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TRAPPIST-1 is an ultra-cool dwarf star in the constellation Aquarius, orbited by a total of seven planets, all around the size of the Earth.

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Three of them — TRAPPIST-1e, f and g — dwell in their star’s so-called “habitable zone.” The habitable zone, or Goldilocks zone, is a band around every star (shown here in green) where astronomers have calculated that temperatures are just right — not too hot, not too cold — for liquid water to pool on the surface of an Earth-like world.

While TRAPPIST-1b, c and d are too close to be in the system’s likely habitable zone, and TRAPPIST-1h is too far away, the planets’ discoverers say more optimistic scenarios could allow any or all of the planets to harbor liquid water.
In particular, the strikingly small orbits of these worlds make it likely that most, if not all of them, are tidally locked, perpetually showing the same face to their star, the way our moon always shows the same face to the Earth. This would result in an extreme range of temperatures from the day to night sides, allowing for situations not factored into the traditional habitable zone definition.
The system has been revealed through observations from NASA’s Spitzer Space Telescope and the ground-based TRAPPIST (TRAnsiting Planets and PlanetesImals Small Telescope) telescope, as well as other ground-based observatories. The system was named after the TRAPPIST telescope.
Astronomers made the discovery by looking for :-

1) dips in the light emitted by TRAPPIST-1, as this can indicate the presence of an orbiting planet. These dips are known as ‘transits’ and studying them also enables astronomers to learn much about the planets’ composition, sizes and orbits.

2) ‘wobble’ method, measuring radial velocity of the star.
(Information taken from NASA, JPL,web pages).

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