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# Coordinates on the Cosmos

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```									                 Coordinates on the Cosmos

Anirbit

TIFR

October 25, 2009

Anirbit (TIFR)         Coordinates on the Cosmos   October 25, 2009   1 / 33
Some basics

Miles to go before you sleep...

1   Some basics

2   Natural markers in the sky

3   Closer look at the pole and the ascension origin

4   Reference frames from the text-book

5   Setting up the time coordinate

Anirbit (TIFR)         Coordinates on the Cosmos   October 25, 2009   2 / 33
Some basics

What?

Anirbit (TIFR)   Coordinates on the Cosmos   October 25, 2009   3 / 33
Some basics

What?

To specify a spatial coordinate system whose orientation is agreed upon,
one need to specify any two of the following data,

Anirbit (TIFR)         Coordinates on the Cosmos    October 25, 2009   3 / 33
Some basics

What?

To specify a spatial coordinate system whose orientation is agreed upon,
one need to specify any two of the following data,
The x − y plane which in astronomical literature is sometimes called
the fundamental plane or principal plane.

Anirbit (TIFR)         Coordinates on the Cosmos    October 25, 2009   3 / 33
Some basics

What?

To specify a spatial coordinate system whose orientation is agreed upon,
one need to specify any two of the following data,
The x − y plane which in astronomical literature is sometimes called
the fundamental plane or principal plane.
The direction of the z − axis or what is called the zenith or the pole.

Anirbit (TIFR)         Coordinates on the Cosmos     October 25, 2009   3 / 33
Some basics

What?

To specify a spatial coordinate system whose orientation is agreed upon,
one need to specify any two of the following data,
The x − y plane which in astronomical literature is sometimes called
the fundamental plane or principal plane.
The direction of the z − axis or what is called the zenith or the pole.
The location of the origin.

Anirbit (TIFR)         Coordinates on the Cosmos     October 25, 2009   3 / 33
Some basics

What?

To specify a spatial coordinate system whose orientation is agreed upon,
one need to specify any two of the following data,
The x − y plane which in astronomical literature is sometimes called
the fundamental plane or principal plane.
The direction of the z − axis or what is called the zenith or the pole.
The location of the origin.

In various systems we shall see how the above data is speciﬁed using
natural markers.

Anirbit (TIFR)         Coordinates on the Cosmos     October 25, 2009   3 / 33
Some basics

Basics

Anirbit (TIFR)   Coordinates on the Cosmos   October 25, 2009   4 / 33
Some basics

Basics

The International Astronomical Union (IAU) in 1992 recommended
that

Anirbit (TIFR)      Coordinates on the Cosmos   October 25, 2009   4 / 33
Some basics

Basics

The International Astronomical Union (IAU) in 1992 recommended
that
principal plane of the celestial reference system be close to the mean
equator at J2000.0.

Anirbit (TIFR)          Coordinates on the Cosmos     October 25, 2009   4 / 33
Some basics

Basics

The International Astronomical Union (IAU) in 1992 recommended
that
principal plane of the celestial reference system be close to the mean
equator at J2000.0.
the origin of right ascension be as close as possible to the dynamical
equinox of J2000.0.

Anirbit (TIFR)          Coordinates on the Cosmos     October 25, 2009   4 / 33
Some basics

Basics

The International Astronomical Union (IAU) in 1992 recommended
that
principal plane of the celestial reference system be close to the mean
equator at J2000.0.
the origin of right ascension be as close as possible to the dynamical
equinox of J2000.0.
the origin be at the barycenter of the solar system.

Anirbit (TIFR)          Coordinates on the Cosmos     October 25, 2009   4 / 33
Some basics

Basics

The International Astronomical Union (IAU) in 1992 recommended
that
principal plane of the celestial reference system be close to the mean
equator at J2000.0.
the origin of right ascension be as close as possible to the dynamical
equinox of J2000.0.
the origin be at the barycenter of the solar system.
the direction of the axes be ﬁxed with respect to the quasars.

