Presentation on theme: "PHYS216 Practical Astrophysics Lecture 3 – Coordinate Systems 2"— Presentation transcript:
1 PHYS216 Practical Astrophysics Lecture 3 – Coordinate Systems 2 Takes just over an hour… (break may not be needed)Module Leader:Dr Matt DarnleyCourse Lecturer:Dr Chris Davis
2 Calendars & Julian Date Gregorian calendar - used universally for civil purposesJulian calendar - its predecessor in the western worldThe two differ only in the rule for leap years: the Julian calendar has a leap year every fourth year, while the Gregorian calendar has a leap year every fourth year except century years not exactly divisible by 400.The Julian Date (JD) - a continuous count of days and fractions of days since Greenwich noon on 1st January, 4713 BCE.Modified Julian Date (MJD) – a more convenient form of JD.MJD = JD –Swedish version of the Gregorian Calendar, c
3 Calculating Julian Date The Julian Day Number is calculated as follows:1) Express the date as y m d, where y is the year, m is the month number (Jan = 1, Feb = 2, etc.), and d is the day in the month.2) If the month is January or February, subtract 1 from the year to get a new y, and add 12 to the month to get a new m. (This is because we consider January and February as being the 13th and 14th month of the previous year).3) Dropping the fractional part of all results of all calculations (except JD), letA = rounddown(y/100)B = 2 – A + rounddown(A/4)C = rounddown( x Y)D = rounddown( x (m + 1))JD= B + C + D + dThis is the Julian Day Number for the beginning of the date in question at 0:00 hours (Greenwich time). Note half day extra because the Julian Day begins at noon.e.g. JD on 2014 July 31 –A = rounddown(2014/100) = 20B = 2 – 20 + roundown(20/4) = -13C = rounddown( x 2014) =D = rounddown( x (7+1)) = 244JD == (at 0:00 hrs)
4 Calculating Julian Date 1) Express the date as y m d, where y is the year, m is the month number (Jan = 1, Feb = 2, etc.), and d is the day in the month.2) If the month is January or February, subtract 1 from the year to get a new y, and add 12 to the month to get a new m.3) Dropping the fractional part of all results of all calculations (except JD), letA = integ(y/100)B = 2 – A + integ(A/4)C = integ( y)D = integ( (m + 1))JD= B + C + D + dJD is the Julian Day Number for the beginning of the date in question at 0 hours (Greenwich time).e.g. JD on 2014 July 31 -at 00:00 hrs JD =at 06:30 hrs JD =Correspond to seconds!
5 Universal Time Remember: UT (or UTC) = GMT Universal Time is the name by which Greenwich Mean Time (GMT) became known for scientific purposes in 1928.UT is based on the daily rotation of the Earth. However, the Earth’s rotation is somewhat irregular and can therefore no longer be used as a precise system of time.Versions of UT:UT1:The mean solar time at 0° longitude (Greenwich).The Sun transits at noon, UT1.Derived from observations of distant quasars as they transit the Greenwich meridian.UTC – Coordinated Universal Time:Time given by broadcast time signals since 1972Derived from atomic clocks.UTC is kept to within 1 second of UT1 by adding or deleting a leap secondRemember: UT (or UTC) = GMT
6 Solar vs Sidereal TimeSolar Day: Time between successive transits of the sun (noon to noon)Sidereal Day: Time between successive transits of distance stars and galaxies… a sidereal day isn’t quite as long as a normal day!.A sidereal day is about 23 hours, 56 minutes, 4 seconds in length.
