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Rigorous Science

Where to place my space-station so it observes one full planetary revolution per 24 hours?

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For a SciFi project I work on I have a space-station orbiting earth that uses an 8 hour 3 shift system for its staff. Each shift is assigned to one-third of the countries and organizations on earth - namely those that are facing the station during the ~8 hours of the shift.

The above premise requires the station to be placed so that it will stay relatively put in regard to the earth and one of her full rotations.

Q: Where can I put my station so it can observe a full rotation of earth?

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This post was sourced from https://worldbuilding.stackexchange.com/q/91677. It is licensed under CC BY-SA 3.0.

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This is a kind of alternative to KareemElashmawy's answer.
As they point out, the best you can do with a single station is to put it in one of the Lagrange points, but these have problems.

The Earth/Sun L1 point is too far away from Earth, and has fairly high radiation.
The Earth/Sun L2 point has lower radiation, but is also far away, and you'll only ever see the night side of earth.
The Earth/Moon L1 point would be close enough, but you'd be tied to the Moon's day/night cycle, which is 28 days long, and so half the cycle you'd see the Earth's day side, and half the cycle you'd see the Earth's night side, which isn't ideal.
None of these points are stable, and so you'd have to constantly monitor your position and apply corrections to stay on station.

Unless you want to use magic level tech you can't have an orbit that stays solely between the Earth and Sun and is within the orbit of the moon. You would essentially have to constantly expend thrust in order to hover in that position.

So I'd like to propose a "PQ" solution; Have three space stations in geostationary orbit. Each station would stay active while the section of the globe that it's monitoring is in daylight. This has a side advantage that there would be no back side of the planet that one of the stations couldn't see which could be useful for emergency and traffic control purposes.

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