Anirbit (TIFR)          Coordinates on the Cosmos     October 25, 2009   4 / 33
Some basics

Basics

The International Astronomical Union (IAU) in 1992 recommended
that
principal plane of the celestial reference system be close to the mean
equator at J2000.0.
the origin of right ascension be as close as possible to the dynamical
equinox of J2000.0.
the origin be at the barycenter of the solar system.
the direction of the axes be ﬁxed with respect to the quasars.

The International Earth Rotation and Reference Systems Service
(IERS) put these recommendations into eﬀect and prepared a system
which was accepted by the IAU General Assembly in 1997 under the name
International Celestial Reference System (ICRS) which came to
replace the old FK5 system from 1st January , 1998.
Anirbit (TIFR)          Coordinates on the Cosmos     October 25, 2009   4 / 33
Some basics

Basics..contd. (ICRS, ICRF, BCRS, GCRS ITRS)

Anirbit (TIFR)   Coordinates on the Cosmos   October 25, 2009   5 / 33
Some basics

Basics..contd. (ICRS, ICRF, BCRS, GCRS ITRS)
The ICRS is in some sense an abstract concept.

Anirbit (TIFR)        Coordinates on the Cosmos   October 25, 2009   5 / 33
Some basics

Basics..contd. (ICRS, ICRF, BCRS, GCRS ITRS)
The ICRS is in some sense an abstract concept. One of its important
realizations for spatial coordinates is the International Celestial
Reference Frame (ICRF).

Anirbit (TIFR)        Coordinates on the Cosmos    October 25, 2009   5 / 33
Some basics

Basics..contd. (ICRS, ICRF, BCRS, GCRS ITRS)
The ICRS is in some sense an abstract concept. One of its important
realizations for spatial coordinates is the International Celestial
Reference Frame (ICRF).

For optical wavelengths the primary realization of ICRS is the
Hipparcos Celestial Reference Frame (HCRF) based on the
Hipparcos Catalogue,

Anirbit (TIFR)         Coordinates on the Cosmos   October 25, 2009   5 / 33
Some basics

Basics..contd. (ICRS, ICRF, BCRS, GCRS ITRS)
The ICRS is in some sense an abstract concept. One of its important
realizations for spatial coordinates is the International Celestial
Reference Frame (ICRF).

For optical wavelengths the primary realization of ICRS is the
Hipparcos Celestial Reference Frame (HCRF) based on the
Hipparcos Catalogue, which we shall come back to later.

Anirbit (TIFR)         Coordinates on the Cosmos   October 25, 2009   5 / 33
Some basics

Basics..contd. (ICRS, ICRF, BCRS, GCRS ITRS)
The ICRS is in some sense an abstract concept. One of its important
realizations for spatial coordinates is the International Celestial
Reference Frame (ICRF).

For optical wavelengths the primary realization of ICRS is the
Hipparcos Celestial Reference Frame (HCRF) based on the
Hipparcos Catalogue, which we shall come back to later.

The 2 important realizations of ICRS for space-time coordinates
which take General Relativistic considerations into account are the,
Barycentric Celestial Reference System (BCRS)

Anirbit (TIFR)         Coordinates on the Cosmos     October 25, 2009   5 / 33
Some basics

Basics..contd. (ICRS, ICRF, BCRS, GCRS ITRS)
The ICRS is in some sense an abstract concept. One of its important
realizations for spatial coordinates is the International Celestial
Reference Frame (ICRF).

For optical wavelengths the primary realization of ICRS is the
Hipparcos Celestial Reference Frame (HCRF) based on the
Hipparcos Catalogue, which we shall come back to later.

The 2 important realizations of ICRS for space-time coordinates
which take General Relativistic considerations into account are the,
Barycentric Celestial Reference System (BCRS)
Geocentric Celestial Reference System (GCRS)

Anirbit (TIFR)         Coordinates on the Cosmos     October 25, 2009   5 / 33
Some basics

Basics..contd. (ICRS, ICRF, BCRS, GCRS ITRS)
The ICRS is in some sense an abstract concept. One of its important
realizations for spatial coordinates is the International Celestial
Reference Frame (ICRF).

For optical wavelengths the primary realization of ICRS is the
Hipparcos Celestial Reference Frame (HCRF) based on the
Hipparcos Catalogue, which we shall come back to later.

