65803 Didymos is a binary asteroid system and is a near earth asteroid, which makes it an ideal target for redirection experiments, such as the Double Asteroid Redirection Test by NASA. If successful, 65803 Didymos and Dimorphos will become quite famous as being the first asteroid to ever be manipulated by humankind.
A 10 square mile claim would be enough for basic mining operations and local support structure. Hypothetical estimated value in 2022 USD $1 trillion. The number of available claims is limited to 1.
Image Credit: NASA / JPL-Caltech