Coordinates and time

1
Coordinates and time Sections 28 32
2

• Nutation
• This is a wobbling motion of the Earths rotation
  
• axis as it precesses about the ecliptic pole.
• Amplitude of nutation 9.2 arc sec
• Period of nutation 18? yr
• Nutation is caused by the Moon, in fact the
• retrograde precession of the plane of the Moons
• orbit, which also has a period of 18? 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
Earths rotation axis with period 18? 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 ?
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
• observers 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 Earths 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
• observers 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
• (a,d) 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.
• (a,d)2000.0 are for the epoch 2000.0 UT.

30
32. Proper motion of stars (a) Definition Angular
change per unit time in a stars 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
?? ? 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 gt 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
?
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
(d) Parallactic motion of stars This is that part
of the overall proper motion of a star due to
the Suns velocity through space. In
one year Sun moves from S0 to S1, velocity U
km/s.
d
µ1
41
µ1
42
parallactic motion of star towards antapex The
solar velocity is about U 19.6 km/s towards an
apex direction (a,d) 18 h, 34º (which is near
the bright star, Vega).
43
(e) High proper motion stars
?
(??/yr) Barnards 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 Barnards 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.

51
(ii) Bayers Uranometria (1603) Assigned star
names by Greek letter constellation name
(genitive case). Greek letters were roughly in
order of apparent brightness. e.g. ?
Orionis ? Betelgeuse ? Orionis ? Rigel ?
Orionis ? Bellatrix
52
(iii) Flamsteeads Historia Coelestis
(1729) Stars named with a number within each
constellation constellation name
(genitive). Numbers increased W to E
(increasing R.A.). e.g. 58 Orionis
Betelgeuse 19 Orionis Rigel 24 Orionis
Bellatrix
53
(iv) The Bright Star Catalogue (Yale
1940) Used HR numbers (Revised Harvard
Photometry (1908)) for 9100 stars in order of
R.A. e.g. HR 2061 Betelgeuse HR 1713
Rigel HR 1790 Bellatrix All stars to about
mV ? 6.5 have HR numbers.
54
(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. Limiting
magnitude 8.5 to 9.5. e.g. HD 39801
Betelgeuse HD 34085 Rigel HD 35468
Bellatrix
55
(vi) The Bonn and Cordoba Durchmusterungen B
D (1859-62) Catalogue of 324198 stars mainly in
N. hemisphere to mV ? 9.5. Extended in 1886 to
?23? with 134000 more stars. 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.
56
e.g. BD 7? 1055 Betelgeuse BD ?8? 1063
Rigel BD 6? 919 Bellatrix
57
End of sections 28 - 32