The 2 important realizations of ICRS for space-time coordinates
which take General Relativistic considerations into account are the,
Barycentric Celestial Reference System (BCRS)
Geocentric Celestial Reference System (GCRS)
Along with these one also has the International Terrestial
Reference System (ITRS)

Anirbit (TIFR)         Coordinates on the Cosmos     October 25, 2009   5 / 33
Some basics

Basics..contd. (ICRS, ICRF, BCRS, GCRS ITRS)
The ICRS is in some sense an abstract concept. One of its important
realizations for spatial coordinates is the International Celestial
Reference Frame (ICRF).

For optical wavelengths the primary realization of ICRS is the
Hipparcos Celestial Reference Frame (HCRF) based on the
Hipparcos Catalogue, which we shall come back to later.

The 2 important realizations of ICRS for space-time coordinates
which take General Relativistic considerations into account are the,
Barycentric Celestial Reference System (BCRS)
Geocentric Celestial Reference System (GCRS)
Along with these one also has the International Terrestial
Reference System (ITRS) which is a time-dependent, non-inertial
reference system co-moving with the geocenter and rotating with the
Earth.
Anirbit (TIFR)         Coordinates on the Cosmos     October 25, 2009   5 / 33
Some basics

Basics..contd. (ICRS, ICRF, BCRS, GCRS ITRS)
The ICRS is in some sense an abstract concept. One of its important
realizations for spatial coordinates is the International Celestial
Reference Frame (ICRF).

For optical wavelengths the primary realization of ICRS is the
Hipparcos Celestial Reference Frame (HCRF) based on the
Hipparcos Catalogue, which we shall come back to later.

The 2 important realizations of ICRS for space-time coordinates
which take General Relativistic considerations into account are the,
Barycentric Celestial Reference System (BCRS)
Geocentric Celestial Reference System (GCRS)
Along with these one also has the International Terrestial
Reference System (ITRS) which is a time-dependent, non-inertial
reference system co-moving with the geocenter and rotating with the
Earth.
Anirbit (TIFR)         Coordinates on the Cosmos     October 25, 2009   5 / 33
Some basics

Basics...contd.

Anirbit (TIFR)   Coordinates on the Cosmos   October 25, 2009   6 / 33
Some basics

Basics...contd.

The Very Large Baseline Interferometry (VLBI) is the standard
experimental technique used to establish the extragalactic reference frame
and monitor the precession and nutation of the celestial pole in the sky.

Anirbit (TIFR)         Coordinates on the Cosmos    October 25, 2009   6 / 33
Some basics

Basics...contd.

The Very Large Baseline Interferometry (VLBI) is the standard
experimental technique used to establish the extragalactic reference frame
and monitor the precession and nutation of the celestial pole in the sky.

VLBI measurements are not easily accessible to everyone and hence other
easier terrestial reference frames have been designed to which conversions
from ICRS are well-known. The most important of these are,
IERS Terrestial Reference Frame (ITRF)

Anirbit (TIFR)         Coordinates on the Cosmos     October 25, 2009   6 / 33
Some basics

Basics...contd.

The Very Large Baseline Interferometry (VLBI) is the standard
experimental technique used to establish the extragalactic reference frame
and monitor the precession and nutation of the celestial pole in the sky.

VLBI measurements are not easily accessible to everyone and hence other
easier terrestial reference frames have been designed to which conversions
from ICRS are well-known. The most important of these are,
IERS Terrestial Reference Frame (ITRF)
HIPPARCOS Galactic Reference Frame

Anirbit (TIFR)         Coordinates on the Cosmos     October 25, 2009   6 / 33
Some basics

Basics...contd.

The Very Large Baseline Interferometry (VLBI) is the standard
experimental technique used to establish the extragalactic reference frame
and monitor the precession and nutation of the celestial pole in the sky.

VLBI measurements are not easily accessible to everyone and hence other
easier terrestial reference frames have been designed to which conversions
from ICRS are well-known. The most important of these are,
IERS Terrestial Reference Frame (ITRF)
HIPPARCOS Galactic Reference Frame
JPL ephemerides

Anirbit (TIFR)         Coordinates on the Cosmos     October 25, 2009   6 / 33
Some basics

Basics...contd.

