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PHYS216 Practical Astrophysics Lecture 3 – Coordinate Systems 2

PHYS216 Practical Astrophysics Lecture 3 – Coordinate Systems 2. Module Leader: Dr Matt Darnley. Course Lecturer : Dr Chris Davis. Universal Time. Universal Time is the name by which Greenwich Mean Time (GMT) became known for scientific purposes in 1928.

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PHYS216 Practical Astrophysics Lecture 3 – Coordinate Systems 2

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  1. PHYS216 Practical AstrophysicsLecture 3 – Coordinate Systems 2 Module Leader: Dr Matt Darnley Course Lecturer: Dr Chris Davis

  2. Universal Time • 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. • There are several versions of UT. The most import are: • 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 1972 • Derived from atomic clocks. • UTC is kept to within 1 second of UT1 by adding or deleting a leap second • Remember: UT (or UTC) = GMT

  3. Sidereal Time Solar 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. Why?

  4. 4 mins/day = 2 hrs/month = 24 hrs/year • Earth must rotate almost 1o more ( ≈ 360/365) to get the Sun to transit. • Takes approx 4 mins to rotate through 1o • Hence: • a Sidereal Day is 4 mins shorter than the (mean) Solar Day • the 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, so… • The RA of a star = its Hour Angle relative to g. • At meridian transit of any star, LST = RA • LST tells us which RA is currently going through transit • LST - RA of an object = Hour Angle of the object

  5. 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 = 00h • At transit, RA = LST, and the Sun transits at midday, so…. • At midday on March 21st, LST = 0 hrs • At midnight on March 21st, LST = 12 hrs • – this means that targets at RA = 12hrs are transiting • Each month sidereal time moves 2 hours ahead of clock (solar) time • At midday on April 21st, LST = 2 hrs • At midnight on April 21st, LST = 14 hrs • … and so on, in an annual cycle.

  6. When is an object observable? NOTE: LST is equivalent to the Hour angle of the Vernal Equinox! 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) LST = 15 hrs Local time = 1 am g LST = 12 hrs Local time = 10 pm g To Vernal Equinox, g LST = 0 hrs Local time = noon LST = 12 hrs Local time = midnite

  7. When is an object observable? LST = 15 hrs Local time = 11 pm LST = 18 hrs Local time = 2 am LST = 12 hrs Local time = 8 pm g g To Vernal Equinox, g LST = 12 hrs Local time = midnite

  8. When is an object observable? • Example: • The Hyades (open cluster) has RA ≈ 04h 30m, Dec ≈ +15o • Ideally want to observe it when LST = 04h 30m at midnight(why midnight?) • LST = 12 hrs at midnight on March 21st(RA = 12 hr sources transiting…) • 04h 30m is 16.5 hours later than 12 hrs • LST moves on by 2 hours/month w.r.t solar time • 16.5 hours difference = 8.25 months • 8.25 months after March 21st is … • Late November is • the best time to • observe the Hyades.

  9. Calculating Local Sidereal Time Its22:05 PDTon 1st June 2014 at the Mount Laguna Observatory, near San Diego, California. What is the LST and thus the RA of transiting sources? Firstly, lets try a ball park estimate so we know what to aim for… 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 midnight But we’re observing about 2 hours earlier, so RAs that are 2 hrs less transit RA ~ 14 hrs transits at about 10pm at the end of May

  10. Calculating Local Sidereal Time • More detailed example: Its22:05 PDT on 1st June 2014 at Mount Laguna: • Convert time in San Diego to UT/GMT • San Diego is 7 hours behind GMT, so ADD 7 hrs to the local time: • 22 hr 05 min + 7 hr 00 min = 05 hr 05 min UT/GMT = 05:05 on 2nd June

  11. Calculating Local Sidereal Time • More detailed example: Its22:05 PDT on 1st June 2014 at Mount Laguna: • Convert time in San Diego to UT/GMT • San Diego is 7 hours behind GMT, so ADD 7 hrs to the local time: • 22 hr 05 min + 7 hr 00 min = 05 hr 05 min UT/GMT = 05:05 on 2nd June • Calculate the LST for this time and date in Greenwich • First, work out the time difference between noon and the UT calculated above: • 12 hr (noon to midnite) + UT = 17h 05m 00s • Calculate the time gained each day because of the 4 min difference between a sidereal day and a normal (solar) day. NB – you need to multiply the exact number of days since the Vernal Equinox (mid-day on Mar 21st to UT on 2nd June) by 4 minutes: • 71.7083 days x 4 min = 286.8332 min = 4 hr 46 m 50s • Add these two times together: • LST in Greenwich = 17h 05m 00s + 4h 46m 50s = 21:51:50 on 2nd June @ 05:05 UT NB. Keep to 4 decimal places (or six significant figures!)

