Positional Astronomy Observational Astronomy 2019 - Coordinate systems
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Positional Astronomy Observational Astronomy 2019 Part 2 Prof. S.C. Trager Coordinate systems
We need to know where the astronomical objects we want to study are located in order to study them! We need a system (well, many systems!) to describe the positions of astronomical objects. The Celestial Sphere First we need the concept of the celestial sphere. It would be nice if we knew the distance to every object we’re interested in — but we don’t. And it’s actually unnecessary in order to observe them!
The Celestial Sphere
Instead, we assume that all astronomical sources are
infinitely far away and live on the surface of a sphere at
infinite distance. This is the celestial sphere.
If we define a coordinate system on this sphere, we
know where to point!
Furthermore, stars (and galaxies) move with respect
to each other. The motion normal to the line of sight
— i.e., on the celestial sphere — is called proper
motion (which we’ll return to shortly)
Astronomical coordinate
systems
A bit of terminology:
great circle: a circle on the surface of a sphere
intercepting a plane that intersects the origin of the
sphere
i.e., any circle on the surface of a sphere that
divides that sphere into two equal hemispheres
Horizon coordinates A natural coordinate system for an Earth- bound observer is the “horizon” or “Alt-Az” coordinate system The great circle of the horizon projected on the celestial sphere is the equator of this system. Horizon coordinates Altitude (or elevation) is the angle from the horizon up to our object — the zenith, the point directly above the observer, is at +90º
Horizon coordinates We need another coordinate: define a great circle perpendicular to the equator (horizon) passing through the zenith and, for convenience, due north This line of constant longitude is called a meridian Horizon coordinates The azimuth is the angle measured along the horizon from north towards east to the great circle that intercepts our object (star) and the zenith.
Horizon coordinates
The origin of these angles
(coordinates) is the
observer
Note that this is a left-
handed coordinate
system!
The William Herschel Telescope is an alt-az telescope, as are the VLTs.
Horizon coordinates
Nearly all big telescopes
(diameter ≥ 4m, telescopes
built after ~1990, most
“classical” radio telescopes) are
in alt-az mounts
This is the natural coordinate
system for these telescopes
But this system is dependent
on the location of the observer
and time of the observation:
makes consistent cataloguing
of objects difficult!
Equatorial coordinates
+90º
Let’s consider a
coordinate system that is
tied to the astronomical
objects themselves —
and preferably those that
don’t move! ♈
–90º
Equatorial coordinates
+90º
In equatorial
coordinates, the
celestial equator is the
great circle that intersects
both the celestial sphere
and the Earth’s equator:
it’s the projection of the ♈
equator onto the celestial
sphere
–90º
Equatorial coordinates
+90º
The declination δ is the
celestial latitude and is
measured in degrees, with
0º at the equator, +90º at
the North Celestial Pole
(NCP) — the intersection
of the Earth’s north
(rotational) pole with the ♈
celestial sphere — and
–90º at the South
Celestial Pole
–90º
Equatorial coordinates
+90º
The right ascension (RA)
α is the celestial
longitude and is
measured in units of time,
0–24 hours, from west
to east, with 0h at the
Sun’s position when it
crosses the equator from ♈
south to north,
approximately at noon on
21 March in Greenwich,
UK.
–90º
Equatorial coordinates
+90º
The position α=0h, δ=0º is
called the vernal
equinox ♈
this is the sign of the
constellation Aries,
where the vernal
equinox happened
2500 years ago ♈
The equatorial system is a
right-handed system
–90º
Equatorial coordinates
+90º
Because the Earth
precesses around an
average direction
perpendicular to the
ecliptic (the plane of the
Earth’s orbit around the
Sun) due to the torques
exerted on by the Moon,
Sun, and Jupiter (more
♈
later!), the equatorial system
slowly changes with time.
–90º
Equatorial coordinates
+90º
This means that the vernal
equinox and the celestial
equator move with respect
to the distant background
objects (galaxies, quasars).
There we need to assign
an epoch — a date — to ♈
any equatorial coordinate.
(We’ll return to this shortly!)
–90º
Our Gratama Telescope is a polar-axis telescope, as the Isaac Newton
Telescope on La Palma
The local equatorial system
The local equatorial
system is used to point
polar-axis (or “equatorial”)
mount telescopes
These telescopes rotate
around an axis parallel to
the Earth’s rotation axis
In the Northern
Hemisphere, this means
that the primary mount
axis always points northThe local equatorial system
These telescopes track a
star by rotation around
only one axis
Note that this means
that the field of the
image does not rotate,
like it does for an alt-az
telescope
The local equatorial system
In the local equatorial system, the hour
angle HA replaces the right ascension:
HA=LST–α
Here LST is the local sidereal time
(which we’ll define shortly!)
