2. Tracking the position of an asteroid or comet
Geocentric Ephemerides -- Vesta
One of the neat things about these star-like objects (asteroids) or faint fuzzies (comets) is that they move through the sky. Finding and seeing them is one thing, but watching them move through the solar system is pretty neat too!
There are websites and programs that can generate an ephemeris for whichever asteroid or comet you are observing. You'll need to know the latitude and longitude of your observing location, the time zone and some other details, but once the ephemeris is generated, it is pretty accurate for that location. You can try to work directly from the ephemeris, but it might help to plot the position of the comet onto your charts so that you can compare the starfields in your view to the charts. This is best done with a pencil! Be sure to label the points with dates and times. Then look for your target. Once you find your target, look very carefully. Is it where you drew on the charts? It should be close, but you may see a difference. That's okay. Draw the observed position on your charts and you can later compare the 'predicted' path against the 'observed' path.
Why you should use a current ephemeris!
In 1999, I observed and sketched Vesta. Then, in making these pages (in Mar 2007), I decided to generate a chart showing Vesta's position as it was 8 years ago when I made the sketch. I was able to match up many of the stars (whew!), but the position of Vesta is way off. Why such a huge discrepancy? The orbits of asteroids and comets are not static. They are constantly being changed by small effects -- material coming off, gravitational perturbations from the planets and other small bodies, etc. Think about driving to work. You take the same basic route, but each day there may be something (wind, traffic) to cause you to drive a slightly different path. An ephemeris is only good for a certain time period as it is usually based on the most recent observations. Over time, various effects will cause an asteroid's orbit (and it's orbital elements) to change. So a new ephemeris will need to be generated. In generating my chart, I used the orbital elements for Vesta's orbit as it is this year. By running it back in time, I show a different position from what was observed because the orbital elements in 1999 are not exactly the same as in 2007. Likewise, if you try to use the 2007 orbital elements to try to predict where Vesta will be in several years, you will also be off a little. This is because, currently, most planetarium programs can only only do the calculation based on a static set of elements. Perhaps in the future, they will be able to incorporate the various perturbations over time into the calculation so that we can actually get a better idea of the motions both backwards and forwards.
Fig 1: Comparison of a sketch of Vesta done in 1999 and a chart generated 8 years later.
Determining Orbital elements
Believe it or not, before computers, astronomers would observe an asteroid or comet and plot its observed positions and then calculate its orbit. We still sort of do it this way. Newly discovered asteroids and comets are observed and their observed positions are then entered into a computer that calculates the orbit. More observations give better results for the orbit calculation. But many astronomy majors and aerospace engineers still have to calculate those orbital parameters the old-fashioned way! It really isn't that hard, but we're not going to do it here -- yet!