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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. For a variety of reasons, astronomers often need to assign a “time” to an observation. For this they use Universal Time .

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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 For a variety of reasons, astronomers often need to assign a “time” to an observation. For this they use 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 - conceptually it is the mean solar time at 0° longitude (Greenwich). In other words, the Sun transits at noon, UT1. It is derived from observations of distant quasars as they transit the Greenwich meridian. UTC – Coordinated Universal Time, is the time given by broadcast time signals since 1972, and is derived from atomic clocks. UTC is kept to within 1 second of UT1 by adding or deleting a leap second as needed! Remember: UT = GMT

  3. Sidereal Time Our `common sense' notion of a day is based on the time it takes from one transit of the Sun (when the Sun is overhead, i.e. midday) to the next - this is a Solar Day. For astronomers it makes more sense to define this time in terms of distant stars. Pick a distant star (shouldn't matter which!) and measure the time between one transit and the next – this defines a Sidereal Day … but 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? • For optical and Infrared wavelengths we need to observe at night (not so for radio astronomers, who may have to stay awake 24 hours when observing!). • 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 time (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. • When would be the best time to observe • the Hyades if we had access to the • Telescope tonight?

  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 • We are therefore looking • for an LST of about 14 hrs • In other words… • Targets with RA ~ 14 hrs • will be passing through • the meridian at approx. • 10 pm on 1st June.

  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 • Where tloc is the local time in decimal hours, and 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 • HA is therefore 13hr 42m 11.6s – 14hr 03m 00s = 0hr 20m 48.4s Now calculate Altitude and Azimuth..!

  19. Other Things Which Affect Sky Positions - 1(Things you need to know before writing telescope control software!) 1. Nutation In addition to Precession (see last week’s notes)we have Nutation. This is a 9 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(Things you need to know before writing telescope control software!) 2. Refraction Refraction in the Earth's atmosphere 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. (Note that this equation is only really accurate for z << 90o, since 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! • To work this out you 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(Things you need to know before writing telescope control software!) 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(Things you need to know before writing telescope control software!) 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 falling 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(Things you need to know before writing telescope control software!) 5. Proper motions Some nearby stars have significant ‘real’ motion in the plane of the sky (i.e. the star really is moving relative to the Earth). These motions may be up to a few arc-seconds per year and must be taken into account when using catalogue positions. There are separate catalogues of High Proper Motion objects for this purpose. For example, the brightest star in the sky, Sirius, has the following catalogue position and proper motion, m: So in order to observe such an object in the summer of 2013, say, one must precess the catalogue coordinates to that epoch, take account of 13.5 years of proper motion, and then convert to Altitude and Azimuth! Will explain need for cosd term in a couple of slides! Correct the RA and Dec coordinates separately

  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: This movie shows the appearance of the Big Dipper (Ursa Major) for a 200,000 year period between 100,000 BC and 100,000 AD demonstrating the proper motion of the stars. All stars down to 6.5 magnitude are shown, and the timestep is 1000 years

  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 • Even though stars 1 & 2 are • 2 hrs apart in RA, and stars 3 & 4 are also 2 hrs apart in RA, 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 It is often important to know the angular separation, q, of 2 objects on the sky (e.g. binary star components). This is especially useful if you want to know whether you can see two or more objects in one telescope pointing (NB need to know field-of-view of the telescope), or for calculating the proper motion of an object. For two objects, A and B, with coordinates (RA and Dec) aA , dAand aB , dB Dd = dA – dB Da = (aA – aB) cosdmean Where dmeanis the mean declination of both objects, in degrees (only valid if q < 1o). For Da, thecosdmeanterm is required because lines of equal RA converge towards the poles. Hence, angular separation, q,is given by q = √ (Da2 + Dd2)

  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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