7 4 mins/day=2 hrs/month24 hrs/yearEarth must rotate almost 1o more ( ≈ 360/365) to get the Sun to transit.Takes approx 4 mins to rotate through 1oHence:a Sidereal Day is 4 mins shorter than the (mean) Solar Daythe Local Sidereal Time (LST) gets 4 mins later at a given clock time every day.Things to remember:LST is the Hour Angle of the Vernal Equinox, g, (shown later)The RA of a star = its Hour Angle relative to g.At meridian transit of any star, LST = RALST tells us which RA is currently going through transitLST - RA of an object = Hour Angle of the object
8 When is an object observable? On March 21st, the Sun is at the Vernal Equinox, i.e. on March 21st the RA of the Sun = 00hOn March 21st at noon, LST is exactly 12 hrs ahead of the local time (synchronise watches!)At transit, RA = LST, and the Sun transits at midday, so….At midday on March 21st, LST = 0 hrsAt midnight on March 21st, LST = 12 hrs– this means that targets at RA = 12hrs are transitingEach month sidereal time moves 2 hours ahead of clock (solar) timeAt midday on April 21st, LST = 2 hrsAt midnight on April 21st, LST = 14 hrs… and so on, in an annual cycle.
9 When is an object observable? At 00:00 hrs LST on March 21st, a person in Greenwich facing due south would be staring right at the meridian-transiting Sun… (would probably still need a spray tan)On March 21st, as the earth rotates, the HA of g and the LST both increase together.No matter what day it is, LST = always equals the Hour angle of the Vernal EquinoxLST = 15 hrsLocal time = 1 amgLST = 12 hrsLocal time = 10 pmgTo VernalEquinox, gLST = 0 hrsLocal time= noonLST = 12 hrsLocal time = midnite
10 When is an object observable? LST = 18 hrsLocal time = 2 amLST = 15 hrsLocal time = 11 pmLST = 12 hrsLocal time = 8 pmggTo VernalEquinox, gLST = 12 hrsLocal time = midnite
11 When is an object observable? Example:The Hyades (open cluster) has RA ≈ 04h 30m, Dec ≈ +15oIdeally want to observe it on a night when LST = 04h 30m at midnight (why midnight?)LST = 12 hrs at midnight on March 21st (Sources with RA = 12 hr transiting…)04h 30m is 16.5 hours later than 12 hrsLST moves on by 2 hours/month w.r.t solar time16.5 hours difference = 8.25 months8.25 months after March 21st is …Late November isthe best time toobserve the Hyades.
12 What is the approximate Local Sidereal Time Example:Its 22:05 PDT on 1st June 2014 at the Mount Laguna Observatory, near San Diego, California. What is the LST and thus the RA of transiting sources?KEY: on March 21st, RA~12hrs transits at ~midnight (local time)1st June is 2-and-a-bit months later, so add 2 hours per month:RA ~ 16 hrs transits at midnightBut we’re observing about 2 hours earlier, so RAs that are 2 hrs less transitRA ~ 14 hrs transits at about 10pm at the end of MayMarch 22-March 31 = 9 daysApril 1 – Apiril 30 = 30 daysMay 1 – May 31 = 31 day1 June = 1 day2 June = 4.75 hrs = daysTotal = days
13 How does this relate to GMT (UT)? Earth viewed from above…June 1st 2014Time in CaliforniaPDT = pmLST ≈ 14 hrsUT (time inGreenwich)Is 05.05amLST ≈ 22 hrsMarch 22-March 31 = 9 daysApril 1 – Apiril 30 = 30 daysMay 1 – May 31 = 31 day1 June = 1 day2 June = 4.75 hrs = daysTotal = daysRA ~ 18 hrs)June 21st(towardgMarch 21st(toward RA ~ 12 hrs)
14 Calculating Local Sidereal Time To the nearest hour (good enough for a small telescope)Convert local time at the Observatory to UT/GMTUT = tloc + Dttloc is the local time in decimal hours; Dt is the time difference between local and GMT/UT.Calculate the LST at the ObservatoryLST ~ (UT - 12) + Dd . (4/60) – l . (4/60)LST = GMST – l . (4/60)Where ’12’ corrects for the 12 hr time difference between LST and UT on 21 March.Dd is the number of days AFTER the Vernal Equinox (noon on 21 March, when LST = 0 hrs)l is the longitude WEST, in decimal degrees.The factors 4/60 convert both Dd and l to decimal hours. Your answer will therefore be in decimal hours.Try this example:What is the LST at the Armagh Observatory, l = o W, at BST on 28 March?UT =19.00 – 1.0 = 18.00Delta-d = 7 days 18 hrs = 7.75 daysGMST = hrsLST = x(4/60) = = 6 hrs 04 min