The Very Large Baseline Interferometry (VLBI) is the standard
experimental technique used to establish the extragalactic reference frame
and monitor the precession and nutation of the celestial pole in the sky.

VLBI measurements are not easily accessible to everyone and hence other
easier terrestial reference frames have been designed to which conversions
from ICRS are well-known. The most important of these are,
IERS Terrestial Reference Frame (ITRF)
HIPPARCOS Galactic Reference Frame
JPL ephemerides

We shall have a closer look at the Hipparcos catalogue later.

Anirbit (TIFR)         Coordinates on the Cosmos     October 25, 2009   6 / 33
Some basics

Little bit about ITRS and ITRF

Anirbit (TIFR)   Coordinates on the Cosmos   October 25, 2009   7 / 33
Some basics

Little bit about ITRS and ITRF

The International Terrestrial Reference System (ITRS) constitutes a set of
prescriptions and conventions together with the modelling required to
deﬁne origin, scale, orientation and time evolution of a reference system
co-rotating with the earth. The system is realised by the International
Terrestrial Reference Frame (ITRF)

Anirbit (TIFR)         Coordinates on the Cosmos    October 25, 2009   7 / 33
Some basics

Little bit about ITRS and ITRF

The International Terrestrial Reference System (ITRS) constitutes a set of
prescriptions and conventions together with the modelling required to
deﬁne origin, scale, orientation and time evolution of a reference system
co-rotating with the earth. The system is realised by the International
Terrestrial Reference Frame (ITRF)

The ITRS is the recommended system in which to express positions on the
Earth.

Anirbit (TIFR)         Coordinates on the Cosmos    October 25, 2009   7 / 33
Some basics

Little bit about ITRS and ITRF

The International Terrestrial Reference System (ITRS) constitutes a set of
prescriptions and conventions together with the modelling required to
deﬁne origin, scale, orientation and time evolution of a reference system
co-rotating with the earth. The system is realised by the International
Terrestrial Reference Frame (ITRF)

The ITRS is the recommended system in which to express positions on the
Earth. Practical realization of ITRS is the International Terrestial
Reference Frame (ITRF) which is a set of reference points on the
surface of the Earth whose adopted positions and velocities ﬁx the rotating
axes of the ITRS.

Anirbit (TIFR)         Coordinates on the Cosmos     October 25, 2009   7 / 33
Natural markers in the sky

Miles to go before you sleep...

1   Some basics

2   Natural markers in the sky

3   Closer look at the pole and the ascension origin

4   Reference frames from the text-book

5   Setting up the time coordinate

Anirbit (TIFR)                 Coordinates on the Cosmos   October 25, 2009   8 / 33
Natural markers in the sky

Reference points

Anirbit (TIFR)                 Coordinates on the Cosmos   October 25, 2009   9 / 33
Natural markers in the sky

Reference points

The realization of ICRF consists of a set of precise coordinates of
extragalactic radio sources, which are classiﬁed into 3 categories,

Anirbit (TIFR)                 Coordinates on the Cosmos   October 25, 2009   9 / 33
Natural markers in the sky

Reference points

The realization of ICRF consists of a set of precise coordinates of
extragalactic radio sources, which are classiﬁed into 3 categories,
Deﬁning these are the ones which have a large number of
observations over a suﬃciently long data span to assess positional
stability. These maintain the axis of the ICRS.

Anirbit (TIFR)                 Coordinates on the Cosmos   October 25, 2009   9 / 33
Natural markers in the sky

Reference points

The realization of ICRF consists of a set of precise coordinates of
extragalactic radio sources, which are classiﬁed into 3 categories,
Deﬁning these are the ones which have a large number of
observations over a suﬃciently long data span to assess positional
stability. These maintain the axis of the ICRS.
Candidate are the sources which have insuﬃcient number of
observations or an observation time too short to be considered
reliable. With advancement of technology Candidates could become
Deﬁning.

