Coordinates and time Sections 28 – 32

1. Coordinates and time Sections 28 – 32

2. Nutation • This is a wobbling motion of the Earth’s rotation • axis as it precesses about the ecliptic pole. • Amplitude of nutation = 9.2 arc sec • Period of nutation = 18⅔ yr • Nutation is caused by the Moon, in fact the • retrograde precession of the plane of the Moon’s • orbit, which also has a period of 18⅔ yr.

3. Nutation The path of the north celestial pole as a result of precession and nutation. Right: zoom in of NCP path.

4. + Luni-solar precession shows the wobbling of the Earth’s rotation axis with period 18⅔ yr, known as nutation. 

5. 29. The calendar (a) Julian calendar Introduced ~ 45 B.C. to replace the early Roman calendar, by Julius Caesar. The Julian calendar was based on 1 year = 365¼ days, whereas early Roman calendar had 10 months and 355 days. Seasons became out of step with year (46 B.C. had 445 days to catch up, bringing equinox to Mar 25).

6. Julian calendar introduced the leap year (year of 366 days every 4th year). Julian year exceeds tropical year (365.2422 d) by 11 m 14 s so equinox slowly becomes earlier each year by ~ 3 d in 4 centuries. In 325 A.D. it was on Mar 21, in 1600 on Mar 11. The 7-day week introduced into Julian calendar by Emperor Constantine in 321 A.D. ≃ length of time for quarter lunation (cycle of lunar phases).

7. (b) Gregorian calendar Introduced by Pope Gregory XIII in 1582. Oct 15, 1582 followed Oct 4 to restore equinox to Mar 21. Leap years omitted on 3 years every 4 centuries, (namely those years which are multiples of 100 but not 400). Thus 1700, 1800, 1900 not leap years; 2000 was a leap year.

8. In 4 centuries there are 97 leap years. Number of days = (365  400) + 97 d = 146097 days Mean length of Gregorian year = 146097 / 400 = 365.2425 d ≃ tropical year (365.2422 d) England (and American colonies) adopted Gregorian calendar in 1752 (Sept 14 followed Sept 2). Russia, eastern Europe not till 20th C (in 1917).

9. 30. More on time-keeping systems (a) Mean solar time The mean Sun defines the length of the mean solar day which is the basis for civil time-keeping (see section 9). Mean solar day = interval between successive meridian transits of mean Sun.

10. MST depends on longitude of observer. Greenwich mean solar time is MST in Greenwich (longitude λ = 0º). MSD changes in length due to changes in Earth rotation rate (see section 16(b)), requiring a leap second to be added (on average 1 s a year to 18 months).

11. (b) Universal time (= Greenwich Mean Time) • UT (or GMT) is the mean solar time at • Greenwich (longitude 0). • UT advances at the mean solar rate, but has • the same value at all locations at a given instant. • Four categories of UT: • UT0 Uncorrected time based on Earth rotation, • as observed by an observer at a fixed location.

12. UT1 This is UT0, but corrected for changes in an • observer’s longitude, due to polar motion. UT1 • is still influenced by variations in Earth rotation • rate, so its advance is not uniform. • UT2 This is UT1, but corrected for the seasonal • variations in the Earth’s rotation rate. • UTC = Coordinated Universal Time. Related to • UT1, but leap seconds are introduced when • required so that UTC differs from International • Atomic Time by an integral number of seconds.

13. Leap seconds in UTC are added if required, usually end of June or Dec. On average 1 leap second every 18 months such that UTC – UT1  0.90 s UTC advances at uniform rate, but some years are longer than others. In astronomy, UT times and dates are written in the format: 2003 Aug 12 d 12 h 30 m 3.1 s UTC or 2003 Aug 12.5209 UTC.

14. (c) Converting from universal time to • sidereal time • The relationships between UT and local sidereal time • depends on the date (time of year) (t) and the • observer’s longitude (). • To find LST the steps are: • Find number of days elapsed since 12 h UT1 • on Jan 1 (this is t).