15 Calculating Local Sidereal Time more precisely The precise formula for calculating LST must take into account the Earth’s Nutation and Precession (see e.g. the Astronomical Almanac published by the US and UK Nautical Almanac Offices: aa.usno.navy.mil/faq/docs/GAST.php).1. Convert UT Date and Time to a precise Julian dateJD - see slides at start of this lecture …2. Calculate the number of days, D, since 1 January, 2000 at 12 hrs UT.D = (JD – )3. Calculate GMSTGMST = ( D)(this number will probably be large; reduce it to within 24hrs by subtracting some multiple of 24)4. Correct for Longitude of observatory (add if E of Greenwich, subtract if W)LST = GMST +/- l . (4/60)
16 Calculating Local Sidereal Time An example: LST at UT on 31st July, 2014 in Armagh (6.65o W)1. Convert UT Date and time to a precise Julian dateJD =2. Calculate the number of days, D, since 1 January, 2000 at 12 hrs UT.D = ( – ) =3. Calculate GMSTGMST = ( )= hrs ( ) = hrs4. Correct for Longitude of observatory (add if E of Greenwich, subtract if W)LST = – = hrs, or 16:10:51(Calculation done with Excel. You may get slightly different numbers depending on how your calculator handles these very big numbers; but you should get to within a minute of time.)
19 Calculating Alt-Az from RA, Dec, and Sidereal Time So how do I point my telescope at M3 ?Need to know:RA (a) and Dec (d)Latitude of the observatory, fLocal Sidereal Time, LSTRemember: to calculate Alt and Az, you ONLY need HA, d , and f.Need to remember:HA is the time since the target transitedLST is equivalent to the RA that is transitingTherefore: HA = LST - RAExample:Target is M3, RA: 13h 42m 11.6s Dec: +28° 22’ 38.2″ (current epoch)LST is 14 hrs 03 min on Mount Laguna (latitude, f = o)Now, calculate (i) HA from the RA and LST and (ii) the Altitude and AzimuthHA = LST – RA : hrs hrHA = hrs (HA is +ve, target is setting; 0 < HA < 12 hrs)HA = degDec: deg. HA = deg. , Latitude = oAltitude, a = deg = 83o 40’ 43”Azimuth, A = deg = 226o 27’ 47”
21 Other Things Which Affect Sky Positions – 1 1. NutationA 9 arcsec wobble of the polar axis along the precession path - caused by the Moon’s gravitational pull on the oblate Earth.Main period = years.R = Rotation of earthP = PrecessionN = Nutation
22 Other Things Which Affect Sky Positions – 2 2. RefractionDisplaces a star's apparent position towards the zenith.R ≈ tan zwhere R is in arcminutesand z, the zenith distance, is in degrees.(only accurate forz << 90o,becausetan90 = ∞ )
23 How does refraction affect the sun’s appearance at sunrise/sunset? Due to refraction, the Sun appears to set 2 minutes AFTER it actually does set!Need a more precise empirical formula:R = cot ( 90-z /[90-z+4.4] )At z = 90o: R = cot (7.31/4.4) = arcmin. R ≈ 0.5 deg.If it takes 6 hrs for the sun to move from zenith to the horizon, i.e. through 90 deg, it takes 6 hrs x 0.5/90 = hrs = 2 minutes to move 0.5 deg.
24 Other Things Which Affect Sky Positions – 3 3. Height above sea levelObserver's height above sea level means that the observed horizon is loweron the celestial sphere, so the star's apparent elevation increases.Measured angle of elevation, q ’, above the observed horizon = q + awhere displacement, a, in arcmins is given by:a = 1.78 √h(h = height above sea level, in metres)Q. Which is perpendicular to the radius of the Earth, the Celestial or the Observed Horizon?
25 Mauna Kea Observatory Big island, Hawaii The summit of Mauna Kea in Hawaii is 4200 m above sea-level,h = 4200 m; therefore, a = 115 arcmin – that’s almost 2 degrees!