So knowing the time of day (the LST)
and the α,δ of an object, it’s very easy
to locate your object with a polar-axis
telescope.
HA varies from –6 h at the eastern
horizon (rising) to 0 h at the zenith to
+6 h at the western horizon (setting)
Note that the minus sign makes this a
left-handed coordinate system!Equatorial coordinates A note about fixed angular sizes in (any) equatorial coordinate system: Fixed angular sizes get longer in longitude of the coordinate system (e.g., right ascension) as one goes goes towards the pole – i.e., towards higher absolute latitude |δ| – by a factor that goes as 1/cos(δ) Galactic coordinates It is sometimes convenient to use the Milky Way itself to define a coordinate system For example, if you want to know the positions of globular clusters relative to the bugle and disk or need an estimate of the interstellar dust extinction or the stellar density towards an object
Galactic coordinates It is sometimes convenient to use the Milky Way itself to define a coordinate system For example, if you want to know the positions of globular clusters relative to the bugle and disk or need an estimate of the interstellar dust extinction or the stellar density towards an object Galactic coordinates In galactic coordinates, the plane of the Galaxy defines the (celestial) equator, assuming that the Sun sits exactly in the plane (which isn’t quite true)
Galactic coordinates In this system, the galactic longitude l (often written lII) is measured in degrees, with 0º on a line connecting the Sun with the center of the Galaxy (roughly...) and increasing in a right- handed fashion Galactic coordinates The galactic latitude b (bII) is also measured in degrees, with b=0º at the equator.
Galactic coordinates
The system is precisely
defined by the direction of
the North Galactic Pole
(NGP):
↵NGP (B1950) = 192.25 = 12h 49m
NGP (B1950) = +27.4 = +27 240
and by the Galactic
longitude of the North
Celestial Pole:
lNCP = 123
Galactic coordinates
The first set of coordinates α=12h49m NCP l=123º
implies that the celestial δ=27.4º
and galactic equators are
tilted by 90º–27.4º=62.6º
line o
These two great circles
f nod
cross at two nodes, and
es
the line of nodes that l=33.0º
connect them is the axis α=18h49m
that transforms one plane
to the otherGalactic coordinates
α=12h49m NCP l=123º
The equators cross at δ=27.4º
lnode = 123 90 = 33
B1950
↵node = 12h 49m + 6h = 18h 49m
for the ascending node
line o
f nod
the extra 90º angles in l
es
and α shift from the l=33.0º
NCP and the galactic α=18h49m
equator to the nodes
Galactic coordinates
Using the cosine law of spherical trigonometry, one can
show that the transformation from α,δ to l,b is
cos b cos(l 33 ) = cos cos(↵ 282.25 )
cos b sin(l 33 ) = cos sin(↵ 282.25 ) cos 62.6 + sin sin 62.6
sin b = sin cos 62.6 cos sin(↵ 282.25 ) sin 62.6
where the last equation gives the sign of b — i.e., the
proper quadrant of the GalaxyGalactic coordinates
To transform from l,b to α,δ use
cos sin(↵ 282.25 ) = cos b sin(l 33 ) cos 62.6 sin b sin 62.6
sin = cos b sin(l 33 ) sin 62.6 sin b cos 62.6
Note in both transformations that α,δ must be in B1950
coordinates!
Other coordinate systems
Ecliptic coordinates
used mostly for satellite navigation, where knowledge
of the Sun–spacecraft angle is critical; uses the plane
of the ecliptic as the celestial equator
Supergalactic coordinates
used for determining the positions of galaxies and
clusters of galaxies relative to the Virgo Cluster–Local
Group–Coma Cluster plane; rarely usedTwo issues...
1. Epoch: For the equatorial coordinate system, a date must be
specified to know where the vernal equinox was when the
positions where defined. Two epochs are commonly used:
B1950, based on the Besselian year and refers to the Earth’s
orientation at 22h 09m UT on 1949 December 31
J2000, based on the Julian year and refers to the Earth’s
orientation at ≈noon in Greenwich UK on 2000 January 1.
Nearly all astronomers now use J2000, but older papers
use B1950 (and the Galactic coordinate system is specified
in B1950)
Gaia’s DR2 catalogue will replace Hipparcos in the next few weeks!
