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The star GJ 581 is interesting because it is a multiplanet system but the exact number of planets has been controversial (it is thought to be between 5 and 6). In multiplanet systems, each planet is not necessarily detected by its own unique signal. The signals from all planets are convolved in a complex manner and the the system parameters have to be deduced by modeling the signal as composite. What is even more curious about the GJ 581 system is that two of its planets, GJ 581 d and GJ 581 g were listed in July 2012 in the top 5 potentially habitable planets list proposed by the Planetary Habitability Laboratory (PHL). One of the two planets in the list associated with GJ 581, (GJ 581 g) is not even universally agreed to exist (i.e., it could be a result of statistical noise). A good summary is given in a 2012 paper by R. Baluev, who in fact concludes that only three planets may be real, and that GJ 581 f and GJ 581 g are merely artifacts of noise.
The star GJ 581 is about 20.3 light years from Earth, its mass is about a third of that of our Sun, and its size is also about a third that of our Sun. In August 2012, the Extrasolar Planets Encyclopedia listed only four planets in the GJ 581 system as confirmed (GJ 581 b, c, d, and e). The masses range from about 2 to 16 Earth masses, but none of the planets have radius measurements. Without radius measurements, there are no constraints on the bulk density, and the compositions are ambiguous.
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Regarding the prospect of GJ 581 d and GJ 581 g, and the to-and-fro debate about the existence (or otherwise) of the planet g, please read the article How many habitable planets have been found?, which also has some references to the scientific literature about the debate for GJ 581 g.
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File under: GJ 581 multiplanet system; GJ 581 d and GJ 581 g potentially habitable planets.