When an astronomer says a comet is “bright”, it means that the comet will be brighter than magnitude 12. At this magnitude, the comet will be visible to the eye in moderate aperture amateur telescopes, rather than requiring substantial exposure times with film of CCD cameras. To the ordinary person on the Clapham Omnibus, this is still extremely faint; people with good eyesight under ideal dark sky conditions can see objects as dim as magnitude 6.6, over 100 times brighter than a magnitude 12 object.
Cassini in orbit around Saturn with the location of Elenin shown, Elenin is too dim to be seen, click to embiggen
Not surprisingly, the astronomical use of “bright comet” can cause considerable confusion, especially as most people don’t have a good feel for the brightness of objects in the sky. Comet C/2010 X1 Elenein is a “bright” comet; although it is currently around magnitude 14, it will reach a magnitude of somewhere between 6 (just visible to the unaided eye) and 4 (about as bright as epsilon Crucis, the 5th and dimmest star in the Southern Cross) at its brightest.
Why the variation? The brightness of an object like an asteroid depends on how big it is, how far it is from the Sun and us, and how shiny it is. Calculating the brightness of an asteroid at closest approach is fairly straightforward, even if we are a bit uncertain about how shiny and big it is.
Gustavo Muller's image of Elenin on August 8, 2011, from the Aerith gallery.
Unlike asteroids, we are not seeing the surface of the comet per se (except when it is very, very far from the Sun), but light reflected from the tenuous haze of dust and gas that boils off the “dirty snowball/icy dirtball” that is a comet. The coma of a comet can extend many thousands of kilometres from the surface.
The Great Comet was around 30km in diameter and had a coma nearly as big as the Sun, comet Halley is 6x15 km and had a coma 100,000 km wide when it last approached Earth, C/2010 X1 Elenin is roughly 3-4 Km and has a coma around 50,000 km wide. The coma is a pretty good vacuum by Earth standards, but there is enough dust and fluorescing gas in this thin haze to make the comet glow brighter than the mere iceball would.
How bright the comet is depends an exactly how active it is (ie how much dust and gas it produces and the size of the coma), which depends on a complex set of properties (if there are lots of rifts in the organic/silicate crust that coats the comet surface to blast out dust and gas, for example). We don’t have an exact handle on exactly what makes a comet bright, and there is substantial discussion on the comet lists about the best way to estimate the development of cometary brightness.
Light curve of comet Elenin, from Aerith, click to embiggen.
However we have a number of good rules of thumb. Comets that have just dropped in from the Oort cloud, like Elenin, are intrinsically dim. That is they tend produce much more gas than reflective dust and usually do not put on much of a show.
Again, there have been exceptions, comet 2006 P1 McNaught was initially expected to be very bright, around magnitude 2, but ended up around an astounding magnitude -1 when we could first see it again after it passed behind the Sun (although it’s brightness dropped rapidly after that). Still by following the light curve of a comet we can get a good idea of its brightness. The light curve of Elenin is still developing, but it looks on track to be somewhere between just visible to the unaided eye to being dimly visible.
People also confuse the concept of “bright” in terms of a comet and “big”. And example is here:
Elenin passed fairly close to Saturn in Mid-Late 2009. Cassini was in the area, taking pictures of Saturn and it's moons. It had just wrapped up its scheduled mission when project planners extended it.
So a big comet was nearby, and Cassini never saw it? This means either:
A) NASA saw Elenin with Cassini in 2009 (or earlier) and decided not to tell us
B) NASA did NOT see Elenin in 2009 because it's not really a bright comet after all
C) NASA did NOT see Elenin in 2009 due to chance or incompetence.
Rings of Saturn as seen from Cassini. See the Stars? No, they are all washed out in the image (click to embiggen)
Now there is a couple of issues here, “fairly close” was a large chunk of 1 AU away, what looks “close” on a JPL animation is still an enormous distance way (see the image at the top of the post). And again, the mistaken concept of “bright”. At the time (2009) Elenin was still fairly dim, around magnitude 22, just a tiny bare lump of ice with only the faintest traces of a coma around it, far from the illumination of the Sun.
You can use the JPL horizons program to find out how bright it would seem from Cassini. Turns out it’s around magnitude 22 as well (the comet was closer, but as seen from Saturn and Cassini it would only be partially illuminated).
Spica as imaged by the Cassini cameras (click to embiggen)
Now have a look at the typical image from Cassini (see above), can you see the background stars? No, Cassini is photographing relatively bright objects, and the typical exposures are too short for all but the brightest stars, let alone a dim comet.
Occasionally the spacecraft does do a long exposure image of the stars, for navigation purposes. The image to the left is just such an image centered on Spica, (alpha Virginis). The dimmest star in this image is magnitude 9, well above the brightness of Elenin. Even if a navigation image has been taken which had been pointing in Elenins direction (in general Cassini wasn’t pointing anywhere near Elenin), it couldn’t have picked the comet up.
NASA’s failure to pick up Elenin is not due to incompetence, bright comets are not bright for their entire journey around the Sun, but typically brighten substantially only during the closest approaches to the Sun, in principle Cassini could not have picked the comet up. Elenin won’t be spectacular, but at the very least will look nice through binoculars under a dark sky.