That's the Death Star.
Some guy on Blogspot calculated the distance the Death Star would have to be from Earth in order to perfectly eclipse the sun. He arrived at an answer of 18,000 km. Source: Source:
Total eclipse of the Death Star
Summary:
In this statement from August 22, 2017 by CW Magee Jr., the author expresses his regret for not being able to witness the solar eclipse in person due to being on the wrong side of the planet. He then goes on to use the occasion of the eclipse to calculate the conditions under which the Death Star from Star Wars could potentially eclipse the sun as viewed from Earth.
The author first defines the size and density of the Death Star, assuming a diameter of 100 miles and a density of 800kg/m3. He then calculates that the Death Star needs to subtend a larger angle of sky than the Sun to eclipse it, which requires it to be closer than approximately 18,300 km from Earth.
Magee goes on to discuss the orbital velocities and distances of the Death Star and the Earth, noting that if the Death Star were in geosynchronous orbit, it would not eclipse the sun but only block out a quarter of its light. However, if it were in low Earth orbit, it could easily eclipse the Sun and appear much larger to observers on the ground.
The author also discusses the concept of the Roche Limit, which determines the closest approach a satellite can orbit a planet without being torn apart. He calculates that the Roche Limit for the Death Star is 15,263 km, which is closer than the maximum eclipse distance of approximately 18,300 km, leaving a range of orbital radii where the Death Star could not be tidally disrupted but still eclipse the sun. However, he notes that totality would only last less than 15 seconds for an observer in this range, which is almost the exact elapsed time from the command "Fire when ready" to weapon discharge in Star Wars.
