|D/1766 G1 (Helfenzrieder)
J. E. Helfenzrieder (Dillingen) discovered this comet on 1766 April 1.85. Independent discoveries were made by C. Messier (France) on April 8.85 and C. F. Cassini de Thury (France) on April 8.86. Messier said the comet was then visible to the naked eye near the horizon and exhibited a tail 4° long. Cassini described the comet as bright, with a tail 3° to 4° long.
The comet continued to be visible to the naked eye until lost to Northern Hemisphere observers. A. Brice (Kirknewton) easily saw the comet with the naked eye on April 9 and said the tail was about 4° long. He noted that a telescope revealed a very distinct nucleus that had the appearance of a star of magnitude 4 or 5. Cassini de Thury saw the comet on the evening of the 9th and noted little change in appearance since the previous evening; however, on the 10th he said the comet had faded and the tail had become less distinct, although he partly attributed this to the nearby moon.
The comet was last seen on April 12. Cassini de Thury saw it on April 12.82 and noted it was still barely visible to the naked eye. Messier saw the comet on April 12.83 and said it was very near the horizon and appeared "very faint". He added that the nucleus was ill-defined, while the tail extended 1.5°. Messier said the sky was equally as clear on April 13, but his searches around Alpha Arietis near the horizon revealed no trace of the comet. Cassini de Thury said clouds covered the region near the horizon during the first few days following April 12, and, thereafter, the comet was poorly placed for observations. Cassini de Thury searched whenever possible, but found nothing.
Shortly after the Northern Hemisphere observations ended, A. G. Pingré computed an orbit indicating a perihelion date of 1766 April 17.51. He suggested the comet be searched for in the morning sky during June.
The comet was finally recovered in the morning sky by de la Nux (Bourbon Island) on April 29.08. It was then situated 20° from the sun. De la Nux continued to observe the comet on the mornings of May 1 to May 9, only missing the 4th. The comet was also seen at the Cape of Good Hope in South Africa on the morning of the 8th. The comet was last detected on May 13.04, by de la Nux. It was then about 8° above the horizon, but was being blocked by the mountains. De la Nux said it was only visible in a telescope.
In 1784 Pingré revised his parabolic orbit with a perihelion date of April 23.37 and this satisfied astronomers for a while; however, in 1821 J. K. Burckhardt began investigating this orbit and noticed that the comet moved in a short-period orbit. He determined the perihelion date as April 27.49 and the orbital period as 5.02 years. Later elliptical orbits were calculated by C. W. Wirtz (1915) and D. K. Yeomans (1985). Wirtz determined the period as 4.51 years, while Yeomans determined itas 4.35 years. Wirtz also noted that his orbit indicated the comet had passed 0.03 AU from Jupiter on 1763 November 11. Prior to this encounter, the comet would have last passed perihelion on 1760 November 15.56, and would have had an orbital period of 4.85 years.