How bright will Wirtanen get?
Wirtanen is predicted to get as bright as magnitude 3. What does that mean? Will I be able to see it with the naked eye? Binoculars? Or will I need a telescope?
Magnitudes
The magnitude system is an astromical classification for brightness. For historical reasons, smaller magnitudes denote brighter objects, and the scale is logarithmic, so each step in magnitude is ~2.512 times brighter than the previous one (5 magnitudes is 100 times brighter). Typically, a 5th manitude star is considered bright enough for most people to see with the naked eye, though some people, especially in regions with very dark skies, can see to 6th or even 7th magnitude.
Predicting Cometary Brightnesses
Predicting the brightness of an asteroid is pretty straightforward, because an asteroid is a solid rock of a fixed size. Once it is observed, its brightness at other times can be predicted fairly closely by scaling for the heliocentric and geocentric distance changes to correct for the r2 falloff with changing distance. (Okay, there are some other corrections that need to be included, but they tend to be small and well-understood.)
The brightness of comets, and close approachers in particular, are notoriously difficult to predict, for several reasons. First, comets are detected by the sunlight that is reflected off the dust and gas in their comae, instead of the solid nucleus. Because the coma is related to the comet's activity, its inherent brightness changes over the course of the orbit, and not always in a predictable manner (closer to the Sun doesn't always mean more activity). For newly discovered comets, predicting the future brightness is often little more than a guess, which has resulted in many "comet of the century" announcements that end up fizzling out. For comets that have been observed on previous apparitions, on the other hand, predictions have a firmer basis, because we can assume that they will exhibit the same behavior (whatever that is) form one orbit to the next. It is then a simple matter of scaling the brightness at a given time for the different distances, as is done with asteroids.
Comet Wirtanen Predictions
As far as we can tell, comet Wirtanen is fairly stable from one orbit to the next, so previous observations can be used somewhat reliably to predict how bright it will get. This is where the Yoshida and MPC predictions1, plotted on the status page, come from. Yoshida uses the total brightness recorded in previous apparitions, while the MPC uses small aperture measurements that result in a fainter prediction.
In his forecast, Yoshida uses the brightness from previous apparitions to predict that Wirtanen will reach a total brightness of ~3rd magnitude at close approach. This suggests that Wirtanen should easily reach naked eye brightness, right?
It's not quite that simple, because of the second complication relating to comets: the light from a comet is spread out over its coma, instead of being concentrated into a point source (as in stars and asteroids). So the brightness that is measured depends on how much of the coma that is included in the measurement. The total magnitudes used by Yoshida attempt to account for all the light in the coma, while the MPC magnitudes only represent the portion of the light that was covered by whatever aperture was used for the measurement.
The problem for comet Wirtanen (and other close approachers) is that, as it gets closer and closer to the Earth, its coma gets spread out over a bigger and bigger area of the sky. (Consider that at closest approach, the physical scale is only 57 km/arcsec, so the coma, which extends hundreds of thousands of kilometers from the nucleus, may be spread over many degrees on the sky.) How this affects its appearance depends on exactly how the gas and dust are distributed spatially around the nucleus. More centrally condensed material (e.g., dust) will not be spread out on the sky as the more diffuse gas contribution. Unfortunately, not only is little known about the comet, but its approach to the Earth is historically close, so we don't have the knowledge to predict how these factors will impact the comet's ultimate brightness. Thus, even if Wirtanen does reach a total magnitude ~3, it's possible that the light may be too spread out to see with the naked eye. This is especially true in cities and areas with a lot of light pollution, which can greatly reduce the contrast of the comet's coma.
The Good News
Wirtanen is going to be bright. As of early November it had a total brightness around mag ~8 and appeared to be following Yoshida's total magnitude prediction, though we don't know what that will really mean around close approach. However, even if it does not reach naked eye brightness, it will still be a great object to view with binoculars or a small telescope! And as with any astronomical observation, it is best to go to a dark site outside of the city to get the best experience.
1. From Seiichi Yoshida's Comet Page and the MPC database.↩