It is often a difficult task to predict the behaviour of a comet. For example, no one knows for sure the evolution of a comet's brightness or tail. And there are still a few periodic comets with poorly known orbits, making predictions about their next perihelion date very uncertain. One prominent example was comet P/Swift-Tuttle, the progenitor of the Perseids, which finally came to perihelion in 1992, ten years later as most had expected.

A similar case is that of comet P/Pons-Gambart. This periodic comet was only seen at one apparition, in 1827, when it passed perihelion on June 7. Due to investigations by Ogura (1917) and Nakano (1978) , the period of revolution seems to be in the range of 46 - 67 years. In 1979, Hasegawa considered the possible identity P/Pons-Gambart = C/1110 K1. According to his computations, comet C/1110 K1 had fairly similar elements, reaching perihelion on 1110 May 18. More about comet C/1110 K1 can be found in Gary Kronks book "Cometography", Volume 1, p. 193 ff.

In their paper "Periodic Comets Found in Historical Records" (Publ. Astron. Soc. Japan 47, 699-710, 1995), Hasegawa and Nakano tried to link the orbits of Pons-Gambart and 1110 K1, resulting in a period of revolution of 65.58 years for Pons-Gambart in 1827, the excentricity of its orbit being e = 0.9503946. With these elements, the next perihelion of the comet should be as late as 2022 Jan 31.

In addition, the authors present a table of previous perihelion times of Pons-Gambart, starting from the year -194 until 2022. According to this table, there should have been five additional perihelia with good observing conditions after the apparition of 1110, including that of 1827. But there is only one historical record of a comet in 1239, which could have been comet Pons-Gambart. Due to Hasegawa and Nakano, a more recent perihelion passage took place on 1892 June 12. According to this perihelion date, the comet should have been visible as a 4 mag circumpolar object in the northern sky at the end of June of this year, strolling through the Big Dipper at the beginning of July with a magnitude of 5,5 mag. However, no appropriate comet was observed. It seems unlikely to assume that such a bright object was simply overseen in 1982. Thus, if one is not willing to accept the ad hoc assumption that the comet was unusually faint during this apparition, serious doubts arose about the given perihelion time in 1892. As a consequence, the orbital resolution of Hasegawa and Nakano for Pons-Gambart in 1827 must be considered as uncertain.

I therefore found it interesting to make my own investigations regarding the orbit of comet Pons-Gambart. With the help of integration machines in REDSHIFT3, SOLEX 7.0 (a public- domain program written by Aldo Vitagliano) and DANCE OF THE PLANETS, I integrated various sets of osculating elements of Pons-Gambart backward in time until 1110 , starting from the year 1827. The starting elements were chosen from GUIDE7, with the exception of the excentricity e, which I varied in the range e=0.943 to e=0.952, corresponding to osculating periods of revolution in 1827 from 53 to 69 years.

In the adjacent figure, the resulting perihelion times are plotted as a function of the osculating excentricity in 1827. The "should be" perihelion in 1110 is indicated by a horizontal line. Integrations performed with REDSHIFT 3 are labeled by a cross (+), those computed with SOLEX 7 are shown as a circle (o); the Hasegawa-Nakano-solution is marked with a red circle. The results of both used programs seem to be consistent. Also, some tests with DANCE yield fairly similar results.

Perihelion dates versus eccentricity

As the figure demonstrates, there are several possible intervals for the excentricity in 1827 in order to yield perihelia not far from the year 1110. The first such interval goes from e=0.9446 to 0.9455 with computed perihelion times between 1103 and 1112. Given such excentricities, Pons-Gambart would have returned as early as 1990 - 1995, but the comet was not discovered during those years.

The solution e=0.9503946 of Hasegawa and Nakano fits very well in this figure, lying in the interval e=0.9499 - 0.951 of hopeful values for the excentricity. As already mentioned above, in this case we have to wait another twenty years for the next return of comet Pons-Gambart.

However, there is some hope for an earlier return of the comet. As can be seen from the figure, there are two other good fits for the excentricity, namely around e=0.94667 and at the sharply defined value e=0.948379, were the perihelia make a steep jump backward in time (resulting in 12 revolutions of the comet until 1827 in each case). This jump could have its origin in the 14th century, where due to DANCE the comet in 1365 had an aphelion unusual far from the sun, although the program didn't reveal any single reason for this.

Integrating from 1827 onward, the former value of e yields the next return at the end of the year 2003, while the latter value results in a perihelion in 2012. Anyway, if the comet was not already overlooked in recent years and has yet to come, a return of Pons-Gambart prior to the end of the year 2003 seems to be very unlikely.

See also the article by Andreas Kammerer.

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