  12. Calculating Local Sidereal Time • More detailed example: Its22:05 PDT on 1st June 2014 at Mount Laguna: • Convert time in San Diego to UT/GMT • San Diego is 7 hours behind GMT, so ADD 7 hrs to the local time: • 22 hr 05 min + 7 hr 00 min = 05 hr 05 min UT/GMT = 05:05 on 2nd June • Calculate the LST for this time and date in Greenwich • First, work out the time difference between noon and the UT calculated above: • 12 hr (noon to midnite) + UT = 17h 05m 00s • Calculate the time gained each day because of the 4 min difference between a sidereal day and a normal (solar) day. NB – you need to multiply the exact number of days since the Vernal Equinox (mid-day on Mar 21st to UT on 2nd June) by 4 minutes: • 71.7083 days x 4 min = 286.8332 min = 4 hr 46 m 50s • Add these two times together: • LST in Greenwich = 17h 05m 00s + 4h 46m 50s = 21:51:50 on 2nd June @ 05:05 UT • Correct for the longitude of Mount Laguna – which is 116.428o West • 1o is equivalent to 4 min, so 116.428ox 4 = 465.712 min = 7 hr 45 m 43s • SUBTRACT this from LST in Greenwich (because longitude is W) • 21 hr 51 m 50s – 7 hr 45 m 43s = 14 hr 06 min 07sec • Answer: On 2nd June @ 05:05 UT/22.05 PDT at Laguna Obs, LST = 14:06:07

  13. Calculating Local Sidereal Time Earth viewed from above… June 1st 2014 Time in California PDT = 10.05 pm LST ≈ 14 hrs UT (time in Greenwich) Is 05.05am LST ≈ 22 hrs June 21st (toward RA ~ 18 hrs) g March 21st (toward RA ~ 12 hrs)

  14. Calculating Local Sidereal Time • In a more formulaic way • Convert local time at the Observatory to UT/GMT • UT = tloc + Dt • tlocis the local time in decimal hours;Dt is the time difference between local and GMT/UT. • Calculate the LST at the Observatory • LST = 12 + UT + Dd . (4/60) – l. (4/60) • Where ’12’ corrects the time from noon to midnight, UT is the Universal Time, Dd is the number of days AFTER the Vernal Equinox (noon on 21 March, when LST = 0 hrs), andlis the longitude WEST, in decimal degrees. The factors 4/60 convert both Ddand lto decimal hours. Your answer will therefore be in decimal hours. • Try this example: • What is the LST at the Armagh Observatory, l = 6.6500o W, at 19.00 BST on 28 March?

  15. Messier objects at 14 hrs RA?

  16. M 101 Messier objects at 14 hrs RA? M 3

  17. 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, f • Local Sidereal Time, LST • Remember: to calculate Alt and Az, you ONLY need HA, d , and f. • Need to remember: • HA is the time since the target transited • LST is equivalent to the RA that is transiting • Therefore:HA = LST - RA

  18. 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, f • Local Sidereal Time, LST • Remember: to calculate Alt and Az, you ONLY need HA, d , and f. • Need to remember: • HA is the time since the target transited • LST is equivalent to the RA that is transiting • Therefore:HA = LST - RA • Example: • M 3 - RA: 13h 42m 11.6s Dec: +28° 22′38.2″ (assume current epoch) • Its 22.05 pm on Mount Laguna – LST is 14hrs 03 min, latitude, f = 32.84o • Calculate HA from the RA and LST… Now please calculate Altitude and Azimuth..!

