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Transcript

ASTR211: COORDINATES AND TIME Coordinates and time Prof. John Hearnshaw Sections 28 – 32 ASTR211: COORDINATES AND TIME 28. Nutation This is a wobbling motion of the Earth’s rotation axis as it precesses about the ecliptic pole. 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. Prof. John Hearnshaw Amplitude of nutation = 9.2 arc sec Period of nutation = 18⅔ yr ASTR211: COORDINATES AND TIME The path of the north celestial pole as a result of precession and nutation. Right: zoom in of NCP path. Prof. John Hearnshaw Nutation ASTR211: COORDINATES AND TIME Luni-solar precession shows the wobbling of the Earth’s rotation axis with period 18⅔ yr, known as nutation. Prof. John Hearnshaw + ASTR211: COORDINATES AND TIME 29. The 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). Prof. John Hearnshaw (a) Julian calendar ASTR211: COORDINATES AND TIME Julian calendar introduced the leap year (year of 366 days every 4th year). 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). Prof. John Hearnshaw 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. ASTR211: COORDINATES AND TIME (b) Gregorian calendar 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. Prof. John Hearnshaw Introduced by Pope Gregory XIII in 1582. Oct 15, 1582 followed Oct 4 to restore equinox to Mar 21. ASTR211: COORDINATES AND TIME In 4 centuries there are 97 leap years. Number of days = (365 400) + 97 d = 146097 days England (and American colonies) adopted Gregorian calendar in 1752 (Sept 14 followed Sept 2). Russia, eastern Europe not till 20th C (in 1917). Prof. John Hearnshaw Mean length of Gregorian year = 146097 / 400 = 365.2425 d ≃ tropical year (365.2422 d) ASTR211: COORDINATES AND TIME 30. More on time-keeping systems (a) Mean solar time Mean solar day = interval between successive meridian transits of mean Sun. Prof. John Hearnshaw The mean Sun defines the length of the mean solar day which is the basis for civil time-keeping (see section 9). ASTR211: COORDINATES AND TIME MST depends on longitude of observer. 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). Prof. John Hearnshaw Greenwich mean solar time is MST in Greenwich (longitude λ = 0º). ASTR211: COORDINATES AND TIME (b) Universal time (= Greenwich Mean Time) UT (or GMT) is the mean solar time at Greenwich (longitude 0). Four categories of UT: • UT0 Uncorrected time based on Earth rotation, as observed by an observer at a fixed location. Prof. John Hearnshaw UT advances at the mean solar rate, but has the same value at all locations at a given instant. ASTR211: COORDINATES AND TIME • 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. • 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. Prof. John Hearnshaw • UT2 This is UT1, but corrected for the seasonal variations in the Earth’s rotation rate. ASTR211: COORDINATES AND TIME 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 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. Prof. John Hearnshaw UTC advances at uniform rate, but some years are longer than others. ASTR211: COORDINATES AND TIME (c) Converting from universal time to sidereal time To find LST the steps are: • Find number of days elapsed since 12 h UT1 on Jan 1 (this is t). Prof. John Hearnshaw The relationships between UT and local sidereal time depends on the date (time of year) (t) and the observer’s longitude (). ASTR211: COORDINATES AND TIME • 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 24 1 sidereal day t 1 solar day t UT 0 Prof. John Hearnshaw 0 ASTR211: COORDINATES AND TIME • Use the relation UT1 LST = 1.0027378 + λ + GST (at 0h UT1) depends on time longitude depends on date of day during year Note: 1.0027378 = ratio of mean solar day to sidereal day. Prof. John Hearnshaw where longitude (in h m s) ASTR211: COORDINATES AND TIME (d) Standard time (or zone time) 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. Prof. John Hearnshaw Earth is divided into about 24 longitude zones. Standard time is same everywhere inside a given zone. ASTR211: COORDINATES AND TIME Prof. John