A221 HW #2 - Help

Problem 2

  • This problem requires numerous conversions from solar to sidereal hours, and back again. Remember, 1 sidereal hour equals 0.99727 solar hours (derived from 365.25 solar days/ 366.25 sidereal days in a year).
    Thus, 4 solar hours = 4 / 0.99727 sidereal hours

  • LST = GMST + longitude
    where GMST is the Greenwich Mean Sidereal Time at the desired UT and longitude is the longitude measured in hours (longitude in degrees divided by 15.). By convention, western longitudes are negative.

  • Transit occurs when the LST = RA of the object. Transit times (EDT) can be calculated by determining the time difference between LST at midnight (0h EDT) and the RA of the object. This time difference (converted from sidereal to solar hours!) is the time difference between midnight and the transit time of the source. If the RA of the source is smaller than the LST at midnight, the source transited prior to midnight. If the RA of the source is larger than the LST at midnight, the source transits after midnight. HOWEVER, RA and LST are kept on 24 hour clocks. 0 h 0 m 0 s is 1 min away from 23 h 59 m 0 s, not 23h and 59s.

  • I found it much easier to do the problems in "decimal degrees" and "decimal hours". To convert from the given values (X hour Y min Z sec) to decimal hours:
    X + (Y/60.) + (Z/3600.)
    However, the answers should be given in standard time units (hours min secs), so remember to convert back to these units after you have done the arithmetic.

  • For part c, your calculator will probably give you the hour angle in degrees. To convert from degrees to hours (the proper unit for the hour angle), remember that there are 15 degrees in 1 hour.

  • For part d, you will want to convert the (sidereal) hour angle into a (solar) time difference in order to determine when (in EDT) the objects will rise and set.

  • For part f, during the month of September, CTIO is located within the Chilean Standard Time Zone = 4 hr West.