AST352L--Spring 1998

Determining the Position of a Comet

2. The Position In Space

This assignment is DUE on Friday, April 17.

The elements of the orbit of Comet Encke (referred to the J2000 reference frame) are

a=2.2091401 AU

e=0.8502196

I=11.94524°

Longitude of Node (Big Omega)=334.75006°

Argument of Perihelion (little omega)=186.23352°

T=1990 October 28.54502, Dynamical Time

In your previous assignment, you will have calculated the position and velocity of the object within the orbital plane, on October 5, 1990 (Dynamical Time). I did the calculation and got

x	-0.0692692538
y	-0.6675211908
xdot	0.0218677879
ydot	0.0164230198

Here's what you need to do now to complete the job:

1. Calculate the quaternion that takes you from the orbital plane to the equatorial reference frame. You will need to perform the additional rotation to take you from the ecliptic to the equatorial reference frame. Use the value of the obliquity of the ecliptic for the epoch J2000.0: 23°26'21.448"
2. Using this quaternion, calculate the (x,y,z) position of Encke's comet in the equatorial reference frame J2000.0, referred to the Sun.
3. Go to the Ephemeris for the year 1990; look up the rectangular coordinates of the Sun referred to the J2000 reference frame on the date in question (Table C23)
4. Compute the (x,y,z) coordinates of Encke's comet, as seen from the Earth.
5. Compute the right ascension and declination of the comet. Don't forget to use the two-argument arctangent routines or your rectangular-to-polar key on the calculator. Also, don't forget that the (x,y,z) that you've calculated are not a unit vector, so you'll need to divide this vector by its length to get a unit vector.
6. EXTRA CREDIT. For extra credit, callculate the time it took the light to get from the comet to the Earth. Then subtract this amount of time from the date of the observation, and recompute the (x,y,z) position of the comet, referred to ths Sun, for this slightly earlier time. Using the same rectangular coordinates of the Sun you found before (since that is the instant of the observation), recompute the (x,y,z) coordinates of the comet, as seen from the Earth, and then the right ascension and declination of the comet. HINT: This will be very easy to do if you use a spreadsheet to do your calculations; all you will have to do is determine the light time and plug the new time into the spreadsheet and let it recompute the result. (The extra credit part of the assignment counts 20% extra on top of your grade for this assignment).