Transcript Week 2
Announcements •Homework set 1 is due today •Homework set 2: Chapter 2 # 43 & 45 plus supplemental problems •Use Exam Formula Sheet as you do the homework to familiarize yourself with where things are on it. Terrestrial Coordinates Longitude is measured CCW (+) or CW (-) around from Greenwich England Latitude is measured North or South of the equator Both are measured in degrees, minutes and seconds Celestial Coordinates The angle between the celestial equator and the ecliptic is 23.5° Right Ascension (RA) is measured CCW from the Vernal Equinox and is in hours, minutes and seconds Declination (Dec) is measured above (+) or below (-) the celestial equator and is in degrees, minutes and seconds See Appendix A6 for more on celestial coordinates Finding the CE and NCP at your latitude Altitude of NCP above due north horizon along the meridian (the North Point) is just f, your latitude (+ for north, - for south) Altitude of the celestial equator above due south horizon along the meridian (the South Point) is 90°-f Sidereal Time Sidereal time is the time with respect to the background stars. One sidereal day is the true rotational period of the Earth. Uncorrected, it is 23 hours 56 minutes 4.091 seconds. However, one sidereal day is 24 sidereal hours Calculating Sidereal Time Step 1 First: convert standard time to universal time For Central Standard Time UT = CST + 6 hours For Central Daylight Time UT = CDT + 5 hours If result is greater than 24 hrs, subtract 24 and add 1 to the date. Calculating Sidereal Time Step 2 Calculate the Greenwich Sidereal Time (GST) Look up the sidereal time at 0 hrs Greenwich for the date and add the sidereal interval to it. If you don’t own a current Astronomical Almanac, use the following formula to find GST GST = G + 0.0657098245xN + 1.00273791xUT where G = GST at 0 hrs on “zeroth day” of that year N = number of days since the beginning of the year Calculating Sidereal Time Step 4 Correct for local longitude Divide local longitude by 15° and add (if east of Greenwich) or subtract (if west of Greenwich) to GST to get Local Sidereal Time (LST) LST = GST ± (Longitude/15°) Julian Date Useful for calculating time interval between two dates. Julian dates start at noon UT The Julian Date (JD) is the number of days since January 1, 4713 BCE JD 2,451,544.5 365 Year 2000 N L Where N is the day number and L is the number of leap years since 2000 Examples Find the current sidereal time (4:45pm) and the current Julian date First, find current sidereal time (LST) then find Julian date Solution for LST LST G 0.0657098245 N 1.00273791(CST 6) ( Long /150 ) Using the formula for LST on the formula sheet, we will need to know the time (4:45pm), G for 2014, N for January 28 and the longitude of Clarksville, TN. In 24 hour decimal format 4:45pm = 16:45 = 16.75 The USNO location for Clarksville, TN is 87°22’ = 87.37° From the formula sheet G2014 = 6.63886 From the formula sheet NJanuary 28 = 28 Final value for LST LST 6.63886 0.0657098245 28 1.00273791(16.75 6) (87.37 15o ) 25.46635587 Subtract 24 since this is greater than 24 1.46635587 1: 27 : 58.9 You can check the value in Stellarium by determining the Right Ascension of a star on the meridian at 4:45pm on January 28, 2014 A word about significant figures and time Solution for Julian Date JD 2, 451,544.5 365 (Year 2000) N L From the equation for JD on the formula sheet we need N for January 28 and L for 2014 N = 28 L = 3 (2004, 2008 & 2012 were the three leap years) Plugging in the numbers JD 2, 451,544.5 365 (2014 2000) 28 3 2, 456, 685.5 This can be checked on the USNO Data Services page using their Julian Date Conversion calculator (Use Sunrise/Sunset – Moonrise/Moonset Times link on www.apsu.edu/astronomy)