Two issues...
2. Reference Frames: Coordinate systems are difficult
to use without signposts, so special calibrating objects
are used to determine coordinates. B1950 coordinates
were based on the FK4 (Fundamental Katalog 4).
J2000 coordinates were originally based on the FK5 but
are now based on the ICRS (International Celestial
Reference System). ICRS is based on very accurate
VLBI-based positions of >600 extragalactic radio
sources. The Hipparcos catalog of stellar positions (etc.)
has been tied to ICRS to within 0.5 milliarcseconds.Motions of stars, apparent
and real
Let’s use the horizon A zenith
B
P
coordinate system and NC
see how stars move on δ
e θB
ris
the sky during a night. r
po
ato
lar
qu
Consider a northern le
ax
t tia
is
se l es
ce
hemisphere site like 53º
Groningen (θlat≈+53º) N
W looking east
S
Motions of stars, apparent
and real
Stars with
✓lat 90 < < 90 ✓lat
A zenith
B
rise from the east and set in NC
P
the west, just like the Sun
e
δ
ris θB
Stars with r
po
ato
lar
qu
le
ax
t tia
is
se l es
> 90 ✓lat ce
53º
N S
(like star A) are always W looking east
above the horizon and just
circle around the NCPMotions of stars, apparent
and real
Stars with
0 < < 90 ✓lat ,
A zenith
B
like star B, rise north of NC
P
east, moves towards the
δ
south until they transit the ris
e
r
θB
po
meridian (directly south of ato
lar
qu
le
ax
t tia
the zenith), then move
is
se l es
ce
westwards and set north of N
53º
S
west. They cross the W looking east
meridian at a maximum
altitude
✓B = 90 ✓lat +
Motions of stars, apparent
and real
Stars with
0 < < 90 ✓lat ,
A zenith
B
like star B, rise north of NC
P
east, moves towards the
δ
south until they transit the ris
e
r
θB
po
meridian (directly south of ato
lar
qu
le
ax
tia
the zenith), then move t
is
se l es
ce
westwards and set north of N
53º
S
west. They cross the W looking east
meridian at a maximum
altitude
✓B = 90 ✓lat +Parallax
Consider the Earth, 1 AU
away from the Sun at
position E1. Six months ϖ
later, the Earth is at
position E2, but the star
has remained in the same d
place relative to the Sun.
Then, as seen from Earth,
the star appears to have 1 AU
subtended an angle 2ϖ E1 E2
Sun
on the sky.
Parallax
Consider the Earth, 1 AU
away from the Sun at
position E1. Six months
later, the Earth is at
position E2, but the star
has remained in the same
place relative to the Sun.
Then, as seen from Earth,
the star appears to have
subtended an angle 2ϖ
on the sky.Parallax
Consider the Earth, 1 AU
away from the Sun at
position E1. Six months
later, the Earth is at
position E2, but the star
has remained in the same
place relative to the Sun.
Then, as seen from Earth,
the star appears to have
subtended an angle 2ϖ
on the sky.
1 AU=1.496x10^13 cm
Then if r (=1 AU) is the radius of the Earth’s orbit, we
find r
= tan rad
because dϖ is clearly small; then converting to
seconds of arc,
= 206265 rad
Defining 1 AU such that 206265
d= AU
and 1 parsec as the distance at which a star would
have a parallax of 1″:
1 pc = 206265 AU = 3.086 1013 km = 3.26 light years
The distance to a star with observed parallax ϖ″ is
then 1
d= pcIf the star lies at the ecliptic pole, it traces out a circle on its parallactic path If the star lies in the ecliptic plane, it traces out a line Aberration of starlight The velocity of the Earth as it orbits the Sun causes another apparent shift of stellar positions called aberration. It’s actually an effect of special relativity, but it can be determined to within ~1 mas using a classical analogy. Imagine sitting on a train while it’s raining: if the train is sitting still, the rain goes straight down the windows; but if the train is moving, the rain goes diagonally down the windows, because the train has moved during the time it takes the rain to move — straight down, in its reference frame — from the top to the bottom of the window
Aberration
Consider...
