To find the diameter of Mercury using the distance halfway around the planet, we can use the relationship between the circumference and the diameter of a circle, which is given by the formula:
\[ \text{Circumference} = \pi \times \text{Diameter} \]
Given that the distance halfway around Mercury is 4,761 miles, the full circumference would be:
\[ \text{Circumference} = 2 \times 4,761 = 9,522 \text{ miles} \]
Now we can rearrange the circumference formula to solve for the diameter:
\[ \text{Diameter} = \frac{\text{Circumference}}{\pi} \]
Using the approximate value of \(\pi \approx 3.14159\):
\[ \text{Diameter} = \frac{9,522}{\pi} \approx \frac{9,522}{3.14159} \approx 3,032 \text{ miles} \]
Rounding to the nearest mile gives us the diameter as approximately 3,031 miles.
Thus, the answer is:
3,031 mi.