Dieter Egger @ FESG TUM
 
Comet's position in different reference frames
Compute the position of a comet in different reference frames at a given epoch and for a given observer.

The applets

  • Calendar (TimeBase)
  • CometOrbit
  • Observer
  • Transform

will do the job.

Of course you might run several occurences of your web-browser including the corresponding applets (one per browser) and transfer the intermediate results manually by copy and paste.
But it is much more convenient to collect the applets on a single page and thus to profit by their mutual communication capability.

CometOrbit differs from PlanetOrbit in only two details:

  • specify distance of perihelion instead of semi-major axis
  • specify perihelion passage time instead of mean anomaly

Moreover the reference system is mostly fixed to epoch J2000

We have neglected the influence of precession for the time span between J2000 (the epoch of the orbit elements' reference system) and the actual epoch of date. You may check the TimeLink-page and see that the precession angles are indeed very small nowadays (about one minute of arc).

Example:

Compute the position of Hale-Bopp in the evening sky at the 20th of March 1997 at 7:30 pm (19:30 UTC). Assume the observer residing in Munich (longitude 11 degrees, latitude 48 degrees, height 550 m above sea level).

The following steps will solve the problem:

  • Enter the observer in the Observer applet.
  • Select Hale-Bopp in the CometOrbit applet.
  • Enter date and time in the Calendar (TimeBase) applet.
  • In the Transform applet choose "Topocentric horizon system" as target reference frame (right hand side).
  • Select polar coordinates.

Maybe that you have to repeat one of these steps in order to get correct results (Netscape 6.2 did not function properly)

For the values of our example, you should finally read

1.31611... (AU) for r (distance)
218.04201... (deg) for ph
74.08499... (deg) for th

phi is the angle counted from South to East, theta is the angle counted from the zenith to the horizon. If you are better acquainted with azimuth A and elevation e, you may easiliy calculate them using

A = 180 - ph (= 321.95799 for the example)
e = 90 - th (= 15.91501 for the example)

 

Dieter Egger,  last update 2002-02-27