameter of Mercury, to the nearest mile, is approximately:
3,031 mi.