a stationary telescope
θaber
a telescope moving
with the Earth, seen in
the Earth’s frame
and a telescope moving Stationary
with the Earth, seen in vEarth vEarth
a stationary reference
frame Earth frame Stationary frame
Aberration
The maximum effect — for objects perpendicular to the
Earth’s orbit (the ecliptic) — is
vEarth 2.979 ⇥ 106 cm s 1
✓aber,max ⇡ = = 0.994 ⇥ 10 4
rad = 20.500
c 2.998 ⇥ 1010 cm s 1
So a star at the ecliptic pole will trace out a circle of
radius 20.5″ every year; stars at the equator will move
to and fro on a line
The effect depends entirely on the time of year and the
direction of the objectAberration
ec
lip
tic
Aberration
ec
lip
ticAberration Note however that all objects in the same direction suffer the same aberration, so it’s impossible to detect aberration from images of small regions of the sky Note also that the Earth’s rotation also causes an aberration called diurnal aberration, which is a very small effect (
Precession
Ecliptic pole
NCP in 12885 years NCP today
Because the Moon’s orbit
is almost in the plane of fixed stars fixed stars
the ecliptic, and because 23.45º
it is so close, it combines
with the Sun (and Jupiter, Earth
e)
(ecliptic plan
also in the ecliptic plane) cele
track of Sun
stia
to exert a torque that or in 12
885
year
s l equ
ato
r to
day
equat
results in a 25770-year cele
stial
precessional period fixed stars fixed stars
Precession
Ecliptic pole
NCP in 12885 years NCP today
fixed stars fixed stars
This causes the equatorial
23.45º
coordinate system to
move (precess) with Earth
e)
respect to the cele
track of Sun
(ecliptic plan
stia
background stars or in 12
885
year
s l equ
ato
r to
day
equat
stial
cele
fixed stars fixed starsPrecession
Ecliptic pole
NCP in 12885 years NCP today
Note that the Earth’s orbit
is fixed in space, and
therefore so is the ecliptic
fixed stars fixed stars
23.45º
As Earth precesses away
from its current position,
Earth
the celestial equator starts (ecliptic plan
e)
track of Sun
to slip to the west, and so s
cele
stia
l
year equ
the intersection of the equat
or in 12
885 ato
r to
day
stial
celestial equator and the cele
ecliptic — the vernal
fixed stars fixed stars
equinox — does as wellPrecession
Ecliptic pole
NCP in 12885 years NCP today
Since the vernal equinox
defines the zeropoint of right
ascension, (fixed) stars will have
increasing right ascension as fixed stars
23.45º
fixed stars
the Earth precesses (and their
declinations will also change)
Earth
This is the precession of the track of Sun
(ecliptic plan
e)
equinoxes and is why we must year
s
cele
stia
l equ
885
always specify a date — an
ato
or in 12 r to
day
equat
stial
epoch — when giving the cele
equatorial coordinates of an fixed stars fixed stars
objectBy 21 March of this year (2019), the equinox had slipped by nearly 16′ to
the west from its J2000.0 position…
Precession
Ecliptic pole
NCP in 12885 years NCP today
fixed stars fixed stars
The rate of this precession 23.45º
of the equinoxes is
Earth
360 ⇥ 360000 / / 25770 yr = 50.300 /yr (ecliptic plan
e)
track of Sun
cele
s stia
or 42′ in 50 years year l equ
885 ato
or in 12 r to
day
equat
stial
cele
fixed stars fixed stars
Nutation
Nutation is often separated from precession but is
actually just the small-scale wobbles around the steady
precession caused by the same processes, plus some
less-predictable wobbles due to ocean–crust
interactions on Earth
It has an amplitude of ≈9″ with a period of 18.6 yearsTwo other motions Refraction: the Earth’s atmosphere moves images, with an angle depending on altitude and wavelength, due to atmospheric refraction; we’ll come back to this later Proper motion: stars have motions relative to very distant background objects; their projected motions on the celestial sphere (the plane of the sky) relative to the barycenter of the Solar System are called proper motions. When known, these must be taken into account when pointing to a star. An extreme example is Barnard’s Star, which has a proper motion of 10.25″ per year! The proper motion of Barnard’s Star
The proper motion of
Barnard’s Star
178
mean [ α, δ ], FK4, mean [ α, δ ], FK4, mean [ α, δ ], FK5,
any equinox no µ, any equinox any equinox
space motion space motion
– E-terms – E-terms
precess to B1950 precess to B1950 precess to J2000
+ E-terms + E-terms
FK4 to FK5, no µ FK4 to FK5, no µ
parallax parallax
FK5, J2000, current epoch, geocentric
light deflection
annual aberration
precession-nutation
Apparent [ α, δ ]
Earth rotation
Apparent [ h, δ ]
diurnal aberration
Topocentric [ h, δ ]
[ h, δ ] to [ Az, El ]
Topocentric [ Az, El ]
refraction
Observed [ Az, El ]
Figure 1: Relationship Between Celestial Coordinates
Star positions are published or catalogued using one of the mean [ α, δ ] systems shown at the top.