15. Convert this to Greenwich sidereal time (GST) • using: • GST (at 0 h UT1) on day number t • = 6 h 41 m 50.55 s + (3 m 56.56 s)t where t is in days (an integer). 24 LST 0 t 1 sidereal day UT 24 0 t 1 solar day

16. Use the relation • depends on time longitude depends on date • of day during yearwhere  longitude (in h m s)Note: 1.0027378 = ratio of mean solar day • to sidereal day.

17. (d) Standard time (or zone time) Earth is divided into about 24 longitude zones. Standard time is same everywhere inside a given zone. Advances at mean solar time rate. Meridian passage of mean Sun is close to noon in local standard time. e.g. NZST = UTC + 12 h 00 m.

18. Mean Sun crosses meridian at about 12 h 30 m NZST in Christchurch (172½E of Greenwich), so local MST is ~30 m behind NZST (in ChCh) (mean Sun is due north at 12h 30m NZST in ChCh).

19. Standard time zones as seen from the north pole

20. Standard time zones on the Earth

21. (e) Daylight saving time Usually standard time + 1 h in summer months. e.g. NZDT = NZST + 1 h 00 m.

22. (f) International atomic time (TAI) Introduced in 1971, and based on a line in spectrum of caesium (133Cs). TAI = UT1 on 1958 Jan 1 at 0 h. TAI is based on SI second which = 9,192,631,770 periods of the radiation emitted by 133Cs. (This definition closely matches the ET second, which it replaces.) TAI represents a uniformly advancing time scale, at least to ~ 1 part in 1012 (or to about 1 s in 30,000 years).

23. (g) Julian date A system of specifying time, widely used in astronomy. J.D. = number of mean solar days elapsed since 12 h UT (noon) on 1st January, 4713 B.C. e.g. 1991 Mar 16, 06h00 NZST  JD 2448331.250

24. (h) Ephemeris time (1952 – 1984) Because of irregularities in Earth rotation rate, the MSD is not a fixed unit of time, with fluctuations on ~ the 1-ms level. Ephemeris time is a time advancing at a constant (or uniform) rate. E.T. = U.T. at beginning of 1900 or E.T. = U.T. + T

25. The correction T is now about + 1 minute. 1 second of E.T. is defined as:

26. (i) Terrestrial dynamical time (TDT) Introduced in 1977, to replace ephemeris time. It is based on motions of solar system bodies. TDT is tied closely to TAI and can be considered to progress at a uniform rate. TDT = TAI + 32.184s

27. 31. Positions of stars • Star positions are affected by: • Atmospheric refraction (normally always • corrected for in reducing the observations) • Trigonometric parallax • Aberration of starlight • Nutation • Precession • Proper motion (a result of the true motion of the • star through space, as projected onto the plane • of the sky)

28. The apparent position of a star. This is the • position on the celestial sphere (normally given • in equatorial coordinates R.A. and decn) that is • actually observed at a given instant of time, t. • The apparent position is referred to the true • equator and equinox at the time of observation • from the centre of the Earth. • The true position of a star. This is the position • after correcting for the effects of parallax and • aberration, that is, as seen by an observer located • at the centre of the Sun.

29. The mean position of a star is its heliocentric • position on the celestial sphere, but with the • effect of nutation on the coordinates also removed. • This is done by referring the equatorial coordinates • (α,δ) to the mean equator and equinox for the time • of observation, instead of the true equator and • equinox. The mean position still has the effects • of precession and proper motion included. This is • the position actually used in star catalogues. Mean • positions are quoted for a given epoch, e.g. • (α,δ)2000.0 are for the epoch 2000.0 UT.

30. 32. Proper motion of stars (a) Definition Angular change per unit time in a star’s position along a great circle of the celestial sphere centred on the Sun. Units: in arc s yr-1 or arc s cy-1 (per century) Components:  =  sec sin  (s of time/yr)  =  cos  (/yr)

31. N  =  cos    E W  S  =  sin  sec  Proper motion components in R.A. and dec.

32. (b) Measurements (i) Fundamental p.m. From meridian transit circles. From apparent position of star, correct for refraction, parallax, aberration to obtain true position (o, o) at time to. Repeat observations a long time later to obtain (1, 1) at t1. Differences (10) and (10) are due to nutation, precession, and proper motion. Correct for nutation and precession to obtain p.m.

