Do you have to have a telescope to do astronomy? No, although a nice pair of binoculars would be handy. In fact, if you search the internet for telescope buying advice you'll find lots of sites and they'll usually recommend you start with binoculars first. However, our goal is to get you to observe the asteroids that the Dawn mission will be investigating. And those asteroids are not visible to just your eyes. You will likely need a good pair of binoculars or a small telescope to see them. Should you go out and buy a telescope just for this? No! You'll be better off finding out about what events your local astronomy club, observatory, or space place has setup for observing the asteroids. Then you'll have the chance of looking through other people's telescopes and benefiting from their expertise.
Observing Hartley 2: Sep-Nov 2010
A larger aperture telescope may be needed to visually see the comet through the summer of 2010 as it will remain fairly faint. In September and October the comet will be brightening as it gets closer to the sun and as we get closer to it! By mid to late October, Hartley 2 could be a binocular object!
Fig 2: The above graph is an approximation of what magnitude you can visually observe through a particular aperture telescope. For example to see stars of nearly 14 magnitude, you would need at least a 10" telescope. Through a 30" telescope, you could see stars to about 16 magnitude. Cameras, because of the longer exposures, can see fainter stars for a given aperture. The graph is for point sources. Extended sources like comets usually require a little more aperture for the same magnitude.
Jeff Baldwin of the Stockton Astronomical Society discusses an approximate formula for relating telescope aperture to limiting magnitude for point sources (like asteroids). The actual values are dependent on several factors including the clarity of the night sky, darkness, and the observer's own visual acuity. If you know when your target (asteroid or comet) reaches a particular magnitude, you can roughly determine what minimum size telescope you would need to see the target.
There are two caveats. The first is that this magnitude-aperture relationship is for point sources such as stars, whereas a comet is usually a larger, fuzzier object for which we quote an integrated magnitude. That light is spread out over a larger area, so we generally need a larger aperture for a given magnitude than we would need for a star (or asteroid) of the same magnitude. Often we quote not only a magnitude but also a size and description (ie, star-like, condensed, or diffuse) for the coma of the comet, and that additional information can then give us a better idea of how large a telescope aperture and magnification might be needed to see the comet. The second caveat is that these values are just for visually observing. Long exposures with either a CCD or film camera can see deeper (fainter) than the eye through any given telescope.
Remember, the above graph is just a rough guideline.
If you don't try to observe, you will definitely see nothing. So go out and look!
Observing faint comets
Faint comets (like Tempel 1 was) will usually need a larger telescope. Why? A larger telescope will collect more light and let you see the comet better. But remember, comets are faint fuzzies. In a small telescope, the faint fuzzy will appear dim, but might be easier to see in the larger field of view (better contrast). In a larger telescope, the faint fuzzy will appear slightly brighter because the larger scope collects more light, but if you zoom in too much, the field of view may not have enough of the background to give a good contrast. Other factors also make it difficult to give a concrete answer. This is why it is useful to get some experience with observing with a local astronomy club or observatory.
Archive: Deep Impact -- Tempel 1
The comet might get bright enough after we hit to be seen in binoculars, but more than likely, you'll need to look through a telescope to see it. [Post-impact: In fact, the comet was fainter in general and never brightened significantly. Observations were made with telescopes as small as 4" in aperture, but most observers were using larger telescopes.]
Comet Tempel 1 is a low activity comet, so the coma is likely to be more condensed rather than diffuse, and therefore more star-like. Therefore the estimates from the above graph shouldn't be much more than a couple of magnitudes away from what is expected. [Post-impact: Well, this part of the expectation remained true.]