26 Other Things Which Affect Sky Positions – 4 4. Stellar AberrationCaused by velocity of the Earth around the Sun ( ≈ 30 km/s).Need to point the telescope slightly ahead in the direction of motion.The amount depends on the time of year and the direction of the star.Maximum effect ≈ 20 arcsecLEFT: The angle at which the rain appears to be falling depends on the speed of the rain and the speed at which the person is running: sin q = vman / vrain.RIGHT: For a star near the ecliptic pole, or for a star in the plane of the ecliptic and at right angles to the direction of motion of the Earth around the sun: sin q = vearth / cvearth = 30 km/s and the speed of light, c = 300,000 km/s. Therefore, q = deg = 20 arcsec
27 Angular Separations and converging lines of RA Stars 1 & 2:RA: 10h and 12hDec: 0oStars 3 & 4:Dec: +60oStars 1 & 2 are 2 hrs apart in RAStars 3 & 4 are 2 hrs apart in RAButthe angular separation of stars 1 & 2 is NOT the same as for stars 3 & 4 because lines of right ascension converge towards the poles!★3★4★2★1
28 Angular Separations and converging lines of RA Stars 1 & 2:RA: 10h and 12hDec: 0oStars 3 & 4:Dec: +60oAngular sep of Stars 1 & 2 in degrees:2 hrs = 360o x 2/24 hrs x cos d= 360o x 2/24 hrs x cos 0= 30o= 360o x 2/24 hrs x cos 60= 15o★3★4★2★1
29 Small Angular Separations How to calculate the angular separation, q, of 2 objects on the skyFor two objects, A and B, with coordinates (RA and Dec) aA , dA and aB , dBDd = dA – dBDa = (aA – aB) cos dmeanWhere dmean is mean declination of both objects, in degrees.Angular separation, q :q = √ (Da2 + Dd2)*** This is only valid if q < 1o ***
30 Small Angular Separations (an example) Star A:18h 29m 49.6s +20o17’05”Star B:18h 29m 46.0s +20o16’25”Dd = 40”dmean = +20o16’45”= +20o16.67’= oDa = 3.6 seconds of timeKey: 1 sec of time = 15”.cosdmeanTherefore:3.6 sec of time = 3.6 × 15” × cos20.28oDa = 51”Angular separation, q , is given by:q = √ (Da2 + Dd2) = √ (40× ×51) = 65 arcsecA20:17:00qDdBDa20:16:0018:29:504846
31 Large Angular Separations To calculate the angular separation, q , of 2 objects with a large separation (q > 1o) or in the general case, the following formula can be used:
32 Tangential or “Proper” motions Stars move with respect to “stationary” background galaxies.The brightest star in the sky, Sirius, has the following position and proper motion, m:The get the precise, current epoch coordinates of the star you need to:(a) precess the coordinates AND(b) correct for the star’s proper motion.Correct the RA andDec coordinates separatelyNOTE: These are SPEEDS !!
33 Proper motionsTypical proper motions of nearby stars ≈ 0.1 arcsec/yearStar with highest proper motion is Barnard’s star; PM = arcsec/yearBarnard’s starEvolution of the Great Bear:The changing appearance of the Big Dipper (Ursa Major) between 100,000 BC and 100,000 AD.
34 Asteroids and Comets 18h 29m 49.6s +20o17’05” Asteroids and comets can have very high proper motions (arcseconds per second!)Ephemeris – a table of coordinates over a range of datesEXAMPLENear-Earth Asteroid NEO 2012-DAOn 1 July at UT its coordinates are:18h 29m 49.6s +20o17’05”Its Proper motions isma cos d = 1.0 arcsec/minutemd = 2.0 arcsec/minuteQ. What are its coordinates on 2 July at UT?2 JulyDd1 JulyDa
35 And finally…. A bit of astrology! (Sorry, couldn’t resist)RA~3hrAt mid-day on March 21st, the sun (when viewed from the Earth) is at RA = 0 hrs, midway between the constellations of Aquarius and Pisces (according to the IAU)…What’s the star sign of someone born on March 21st? And why is it “wrong”?RA~1hrRA~5hrEMarch 21st - star sign is Aries (March 21st – April 20th)RA~13hrRA~17hrRA~15hr