Anirbit (TIFR)                 Coordinates on the Cosmos   October 25, 2009   9 / 33
Natural markers in the sky

Reference points

The realization of ICRF consists of a set of precise coordinates of
extragalactic radio sources, which are classiﬁed into 3 categories,
Deﬁning these are the ones which have a large number of
observations over a suﬃciently long data span to assess positional
stability. These maintain the axis of the ICRS.
Candidate are the sources which have insuﬃcient number of
observations or an observation time too short to be considered
reliable. With advancement of technology Candidates could become
Deﬁning.
Other sources include those objects with poorly determined positions
which are useful in deriving various frame transforms.

Anirbit (TIFR)                 Coordinates on the Cosmos   October 25, 2009   9 / 33
Natural markers in the sky

Reference points

Anirbit (TIFR)                 Coordinates on the Cosmos   October 25, 2009   10 / 33
Natural markers in the sky

Reference points

The idea of using extra galactic objects as reference points has been there
for a long time because these are so far away that they appear to be almost
static. We shall later have a brief look at the details of this approximation.

Anirbit (TIFR)                 Coordinates on the Cosmos   October 25, 2009   10 / 33
Natural markers in the sky

Reference points

The idea of using extra galactic objects as reference points has been there
for a long time because these are so far away that they appear to be almost
static. We shall later have a brief look at the details of this approximation.

The number of Deﬁning sources has progressively grown from 23 in 1988
to 212 in 1995.

Anirbit (TIFR)                 Coordinates on the Cosmos   October 25, 2009   10 / 33
Natural markers in the sky

Reference points

The idea of using extra galactic objects as reference points has been there
for a long time because these are so far away that they appear to be almost
static. We shall later have a brief look at the details of this approximation.

The number of Deﬁning sources has progressively grown from 23 in 1988
to 212 in 1995. These consist of mainly Quasars, BL Lac sources and few
Active Galactic Nuclei (AGN).

Anirbit (TIFR)                 Coordinates on the Cosmos   October 25, 2009   10 / 33
Natural markers in the sky

Reference points

The idea of using extra galactic objects as reference points has been there
for a long time because these are so far away that they appear to be almost
static. We shall later have a brief look at the details of this approximation.

The number of Deﬁning sources has progressively grown from 23 in 1988
to 212 in 1995. These consist of mainly Quasars, BL Lac sources and few
Active Galactic Nuclei (AGN).

Comparisons between successive realizations of these “ﬁxed” points have
shown that were small shifts from year to year until the process converged
to better than 0.1mas and to 0.02mas for the relative orientation between
successive realizations.
Anirbit (TIFR)                 Coordinates on the Cosmos   October 25, 2009   10 / 33
Natural markers in the sky

Reference points

The idea of using extra galactic objects as reference points has been there
for a long time because these are so far away that they appear to be almost
static. We shall later have a brief look at the details of this approximation.

The number of Deﬁning sources has progressively grown from 23 in 1988
to 212 in 1995. These consist of mainly Quasars, BL Lac sources and few
Active Galactic Nuclei (AGN).

Comparisons between successive realizations of these “ﬁxed” points have
shown that were small shifts from year to year until the process converged
to better than 0.1mas and to 0.02mas for the relative orientation between
successive realizations.
Anirbit (TIFR)                 Coordinates on the Cosmos   October 25, 2009   10 / 33
Natural markers in the sky

Anirbit (TIFR)                 Coordinates on the Cosmos   October 25, 2009   11 / 33
Natural markers in the sky

The 212 extra galactic radio sources are distributed over the sky with a
median uncertainty of ±0.35mas in right ascension and ±0.40mas in right
declination. The uncertainty from representation of ICRS is then
established to be smaller than ±0.01mas

Anirbit (TIFR)                 Coordinates on the Cosmos   October 25, 2009   11 / 33
Natural markers in the sky

The 212 extra galactic radio sources are distributed over the sky with a
median uncertainty of ±0.35mas in right ascension and ±0.40mas in right
declination. The uncertainty from representation of ICRS is then
established to be smaller than ±0.01mas

