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Often in discussing exoplanets we hear that they are close to the parent star (usually a red dwarf) but then there's a caveat that the planet is tidally locked to that star and that that fact severely decreases prospects for that planet to harbor life.

But how do we know that an exoplanet is tidally locked to a star? I doubt that we can directly observe the rotation of that planet. Does that mean that we conclude that it's tidally locked because that's what our theoretical models tell us, and not that we observe it directly?

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They are probably tidally locked, given some assumptions about age of the planetary system.

There's a formula to calculate how long it'll take for an orbiting object to tidally lock, and one of the outcomes of that formula is that large objects in close orbits don't take very long to tidally lock.

Since many of the exoplanets we've found are large objects in close orbits of old stars, tidal locking is a likely outcome.

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Hobbes's answer is correct for planets assumed to be tidally-locked. There are nevertheless a couple of exoplanets we know definitely aren't tidally locked because their rotations have been measured. The first rotation measurement of an exoplanet was for Beta Pictoris b, which turns out to have an 8-hour rotation period. Another example is 2M1207b with a 10-hour rotation. Admittedly these objects are so far away from their stars that we wouldn't expect them to be tidally locked: the rotation measurements rely on these objects being imaged, which requires a large star-planet separation.

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