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M40
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Title: Gaia Shows That Messier 40 is Definitely Not a Binary Star
Author: Michael R. Merrifield, Meghan E. Gray, Brady Haran

M40 has always been something of an oddity in the Messier Catalogue, since it is just a pair of stars rather than an extended object. Doubts have also been expressed as to whether it is even a physical binary. Here, we note that the Hipparcos/Gaia parallaxes for these two stars remove all doubt: Messier 40 comprises a pair of entirely unrelated stars.

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RE: Messier 40
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Messier 40 Double star Ursa Major (Big Dipper) Handle

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Winnecke 4
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Messier 40 (also M40, Winnecke 4 and HD 238107 + HD 238108) is a magnitude +9.65 and +10.10 G0+F8 optical double star located 510 light-years away in the constellation Ursa Major. 

The double star was discovered by French astronomer Charles Messier using a 8.38 cm (3.3-inch) refracting telescope at the Hôtel de Cluny (now the Musée national du Moyen Age), in Paris, France on the 24th October 1764.

Position (J2000): R.A. 12h 22m 12.5s  |  Dec. +58° 04' 59"

It was subsequently rediscovered by Friedrich August Theodor Winnecke in 1863, and included in the Winnecke Catalogue of Double Stars as number 4.
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RE: Messier 40
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The same night of October 24 to 25, I searched for the nebula above the tail of the Great Bear, which is indicated in the book Figure of the Stars, second edition: its should have, in 1660, the right ascension 183d 32' 41", and the northern declination 60d 20' 33". I have found, by means of this position, two stars very near to each other and of equal brightness, about the 9th magnitude, placed at the beginning of the tail of Ursa Major: one has difficulty to distinguish them with an ordinary [nonachromatic] refractor of 6 feet. Here are their position: right ascension, 182 deg 45' 30", and 59 deg 23' 50" northern declination. There is reason to presume that Hevelius mistook these two stars for a nebula.
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Winnecke 4 (also known as Messier 40 or WNC 4) is a double star in the constellation Ursa Major. It was discovered by Charles Messier in 1764 while he was searching for a nebula that had been reported in the area by Johann Hevelius. Not seeing any nebulae, Messier catalogued this double star instead. It was subsequently rediscovered by Friedrich August Theodor Winnecke in 1863. Burnham calls M40 "one of the few real mistakes in the Messier catalog," faulting Messier for including it when all he saw was a double star, not a nebula of any sort
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