Comet Alcock, formally designated as C/1959 Q2, is a relatively bright non-periodic comet that only appeared for a week in September 1959. It was the second comet discovered by English astronomer George Alcock.

Observational history Shortly after discovering C/1959 Q1 George Alcock found his second comet using a pair of binoculars on the night of 30 August 1959. He described the new comet as a diffuse, sixth-magnitude object with a central condensation and a small tail, located within the constellation Cancer.

Elizabeth Roemer took long-exposure photographs of the comet from the US Naval Observatory on 1 September 1959, reporting a sharply-condensed nucleus and a tail over a degree in length. By the following day, Alois Purgathofer, George van Biesbroeck, and D. P. Elias also observed the comet, where it was reported that the comet had slightly brightened to 5.7 in apparent magnitude. On 4 September it brightened further to magnitude 4.7.

The comet was last seen by Roemer on 6 September 1959 within the constellation Hydra, shortly before an expected solar conjunction the following day.

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