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Pretty simple question I just don’t know the math for. If I want my space station/megastructure that’s orbiting 2000-ish km above Earth to seem roughly as large as the Moon to an observer on the ground, how large would it need to be? My blind best guess is more than ten kilometers long/wide, but I’d like to know exactly how big an object would need to be in order to partially obscure the Moon by at least 50%.

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marked as duplicate by Mołot, bilbo_pingouin, Chronocidal, a CVn Dec 18 '18 at 8:13

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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    $\begingroup$ Your title asks the object to be clearly visible, then your question asks first as large as the Moon and then 50% of the Moon. Can you make up your mind and ask just for one thing? $\endgroup$ – L.Dutch Dec 18 '18 at 6:16
  • $\begingroup$ It's not exactly the same question, but the same math can be applied; just substitute your own values. Hint: the angle subtended by Earth's moon, as viewed from Earth, ranges from 0.49 to 0.55 degrees. $\endgroup$ – a CVn Dec 18 '18 at 8:16
  • $\begingroup$ The questions title seems like a duplicate, but OP is actually asking for size to partially obscure the moon, not size visible from earth as in 'duplicate' $\endgroup$ – bukwyrm Dec 18 '18 at 8:16
  • $\begingroup$ @bukwyrm OP specifies an orbital altitude and an apparent size. The math involved is thus the same; all that's needed is to apply it slightly differently. Whether an object partially or completely obscores another is a function of many things besides merely the two objects' apparent size, not least the angle at which they are observed. $\endgroup$ – a CVn Dec 18 '18 at 8:18
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    $\begingroup$ I don't think this question is a duplicate at all. As the other query says, the ISS is "visible ... but its features cannot be distinguished". IOW, it is not "clearly visible". Z.Schr., I think if you clarified your query by defining what you mean by "clearly visible", and added a link to the other query, it could be reopened as a distinct but related question. $\endgroup$ – elemtilas Dec 18 '18 at 18:16
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The relationship between true size and distance for two objects with the same apparent size is linear. That is, an object twice as far away, and twice the actual size, will appear to be the same size.

The Moon orbits at an average distance of about 385,000 km. (Although the distance between you and the Moon varies by a few thousand km depending on where you are on the planet, that's not a big deal here.) Low Earth orbits vary, but are generally on the order of 1/1000th of this, or ~300 to 400 km. (The International Space Station orbits at a little over 400km.) So your object needs to be about 1/1000th the Moon's radius, or only about 1.7km. That's big in terms of sending things into space - the ISS is only about 100m long, and that's counting all the panels and such - but it's not that big in absolute terms.

However, there are a number of problems with this. One is that while the variations in distance to different parts of the Earth are fairly negligible for the Moon's size, they're not for your satellite's size; it will appear much smaller from distant parts of the Earth than from directly beneath it. A second problem is that the Moon's orbit is somewhat eccentric - it moves up to 5% closer and further from its average distance during its orbit. Naturally, this has a similar effect on its apparent size.

Also, this only ensures that your satellite has roughly the same apparently size as the Moon. Actually occluding the Moon is a much trickier subject. You can look up solar eclipses to get a feel for the geometry involved, but the short version is that the satellite would need to be in a particular orbit, it would only eclipse the Moon every so often, and the eclipse would only be visible on certain parts of the surface.

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