The scattering of rotation parameters of diﬀerent comparisons performed
shows that these axes are stable to ±0.02mas. These estimates of frame
stability is is based on assumptions,

Anirbit (TIFR)                 Coordinates on the Cosmos   October 25, 2009   11 / 33
Natural markers in the sky

The 212 extra galactic radio sources are distributed over the sky with a
median uncertainty of ±0.35mas in right ascension and ±0.40mas in right
declination. The uncertainty from representation of ICRS is then
established to be smaller than ±0.01mas

The scattering of rotation parameters of diﬀerent comparisons performed
shows that these axes are stable to ±0.02mas. These estimates of frame
stability is is based on assumptions,
that the sources have no proper motion.

Anirbit (TIFR)                 Coordinates on the Cosmos   October 25, 2009   11 / 33
Natural markers in the sky

The 212 extra galactic radio sources are distributed over the sky with a
median uncertainty of ±0.35mas in right ascension and ±0.40mas in right
declination. The uncertainty from representation of ICRS is then
established to be smaller than ±0.01mas

The scattering of rotation parameters of diﬀerent comparisons performed
shows that these axes are stable to ±0.02mas. These estimates of frame
stability is is based on assumptions,
that the sources have no proper motion.
that there is no global rotation of the universe.

Anirbit (TIFR)                 Coordinates on the Cosmos   October 25, 2009   11 / 33
Natural markers in the sky

ICRS update

Anirbit (TIFR)                 Coordinates on the Cosmos   October 25, 2009   12 / 33
Natural markers in the sky

ICRS update

An extension of ICRS called the ICRS-Ext.1 has been constructed by
using VLBI data till April 1999 which lists positions and errors in
measurement of a total of 667 objects spanning all categories, Deﬁning,
Candidate and Other.

Anirbit (TIFR)                 Coordinates on the Cosmos   October 25, 2009   12 / 33
Natural markers in the sky

Hipparcos Catalogue

The Hipparcos catalogue provides the equatorial coordinates of about
118000 stars in the ICRS at epoch 1991.25 along with their proper
motions, their parallaxes and their magnitudes in the wideband of the
Hipparcos system.

Anirbit (TIFR)                 Coordinates on the Cosmos   October 25, 2009   13 / 33
Natural markers in the sky

Hipparcos Catalogue

The Hipparcos catalogue provides the equatorial coordinates of about
118000 stars in the ICRS at epoch 1991.25 along with their proper
motions, their parallaxes and their magnitudes in the wideband of the
Hipparcos system.
The astrometric data concerns only 117955 stars.

Anirbit (TIFR)                 Coordinates on the Cosmos   October 25, 2009   13 / 33
Natural markers in the sky

Hipparcos Catalogue

The Hipparcos catalogue provides the equatorial coordinates of about
118000 stars in the ICRS at epoch 1991.25 along with their proper
motions, their parallaxes and their magnitudes in the wideband of the
Hipparcos system.
The astrometric data concerns only 117955 stars.
The median uncertainty for bright stars (Hipparcos wide band
magnitude < 9) = are ±0.77mas and ±0.64mas in right ascension
and declination respectively.

Anirbit (TIFR)                 Coordinates on the Cosmos   October 25, 2009   13 / 33
Natural markers in the sky

Hipparcos Catalogue

The Hipparcos catalogue provides the equatorial coordinates of about
118000 stars in the ICRS at epoch 1991.25 along with their proper
motions, their parallaxes and their magnitudes in the wideband of the
Hipparcos system.
The astrometric data concerns only 117955 stars.
The median uncertainty for bright stars (Hipparcos wide band
magnitude < 9) = are ±0.77mas and ±0.64mas in right ascension
and declination respectively.
Median uncertainties in annual proper motions are ±0.88 and
±0.74mas/yr respectively.

Anirbit (TIFR)                 Coordinates on the Cosmos   October 25, 2009   13 / 33
Closer look at the pole and the ascension origin

Miles to go before you sleep...

