At least in Michigan, amateur astronomy is mainly about keeping track of the weather (you can't observe when it is 100% overcast), the moon phase (dim objects can't be observed when the moon is out), the planets, comets and unusual/rare events (such as Venus transits and the like). It is also learning to use your eyes, telescopes and/or binoculars to find static/unchanging objects (constellations and star clusters, nebulae and galaxies). But for the most part you are looking at objects that many other people have looked at before.
Don't get me wrong, these challenges are enough for most amateur astronomers. Nevertheless a few amateur astronomers find ways to make novel observations; novel observations which can add to scientific knowledge. I will not produce a complete list here, but here are a few ideas...
- If you connect a camera to a computer, it is possible to monitor the night sky for meteors. If you combine your observations with observations made at other locations, you can determine the velocity of the meteor and it's trajectory. Anyone interested should go the web site "Cameras for Allsky Meteor Surveillance," http://cams.seti.org/
- Extrasolar planets: These days, most extrasolar planets are discovered by the Kepler space telescope, however occasionally amateur astronomers find one. One of the more interesting recent discoveries was of a planet orbiting a group of four stars (the first time such an observation has been made). See http://www.wired.com/wiredscience/2012/10/planet-hunters-four-star/
For information about Kepler (see http://kepler.nasa.gov/)
- Another avenue for contributions is variable star research. This requires repeated observations, night after night, for long periods with no guarantee of useful results. But there is the possibility of making a useful contribution. For more information start with this article from Astronomy Magazine: "Fun with double and variable stars" http://www.astronomy.com/en/News-Observing/Urban%20Skies/2006/12/Fun%20with%20double%20and%20variable%20stars.aspx
- For more ideas, see the Association of Lunar and Planetary Observers (http://www.alpo-astronomy.org/) and Pamela Gay's Citizen Science (http://www.starstryder.com/category/citizen-science/)
- Over the past hundred years, most advances in astronomy/physics theory have involved groups of scientists working together. Single individuals making ground breaking advances are rare.
- Any new idea will be subjected to intense criticism; many people can't deal with criticism, but this is fact of life for theoretical science.
- It is essential that you understand all the ideas that come before. If you are proposing a new theory, you must demonstrate that you understand the existing theories and explain why your theory is better.
- In almost all cases, physics and astronomy requires math. A theory without math probably wont be be taken seriously.
- Above all it is hard work.