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If The Moon Was As Close As The International Space Station, It Would Almost Fill The Whole Sky

The moon is really, really big.

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This is what the sky would look like if the moon orbited at the same distance as the International Space Station.

View this video on YouTube

It's sped up slightly. And its the surface of the moon that's at the ISS's distance, not the centre.

At 420km [the moon] orbits much faster than the earth rotates underneath, therefore it will rise in the west and set in the east. The moon would orbit very fast, somewhere between 130 mins and 90 mins.
The moon is well within the Roche limit. At this distance the moon would break up and form a new ring system. The Earth might also be destroyed.