A lot could be said about comets and asteroids, and there are many differences between the two. However, as far as we, the amateur astronomers, are concern, the matters are not that difficult.
Comets are made mostly of ice and rocks. Some of them that are drifting through the solar system, but most of them are located in Kuiper belt (beyond Pluto’s orbit) or Oort’s cloud (even further). Their albedo (light reflective power) is quite low, lower than that of asphalt! That’s the reason we see them only when they are closer to the Sun, and start to sublimate (evaporate, more or less).
In a telescope, distant comets look like smudges, like galaxies. After they get close enough, they start to form tails (due to the sublimation we mentioned earlier). The closer they get, the larger and more beautiful their tails become. Every once in a while, there would be a comet bright enough for human eyes to see. In rare cases some of these comets could become one of the brightest objects, their tails spreading over tens of degrees over the sky. Perfect example for this is the comet Hale Bopp.
When it comes to observing, there are a few things you should consider:
- Faint comets, not visible with naked eye. Use a telescope with lower magnification (40 mm or 25 mm eyepiece).
- Bright comets, visible with naked eye, but still hard to find on the sky. Such comets are going to have small but distinct tails. That might require using a binocular, which has a larger filed of view.
- Very bright comets, which are among the brightest objects on the sky. For comets like these you would have to use a binocular, although you might not be able to fit the entire comet in the field of view. If that’s the case, you might try to study different parts. Best of all, enjoy the view with your own eyes.
All in all, there is only one way to do that, mounting your camera on a telescope. I agree that very bright comets could be photographed from a tripod, but let’s face it, how many times in your life have you seen comets like Hale Bopp? Once? Twice maybe? Granted, people with more years of experience, shall we say, could have better chances.
So, what you need is a telescope, mount (preferably equatorial and motorized), camera, lens with focal length in the range 50-200 mm. The recommended ISO settings (for digital or film cameras) could vary quite significantly. For very bright comets you may use 200-400 or even 100 ISO, for the fainter ones – 400-800 (maybe up to 1600) ISO.
There are plenty of asteroids flying around the Solar system. Most of them are concentrated in the asteroid belt, located between Mars and Jupiter. Others are positioned on Jupiter’s orbit, 60° degrees before or after the planet as viewed from the Sun. They are called Trojan asteroids. Many asteroids are not associated with any group, just buzzing around freely.
The asteroids are made mainly of rocks and metals. Depending on the ratio of the two ingredients, there are different types of asteroids.
Observing asteroids is… well, a bit boring to be honest. They are point sources, and we cannot separate them from stars, no matter how bright they get. We could check their position on the sky every night to find that they are moving. Photographs of the same region taken in different nights are best for tracking asteroids.