Preliminary Orbit of Comet C/2010 X1 (Elenin) on October 14, 2011 (Source: JPL Small-Body Database Browser Orbit Diagram)
From Wikipedia on Comet C/2010 X1...
Comet C/2010 X1 (Elenin) is a long-period comet discovered by Russian astronomer Leonid Elenin on December 10, 2010 at International Scientific Optical Network's robotic observatory near Mayhill, New Mexico, U.S.A. C/2010 X1 has pretty small perihelion distance - about 0.44 AU. This relatively bright comet can reach 8th magnitude on September-October 2011.
From a posting on spaceobs.org...
From new observations of Comet C/2010 X1 (Elenin), the Minor Planet Center has published new orbital parameters. There has been a fundamental change; instead of a perihelion near Jupiter’s orbit, the comet will have an aphelion at Mercury’s orbit! Of course the new comet does not belong to the class of sungrazing comets, but it will be visible in images from the coronagraph installed on the space observatory SOHO.
C/2010 X1 comes within 0.03 a.u. (4.5 million km) of the Earth’s orbit, but only ~0.4 a.u. from the planet itself – not at all threatening to us.
The comet will increase its brightness; in August of 2011 it will be mag. 6-8. By the end of the month and throughout September the comet will be hidden from earthly observers in the rays of the Sun, but it will be easily visible in images from the cosmic coronagraph. At that time the comet’s brightness will be at maximum – about mag. 3-4 (although with passage so close to the Sun anything can be expected). By the way, at that time the comet will again be at the same equatorial coordinates where it was discovered in December of 2010.
Beginning in October, the comet will again become visible for observations from Earth; at that time its brightness will be magnitude 4-5, i.e. the comet will be visible to the unaided eye far from large cities. Visibility conditions from northern latitudes will be favorable – the tailed guest will climb into the northern sky. After that, C/2010 X1 will slowly become fainter and move away from the Earth. By the beginning of 2012 its brightness will be around mag. 11-12.
Link: Article (C/2010 X1 – A Bright Comet of 2011)
Link: Sky and Telescope Article
Link: JPL Information