33. The determination of proper motion from fundamental astrometry at epochs t0 and t1

34. (ii) Fundamental catalogues FK3 Dritter Fundamental Katalog (1937) 1591 stars, epoch 1950.0 (Berlin) FK4 Vierter (4th) … (1963) (Heidelberg) A revision of FK3 FK5 Fifth fundamental catalogue (1988) Heidelberg, epoch 2000.0 N30 Catalogue of 5268 standard stars for 1950.0

35. (iii) Photographic • Plates taken with long focus telescopes. Star • positions measured relative to standard FK5 stars. • Typical errors: position  0.16 • p.m.  0.012/yr • (iv) Main photographic catalogues • Yale Observatory catalogues • Cape Observatory catalogues • These have > 2  105 stars

36. Bruce proper motion survey ~ 105 faint stars of high proper motion • Smithsonian Astrophysical Observatory • Catalogue (SAO) 258,997 stars on FK4 system • PPM catalogue 378,910 stars on FK5 system • ( ~  0.003/yr)

37. (v) From space Hipparcos astrometric satellite (ESA) Nov 1989 – Mar 1993 Hipparcos catalogue 118,218 stars with positions and proper motions to about 1 mas (milli-arc second) precision. FK5 system

38. (c) Proper motion and transverse velocity Radial velocity VR V cos Transverse velocity VTd /p(In above equn, if d in parsecs, p (parallax) in arc s,  in arc s/yr then VT is in A.U./yr) or VT = 4.74 /p(km/s) VR star θ V d VT μ (change in direction in 1 yr) Earth

39. (as 1 A.U./yr = 4.74 km/s). If VR (from Doppler effect), and , p can be measured, then this gives: space motion direction

40. to Apex U (km/s) star 1 S1  b   So (d) Parallactic motion of stars This is that part of the overall proper motion of a star due to the Sun’s velocity through space. In one year Sun movesfrom S0 to S1, velocity U km/s. d μ1

41. to Apex U (km/s) star 1 S1  b   So μ1

42. = parallactic motion of star towards antapex The solar velocity is about U = 19.6 km/s towards an apex direction (α,δ) = 18 h, +34º (which is near the bright star, Vega).

43. (e) High proper motion stars  (/yr) Barnard’s star 10.3 Groombridge 1830 7.05 Lacaille 9352 6.90 61 Cygni 5.22 Lalande 21185 4.77  Indi 4.70

44. Two important catalogues of high • proper motion stars • Luyten Five Tenths catalogue (LFT) 1849 stars with  0.5/yr • Luyten Two Tenths catalogue (LTT) • ~ 17,000 stars with  0.2/yr

45. The motion of Barnard’s star in the sky shows the effects of a high proper motion as well as a large parallax.

46. 33. Note on constellations and star names • (a) Constellations • A constellation = region of sky, originally • identified by mythical figures portrayed by the • stars. • Originally defined by Babylonians ~2000 B.C. • Greeks recognized 48 constellations (described • by Aratus in 270 B.C. and by Ptolemy in the • Almagest in about 150 A.D.).

47. Further southern constellations added in 17th C • and 18th C, including 13 by Lacaille ~1750. • Lacaille divided Argo  Carina, Pyxis, Puppis • and Vela. • Today 88 constellations officially recognized • by the I.A.U. (International Astronomical • Union).

48. (ii) Constellation boundaries • First drawn by Bode in 1801 as curved lines. • Redrawn by I.A.U. in 1928 as straight lines along • arcs of constant R.A. or declination for epoch • 1875.0 (precession has now tilted these arcs • slightly, which are however fixed on celestial • sphere relative to the stars).

49. (iii) Constellation names in Latin (nominative). Each has genitive (or possessive form) N G abbrev. e.g. Crux Crucis Cru Scorpius Scorpii Sco Vela Velorum Vel I.A.U. official abbreviations comprise 3 letters.

50. Star nomenclature • (i) Ancient names for bright stars • These are of Greek, Latin or (especially) Arabic • origin, and are still commonly used for ~50 • brightest stars (northern, equatorial stars). • e.g. Canopus, Sirius, Procyon, Aldeberan.