AST352L--Spring 1998

Time and Coordinates

This assignment is DUE on Friday, February 13. The diagram below is for Problem 7.

Diagram of Ecliptic Coordinates (from Notes)

1. Calculate the Julian Day Number for 0 hours UT on April 4, 1990. SHOW ALL YOUR WORK! Check the result either by going to the web page and using the calculator, or by working the problem back from JD to date using the inverse formula. STATE THE METHOD YOU USED!
   
2. Calculate the GST at 0 hours UT on April 4, 1990. You will need to use the results of the first problem. Express the result in hours and decimal fractions of an hour.
   
3. Using the result from the second problem, calculate the GST at 3 hours 15 minutes on April 4, 1990. Express the result in hours and decimal fractions of an hour.
   
4. Using the result from the second problem, calculate the Universal Time corresponding to 0 hours GST on April 4, 1990. Express the result in hours and decimal fractions of an hour.
   
5. Use your astrolabe to determine the right ascension and declination of Vega.
   Use either the trigonometric or the matrix formulas to determine the altitude and azimuth of Vega at Austin's latitude of 30° 16', at the sidereal time of 15 hours. Check your results using your astrolabe!
   
6. Suppose that Vega's altitude is 60°, and that Vega is West of the meridian. Calculate Vega's hour angle and the sidereal time. Switch mathematical methods: If in Problem 5 you used the trigonometric formulas, use the matrix formulas for Problem 6, and vice versa. Again, check your result on the astrolabe.
   
7. Derive formulas for converting between equatorial and ecliptic systems. You may use either the matrix method or the spherical trigonometric method.
   Hints: If you use the matrix method, the inverse matrix of a rotation matrix is just the transposed matrix. If you use the trigonometric method, you can use the spherical triangles in the diagram below.

Diagram for Spherical Trigonometry