Is it important that a shuttle surrounds the Earth in an circular orbit in order the astronauts (and the shuttle itself) to have 0 apparent weight and so be considered as in state of apparent weightlessness?
No, as long as they are in freefall at all, in an elliptic orbit, or a parabolic curve that will return to earth, both astronauts and shuttle are falling at the same acceleration and so weightless.
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Pkruse
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I don't think it was a part of anybody's design constraints to achieve apparent weightlessness on the Shuttle. That was just a consequence of achieving a stable orbit.