Comet Tempel-Tuttle was "discovered" independently by William Tempel in December 1865 and by Horace Tuttle in January 1866. After this apparition, calculations showed that the comet was in an elliptic orbit with a 33-year period. This information was then used to prove that Tempel-Tuttle was the same comet that had been observed in the year 1366 and again in 1699. The orbit determination was also used to show that T-T was associated with the Leonid meteor shower that occurs every year in November.
Even though astronomers searched for it in 1899 and again in 1932, Tempel-Tuttle was not seen again until 1965, when it was observed as a faint, 16th magnitude object.
Comet Tempel-Tuttle was recovered on March 4, 1997 by Karen Meech, Olivier Hainaut and James Bauer at the University of Hawai`i. At the time it was very faint (22.5 mag), but the recovery proved that it was returning on schedule and that its orbit was very well determined.
The observing geometry when T-T was closest to the Earth was very well-suited for observers in the northern hemisphere: the comet was very close to the north pole, which made it visible all night (similar to Hyakutake's close approach).
On January 18, 1998, Tempel-Tuttle reached its closest point to the Earth at a distance of 0.36 AU (33 million miles). It reached its predicted brightness around 8-9th magnitude, and was observable with a pair of binoculars. At about this time, a short, narrow tail became visible in telescope images.
On February 28, 1998, T-T passed perihelion, at a heliocentric distance 0.977 AU (just inside the Earth's orbit). At this time, the comet had faded slightly compared to its mid-January brightness, but it also exhibited a longer tail. Shortly after reaching perihelion, T-T started to fade rapidly and then went into solar conjunction. Tempel-Tuttle won't be back until the year 2031, but while we await its return, we can enjoy its legacy, the Leonid meteor shower.
The diagram below shows the orbital positions of the Earth and comet during the 1998 apparition. When Tempel-Tuttle is at perihelion, it is very close to the intersection of the two orbits, where the Earth will cross the comet's orbit in November 1998 (see discussions on Meteor Showers and their Relation to Comets and on the Leonid Meteor Shower). The lines extending from the comet's orbit are to locate its position above or below the ecliptic plane, with each line spaced 15 days apart.