The “FK4” systems were used before about 1980 and are usually equinox B1950. The “FK5”
system, equinox J2000, is now preferred, or rather its modern equivalent, the International
Celestial Reference Frame (in the optical, the Hipparcos catalogue). The figure relates a star’s
mean [ α, δ ] to the actual line-of-sight to the star. Note that for the conventional choices of
equinox, namely B1950 or J2000, all of the precession and E-terms corrections are superfluous.Time The calendar and seasons Even though the vernal equinox precesses, it is always the time at which the Sun crosses from the Southern to the Northern Hemisphere on the celestial sphere, marking the beginning of (Northern) spring. Thus the right ascension of the Sun — and not its position relative to the background stars — indicates the season.
The calendar and seasons A sidereal year is the time it takes for the Sun (to appear) to complete a complete circuit of the background stars (~the constellations of the Zodiac) and return to its original position: 1.00 sidereal year = 365.2564 days The calendar and seasons Julius Caesar adopted what is now known as the Julian calendar in 46 BCE. The Julian calendar is tied to the seasons so that 21 March should always take place at the beginning of spring (i.e., the vernal equinox), even though the vernal equinox keeps moving with respect to the background stars. This means that the Julian calendar is based on the tropical year, the time between successive vernal equinoxes.
That is, there were leap years (leap days) in both 1600 and 2000. The offset
was made on Thursday, 4 October 1582; the next day, Friday, was 15
The calendar and seasons October 1582.
The Julian calendar has a year of exactly 365.2500
days — but a tropical year is actually 365.242189
days, shorter than both the Julian and sidereal years!
By 1582, the vernal equinox had slipped back to 11
March. Pope Gregory XIII reset the vernal equinox
back to 21 March (thus removing 10 days!) and also
removed the leap days from century years not evenly
divisible by 400 (e.g., 1700, 1800, 1900, 2100, but not
1600 or 2000).
The calendar and seasons
This means the Gregorian calendar is now
synchronous with the tropical year to within one day in
~3000 years.
Note that only Roman Catholic countries adopted
the Gregorian calendar in 1582 — it took until 1752
for England and its colonies (including the future
USA) and until the Russian Revolution in 1918 for
Russia to do so!Time: sidereal time Sidereal time: the local sidereal time is the right ascension of the meridian passing directly overhead i.e., the right ascension of the zenith right now! Time: solar time Solar time is defined by the transit of the Sun through the meridian — that is, the Sun is “directly overhead” (at its highest point in the sky) at noon solar time.
Time: solar time
A solar day clearly has a variable length due to both
the eccentricity of the Earth’s orbit around the Sun —
Kepler’s second law, an orbit sweeps out equal areas
in equal times, means that the Earth moves faster
when it’s nearer to the Sun than farther away
the tilt of the Earth’s rotational axis with respect to
the ecliptic (obliquity) — the ecliptic’s projection onto
the celestial equator is smaller near the equinoxes
than near the solstices
Time: solar time
+90º
A solar day clearly has a variable length due to both
the eccentricity of the Earth’s orbit around the Sun —
Kepler’s second law, an orbit sweeps out equal areas
in equal times, means that the Earth moves faster
when it’s nearer to the Sun than farther away
the tilt of the Earth’s rotational axis with respect to
♈
the ecliptic (obliquity) — the ecliptic’s projection onto
the celestial equator is smaller near the equinoxes
than near the solstices
–90ºTime: solar time
Because of this variation, astronomers define a mean
solar time that averages the day length to a constant
24 hours
The difference between mean solar time and solar time
is given by the equation of time, which shows that the
length of the solar day varies by ~ ±15 minutes
throughout the year
We can use this to calibrate the time given by a
sundial...
Time: solar time
The equation of time: red curveTime: solar time
The equation of time:
analemma of the Sun
Picture taken at the same Mean Solar Time
Time: solar time
But the mean solar time is still based on the position of
the observer, as it’s based on the point at which the
“fictitious mean Sun” crosses the observer’s meridian
This means that two observers at slightly different
locations will read different times!