  19. Other Things Which Affect Sky Positions – 1 1. Nutation A9 arcsec wobble of the polar axis along the precession path - caused by the Moon’s gravitational pull on the oblate Earth. Main period = 18.66 years. R = Rotation of earth P = Precession N = Nutation

  20. Other Things Which Affect Sky Positions – 2 2. Refraction Displaces a star's apparent position towards the zenith. R ≈ tan z where R is in arcminutes and z, the zenith distance, is in degrees. (only accurate for z << 90o, because tan90 = ∞ )

  21. 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 + 7.31/[90-z+4.4] ) • At z = 90o: R = cot (7.31/4.4) = 34.4 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 = 0.033 hrs = 2 minutes to move 0.5 deg.

  22. Other Things Which Affect Sky Positions – 3 3. Height above sea level Observer's height above sea level means that the observed horizon is lower on the celestial sphere, so the star's apparent elevation increases. • Measured angle of elevation, q’, above the observed horizon = q + a • where 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?

  23. Mauna Kea ObservatoryBig 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!

  24. Other Things Which Affect Sky Positions – 4 4. Stellar Aberration Caused 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 arcsec LEFT: 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 / c vearth = 30 km/sand the speed of light, c = 300,000 km/s. Therefore,q = 0.0057 deg = 20 arcsec

  25. Other Things Which Affect Sky Positions – 5 5. Proper motions Stars move with respect to other stars – and especially background galaxies. The brightest star in the sky, Sirius, has the following position and proper motion, m: Would need to precessthe catalogue coordinates to epoch of observation; i.e. take into acount motion of the star! Correct the RA and Dec coordinates separately Will explain need for cosd term in a couple of slides!

  26. Proper motions Barnard’s star • Typical proper motions of nearby stars ≈ 0.1 arcsec/year • Star with highest proper motion is Barnard’s star; PM = 10.25 arcsec/year Evolution of the Great Bear: The changing appearance of the Big Dipper (Ursa Major) between 100,000 BC and 100,000 AD.

  27. Angular Separationsand converging lines of RA • Stars 1 & 2: • RA: 10h and 12h • Dec: 0o • Stars 3 & 4: • RA: 10h and 12h • Dec: +60o • Stars 1 & 2 are 2 hrs apart in RA • Stars 3 & 4 are 2 hrs apart in RA • But • the angular separation of stars 1 & 2 is NOT the same as for stars 3 & 4 • Why? • Because lines of right ascension converge towards the poles! ★3 ★4 ★2 ★1

  28. Angular Separationsand converging lines of RA • Stars 1 & 2: • RA: 10h and 12h • Dec: 0o • Stars 3 & 4: • RA: 10h and 12h • Dec: +60o • Stars 1 & 2: • 2 hrs = 360ox 2/24 hrs xcosd • = 360ox 2/24 hrs xcos0 • = 30o • Stars 3 & 4: • 2 hrs = 360ox 2/24 hrs xcosd • = 360ox 2/24 hrs xcos60 • = 15o ★3 ★4 ★2 ★1

  29. Small Angular Separations How to calculate the angular separation, q, of 2 objects on the sky For two objects, A and B, with coordinates (RA and Dec) aA , dAand aB , dB Dd = dA – dB Da = (aA – aB) cosdmean Where dmeanis mean declination of both objects, in degrees. NB: thecosdmeanterm needed because lines of equal RA converge towards the poles! Angular separation, q: q = √ (Da2 + Dd2) *** This is only valid if 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’ = +20.28o Da= 3.6 seconds of time What’s q, the angular separation? Key: 1 sec of time = 15”.cosdmean A 20:17:00 q Dd B Da 20:16:00 18:29:50 48 46

  31. 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’ = +20.28o Da= 3.6 seconds of time Key: 1 sec of time = 15”.cosdmean Therefore: 3.6 sec of time = 3.6 × 15” × cos20.28o Da= 51” Angular separation, q,is given by: q = √ (Da2 + Dd2) = √ (40×40 + 51×51) = 65 arcsec A 20:17:00 q Dd B Da 20:16:00 18:29:50 48 46

  32. 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:

  33. (Sorry, couldn’t resist) And finally…. A bit of astrology! RA~3hr At 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~1hr RA~5hr E RA~13hr RA~17hr RA~15hr

  34. End.. See you next week….

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