1   Some basics

2   Natural markers in the sky

3   Closer look at the pole and the ascension origin

4   Reference frames from the text-book

5   Setting up the time coordinate

Anirbit (TIFR)                         Coordinates on the Cosmos   October 25, 2009   14 / 33
Closer look at the pole and the ascension origin

Deﬁnition of the pole

Anirbit (TIFR)                         Coordinates on the Cosmos   October 25, 2009   15 / 33
Closer look at the pole and the ascension origin

Deﬁnition of the pole

The pole and the ascension origin we shall look at are both used within
the framework of the ITRF.

Anirbit (TIFR)                         Coordinates on the Cosmos   October 25, 2009   15 / 33
Closer look at the pole and the ascension origin

Deﬁnition of the pole

The pole and the ascension origin we shall look at are both used within
the framework of the ITRF.
In the 24th General Assembly of IAU via Resolution B1.7 the older concept
of the Central Ephemeris Pole (CEP) has been replaced by

Anirbit (TIFR)                         Coordinates on the Cosmos   October 25, 2009   15 / 33
Closer look at the pole and the ascension origin

Deﬁnition of the pole

The pole and the ascension origin we shall look at are both used within
the framework of the ITRF.
In the 24th General Assembly of IAU via Resolution B1.7 the older concept
of the Central Ephemeris Pole (CEP) has been replaced by the dynamically
deﬁned Central Intermediate Pole (CIP)

Anirbit (TIFR)                         Coordinates on the Cosmos   October 25, 2009   15 / 33
Closer look at the pole and the ascension origin

Deﬁnition of the pole

The pole and the ascension origin we shall look at are both used within
the framework of the ITRF.
In the 24th General Assembly of IAU via Resolution B1.7 the older concept
of the Central Ephemeris Pole (CEP) has been replaced by the dynamically
deﬁned Central Intermediate Pole (CIP) which is speciﬁed by the
GCRS according to the motion of the Tisserand mean Axis of the earth
with periods > 2 days.

Anirbit (TIFR)                         Coordinates on the Cosmos   October 25, 2009   15 / 33
Closer look at the pole and the ascension origin

Deﬁnition of the pole

The pole and the ascension origin we shall look at are both used within
the framework of the ITRF.
In the 24th General Assembly of IAU via Resolution B1.7 the older concept
of the Central Ephemeris Pole (CEP) has been replaced by the dynamically
deﬁned Central Intermediate Pole (CIP) which is speciﬁed by the
GCRS according to the motion of the Tisserand mean Axis of the earth
with periods > 2 days.

CIP has been implemented from 1st January 2003.

Anirbit (TIFR)                         Coordinates on the Cosmos   October 25, 2009   15 / 33
Closer look at the pole and the ascension origin

Deﬁnition of the pole

The pole and the ascension origin we shall look at are both used within
the framework of the ITRF.
In the 24th General Assembly of IAU via Resolution B1.7 the older concept
of the Central Ephemeris Pole (CEP) has been replaced by the dynamically
deﬁned Central Intermediate Pole (CIP) which is speciﬁed by the
GCRS according to the motion of the Tisserand mean Axis of the earth
with periods > 2 days.

CIP has been implemented from 1st January 2003.

Anirbit (TIFR)                         Coordinates on the Cosmos   October 25, 2009   15 / 33
Closer look at the pole and the ascension origin

More on CIP

The salient features of CIP are,

Anirbit (TIFR)                         Coordinates on the Cosmos   October 25, 2009   16 / 33
Closer look at the pole and the ascension origin

More on CIP

The salient features of CIP are,
It takes into account the earth’s diurnal and higher frequency
variations of orientation

Anirbit (TIFR)                         Coordinates on the Cosmos   October 25, 2009   16 / 33
Closer look at the pole and the ascension origin

More on CIP

The salient features of CIP are,
It takes into account the earth’s diurnal and higher frequency
variations of orientation
The direction of the CIP is determined from the nutation-precession
model of the earth determined from the “Non-Rigid Earth Nutation
Theory” ratiﬁed by the IAU.