The time zone system was created to deal with this
problem, with the zeropoint of the system at 0º
longitude — the longitude of Greenwich, UK: this is the
prime meridiannote also that the sidereal second is shorter than the solar second, by the
ratio 0.9973
Time: solar time
Because the Sun moves along the ecliptic by 360º/365.25 days ≈ 1º/
day, the Earth has to rotate 360º+1º every day to keep up with the Sun.
This results in the solar day being ~4 minutes longer than the sidereal
day:
1 mean solar day = 24h 00m 00s (solar time) = 86400.0 s (solar time)
≈ 86400 s [SI]
1 sidereal day = 23h 56m 04.09s (mean solar time) = 86164.09 s
(mean solar time)
which is valid even as the Earth’s rotation rate varies because the mean
solar day lengthens proportionally to the sidereal day.
Time: solar timeTime: solar time Time: Universal Time (1) Universal time (UT1) is based on the motion of the fixed stars but is adjusted so that it is approximately equal to the mean solar time at Greenwich — such that the “fictitious mean Sun” is on the (prime) meridian at noon and that one day equals precisely 86400 s. Formally, 0h UT (midnight in Greenwich) on 1 January is defined to occur at Greenwich LST (=GMST) ≈ 6.7h. 1 January is 285 days after 21 March, so it’s 18.7h (285d/ 365d x 24h) east of the vernal equinox, so α⊙≈18.7h at noon — and midnight is 12h earlier.
Time: physical time
Note that all of these time systems so far have been
angular measurements, not true physical times:
sidereal, solar, mean solar, and universal time all
measure the Earth’s rotation in some way.
Physical times are based on physical measurements:
the SI (atomic) second is based on the hyperfine
transition of 133Cs:
1.0 SI second = 9 192 631 770 cycles of 133Cs
Time: atomic time
TAI (Temps Atomique Internationale) is the current atomic
time, based on the average of ~150 atomic clocks in ~30
countries, and is currently stable to ≈30 µs/century
Note that TAI and UT1 are independent: atomic clocks
have shown that the Earth’s rotational period is lengthening
by a variable rate of ~1.7 ms/century, as the Earth loses
spin angular momentum to the Earth-Moon orbit
Note that this is longer than it seems: integrated, a year
of 365.25 days is 3.1 ms longer than it began...Time: Universal Time (2) UTC (Universal Coordinated Time) was adopted to link the TAI and UT1 systems. It is based on TAI but includes (positive or negative) leap seconds to keep within 0.9s of UT1, so that in some years 31 December has 86399s, 86400s, or 86401s Time: physical time The variations in the length of the day can be large, as big as 3 ms longer than 86400 s [SI]
Gaia uses TCB: barycentric coordinate time
Time: physical time
Terrestrial time (TT) is a time standard not adjusted for
variations in the Earth’s rotation. TAI is a natural choice for this,
but TT was adopted before TAI and is based on “ephemeris
time” (ET).
Each TT day contains exactly 86400 s [SI].
It is now defined as TT=TAI+32.184 s to match ET. TT
effectively keeps track of the leap seconds inserted into UTC
There are also relativistic timescales, TDB and TCB, which try to
synchronize times across the Solar System (instead of just the
Earth, which TT does)
15 (indiction cycle) × 19 (Metonic cycle) × 28 (Solar cycle) = 7980 years
indiction cycle: 15-year late-Roman tax cycle, extended into medieval
Julian Date Europe
Metonic cycle: common multiple of the solar year and the lunar cycle — i.e.,
Julian Date (JD) is an extremely useful way of keeping the time it takes for the lunar cycle to appear at the same solar date
track of observations made over long time periods.
Julian Dates are defined as the number of (Julian) days
Solar cycle: the time it takes for a solar year (including leap years) to begin
since noon on 1 January 4713 BCE (really!) on the same week day
Roughly now — 24 April 2019 at 12h 00m 00s UT1 — is
JD 2458598.0
The beginning of each Julian day is defined to be at
noon in Greenwich, 12h UT1Julian Date The Modified Julian Date (MJD) is often used (because it’s shorter!): MJD=JD–2400000.5 Note that it starts at midnight in Greenwich rather than at noon (in fact, it started precisely at 00h 00m UT on Wednesday 17 November 1858!) Note also that J2000.0 is defined on the Julian day/year (=365.2500d exactly)/century (36525d) system and began at 12h (TDB) 1 January 2000 exactly, i.e., JD2451545.0 (TDB)
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