Download (a) Mean solar time

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 (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).
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