Hearnshaw Mean Sun crosses meridian at about 12 h 30 m NZST in Christchurch (172½E of Greenwich), so local MST is ~30 m behind NZST (in ChCh) (mean Sun is due north at 12h 30m NZST in ChCh). Standard time zones as seen from the north pole Prof. John Hearnshaw ASTR211: COORDINATES AND TIME Standard time zones on the Earth Prof. John Hearnshaw ASTR211: COORDINATES AND TIME ASTR211: COORDINATES AND TIME Daylight saving time Usually standard time + 1 h in summer months. e.g. NZDT = NZST + 1 h 00 m. Prof. John Hearnshaw (e) ASTR211: COORDINATES AND TIME 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). Prof. John Hearnshaw (f) International atomic time (TAI) ASTR211: COORDINATES AND TIME (g) Julian date 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 Prof. John Hearnshaw A system of specifying time, widely used in astronomy. ASTR211: COORDINATES AND TIME (h) Ephemeris time (1952 – 1984) 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 Prof. John Hearnshaw Because of irregularities in Earth rotation rate, the MSD is not a fixed unit of time, with fluctuations on ~ the 1-ms level. ASTR211: COORDINATES AND TIME The correction T is now about + 1 minute. 1 second of E.T. is defined as: Prof. John Hearnshaw length tropical year for 1900 31556925.9747 ASTR211: COORDINATES AND TIME (i) Terrestrial dynamical time (TDT) Introduced in 1977, to replace ephemeris time. It is based on motions of solar system bodies. TDT = TAI + 32.184s Prof. John Hearnshaw TDT is tied closely to TAI and can be considered to progress at a uniform rate. ASTR211: COORDINATES AND TIME 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) Prof. John Hearnshaw 31. Positions of stars ASTR211: COORDINATES AND TIME • 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. Prof. John Hearnshaw • 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 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. Prof. John Hearnshaw ASTR211: COORDINATES AND TIME ASTR211: COORDINATES AND TIME 32. Proper motion of stars Units: in arc s yr-1 or arc s cy-1 (per century) Components: = sec sin (s of time/yr) = cos (/yr) Prof. John Hearnshaw (a) Definition Angular change per unit time in a star’s position along a great circle of the celestial sphere centred on the Sun. ASTR211: COORDINATES AND TIME N = sin sec = cos E W Proper motion components in R.A. and dec. Prof. John Hearnshaw S ASTR211: COORDINATES AND TIME (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. Differences (1 0) and (1 0) are due to nutation, precession, and proper motion. Correct for nutation and precession to obtain p.m. Prof. John Hearnshaw Repeat observations a long time later to obtain (1, 1) at t1. ASTR211: COORDINATES AND TIME 1 o t1 to The determination of proper motion from fundamental astrometry at epochs t0 and t1 Prof. John Hearnshaw 1 o t1 to ASTR211: COORDINATES AND TIME 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 Prof. John Hearnshaw (ii) Fundamental catalogues ASTR211: COORDINATES AND TIME (iii) Photographic Plates taken with long focus telescopes. Star positions measured relative to standard FK5 stars. 0.16 0.012/yr (iv) Main photographic catalogues • Yale Observatory catalogues • Cape Observatory catalogues These have > 2 105 stars Prof. John Hearnshaw Typical errors: position p.m. ASTR211: COORDINATES AND TIME • Bruce proper motion survey ~ 105 faint stars of high proper motion • PPM catalogue 378,910 stars on FK5 system ( ~ 0.003/yr) Prof. John Hearnshaw • Smithsonian Astrophysical Observatory Catalogue (SAO) 258,997 stars on FK4 system ASTR211: COORDINATES AND TIME (v) From space Prof. John Hearnshaw 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 ASTR211: COORDINATES AND TIME Proper motion and transverse velocity VR star θ d Earth V VT μ (change in direction in 1 yr) 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) Prof. John Hearnshaw (c) ASTR211: COORDINATES AND TIME (as 1 A.U./yr = 4.74 km/s). If VR (from Doppler effect), and , p can be measured, then this gives: direction VT 4.74 tan VR pVR Prof. John Hearnshaw space motion 2 4.7 2 V VR p 1 2 ASTR211: COORDINATES AND TIME (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. to Apex U (km/s) 1 S1 b S d star μ1 In one year Sun moves from S0 to S1, velocity U km/s. Prof. John Hearnshaw o ASTR211: COORDINATES AND TIME 1 1 sin 1 b sin d a But parallax is p d U (km/s) star 1 (as μ1 is small) ( a 1 A.U.) b 1 p sin a b U But A.U./yr A.U./yr where U is in km/s a 4.74 S1 b S μ1 o Prof. John Hearnshaw b 1 (rad.) p sin a to Apex ASTR211: COORDINATES AND TIME U 1 p sin 4.74 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). Prof. John Hearnshaw = parallactic motion of star towards antapex ASTR211: COORDINATES AND TIME High proper motion stars Barnard’s star Groombridge 1830 Lacaille 9352 61 Cygni Lalande 21185 Indi (/yr) 10.3 7.05 6.90 5.22 4.77 4.70 Prof. John Hearnshaw (e) ASTR211: COORDINATES AND TIME Two important catalogues of high proper motion stars • Luyten Two Tenths catalogue (LTT) ~ 17,000 stars with 0.2/yr Prof. John Hearnshaw • Luyten Five Tenths catalogue (LFT) 1849 stars with 0.5/yr ASTR211: COORDINATES AND TIME Prof. John Hearnshaw The motion of Barnard’s star in the sky shows the effects of a high proper motion as well as a large parallax. ASTR211: COORDINATES AND TIME 33. Note on constellations and star names (a) Constellations (i)A constellation = region of sky, originally identified by mythical figures portrayed by the stars. • Greeks recognized 48 constellations (described by Aratus in 270 B.C. and by Ptolemy in the Almagest in about 150 A.D.). Prof. John Hearnshaw • Originally defined by Babylonians ~2000 B.C. ASTR211: COORDINATES AND TIME • Further southern constellations added in 17th C and 18th C, including 13 by Lacaille ~1750. • Today 88 constellations officially recognized by the I.A.U. (International Astronomical Union). Prof. John Hearnshaw • Lacaille divided Argo Carina, Pyxis, Puppis and Vela. ASTR211: COORDINATES AND TIME (ii) Constellation boundaries • 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). Prof. John Hearnshaw • First drawn by Bode in 1801 as curved lines. ASTR211: COORDINATES AND TIME I.A.U. official abbreviations comprise 3 letters. Prof. John Hearnshaw (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 ASTR211: COORDINATES AND TIME (b) Star nomenclature 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. Prof. John Hearnshaw (i) Ancient names for bright stars ASTR211: COORDINATES AND TIME Greek letters were roughly in order of apparent brightness. e.g. Orionis Betelgeuse Orionis Rigel Orionis Bellatrix Prof. John Hearnshaw (ii) Bayer’s ‘Uranometria’ (1603) Assigned star names by Greek letter + constellation name (genitive case). ASTR211: COORDINATES AND TIME (iii) Flamsteead’s ‘Historia Coelestis’ (1729) Numbers increased W to E (increasing R.A.). e.g. 58 Orionis = Betelgeuse 19 Orionis = Rigel 24 Orionis = Bellatrix Prof. John Hearnshaw Stars named with a number within each constellation + constellation name (genitive). ASTR211: COORDINATES AND TIME (iv) The Bright Star Catalogue (Yale 1940) e.g. HR 2061 = Betelgeuse HR 1713 = Rigel HR 1790 = Bellatrix All stars to about mV 6.5 have HR numbers. Prof. John Hearnshaw Used HR numbers (Revised Harvard Photometry (1908)) for 9100 stars in order of R.A. ASTR211: COORDINATES AND TIME (v) The Henry Draper Catalogue (Harvard 1918-24) This was a catalogue of spectral types for 225300 stars. The catalogue numbers are commonly used as star names. e.g. HD 39801 = Betelgeuse HD 34085 = Rigel HD 35468 = Bellatrix Prof. John Hearnshaw Limiting magnitude ~8.5 to 9.5. ASTR211: COORDINATES AND TIME (vi) The Bonn and Cordoba ‘Durchmusterungen’ CD (1900-1914) Catalogue of ~580000 stars from 22 to 62 and later (1932) extended to S. Pole. In both BD and CD stars numbered in order of RA in 1 wide declination zones. Prof. John Hearnshaw BD (1859-62) Catalogue of 324198 stars mainly in N. hemisphere to mV 9.5. Extended in 1886 to 23 with 134000 more stars. ASTR211: COORDINATES AND TIME = Betelgeuse = Rigel = Bellatrix Prof. John Hearnshaw e.g. BD + 7 1055 BD 8 1063 BD + 6 919 ASTR211: COORDINATES AND TIME Prof. John Hearnshaw End of sections 28 - 32