Anirbit (TIFR)                         Coordinates on the Cosmos   October 25, 2009   16 / 33
Closer look at the pole and the ascension origin

More on CIP

The salient features of CIP are,
It takes into account the earth’s diurnal and higher frequency
variations of orientation
The direction of the CIP is determined from the nutation-precession
model of the earth determined from the “Non-Rigid Earth Nutation
Theory” ratiﬁed by the IAU.
These models determine a dynamic oﬀset between the GCRS pole
and the CIP.

Anirbit (TIFR)                         Coordinates on the Cosmos   October 25, 2009   16 / 33
Closer look at the pole and the ascension origin

Tisserand Mean Axis

Anirbit (TIFR)                         Coordinates on the Cosmos   October 25, 2009   17 / 33
Closer look at the pole and the ascension origin

Tisserand Mean Axis

Tisserand Mean axis was ﬁrst deﬁned by Siedelman in 1982 as the mean
surface geographic axis.

Anirbit (TIFR)                         Coordinates on the Cosmos   October 25, 2009   17 / 33
Closer look at the pole and the ascension origin

Tisserand Mean Axis

Tisserand Mean axis was ﬁrst deﬁned by Siedelman in 1982 as the mean
surface geographic axis.

How the Tisserand Mean axis moves over the years has been mapped out
pretty accuurately.

Anirbit (TIFR)                         Coordinates on the Cosmos   October 25, 2009   17 / 33
Closer look at the pole and the ascension origin

Deﬁnition of the origin of right ascension

Anirbit (TIFR)                         Coordinates on the Cosmos   October 25, 2009   18 / 33
Closer look at the pole and the ascension origin

Deﬁnition of the origin of right ascension
By abuse of notation we shall call the origin of right ascension as just
“origin” :P

Anirbit (TIFR)                         Coordinates on the Cosmos   October 25, 2009   18 / 33
Closer look at the pole and the ascension origin

Deﬁnition of the origin of right ascension
By abuse of notation we shall call the origin of right ascension as just
“origin” :P

The current deﬁnition of the origin is called the Celestial Ephemeris
Origin (CEO)

Anirbit (TIFR)                         Coordinates on the Cosmos   October 25, 2009   18 / 33
Closer look at the pole and the ascension origin

Deﬁnition of the origin of right ascension
By abuse of notation we shall call the origin of right ascension as just
“origin” :P

The current deﬁnition of the origin is called the Celestial Ephemeris
Origin (CEO) which is a designated point on the equator of the CIP.

Anirbit (TIFR)                         Coordinates on the Cosmos   October 25, 2009   18 / 33
Closer look at the pole and the ascension origin

Deﬁnition of the origin of right ascension
By abuse of notation we shall call the origin of right ascension as just
“origin” :P

The current deﬁnition of the origin is called the Celestial Ephemeris
Origin (CEO) which is a designated point on the equator of the CIP.

The CEO was located on the true CIP equator of J2000.0 at a point
2.012mas from the ICRS prime meridian

Anirbit (TIFR)                         Coordinates on the Cosmos   October 25, 2009   18 / 33
Closer look at the pole and the ascension origin

Deﬁnition of the origin of right ascension
By abuse of notation we shall call the origin of right ascension as just
“origin” :P

The current deﬁnition of the origin is called the Celestial Ephemeris
Origin (CEO) which is a designated point on the equator of the CIP.

The CEO was located on the true CIP equator of J2000.0 at a point
2.012mas from the ICRS prime meridian (consistent the conventional
deﬁnition of the Earth Rotation Angle), at right ascension
00h00m00s.00013416 in the ICRS.

Anirbit (TIFR)                         Coordinates on the Cosmos   October 25, 2009   18 / 33
Closer look at the pole and the ascension origin

Deﬁnition of the origin of right ascension
By abuse of notation we shall call the origin of right ascension as just
“origin” :P

The current deﬁnition of the origin is called the Celestial Ephemeris
Origin (CEO) which is a designated point on the equator of the CIP.

The CEO was located on the true CIP equator of J2000.0 at a point
2.012mas from the ICRS prime meridian (consistent the conventional
deﬁnition of the Earth Rotation Angle), at right ascension
00h00m00s.00013416 in the ICRS.
As the true equator moves in space, the path of the CEO in space is
such that the point has no instantaneous east-west velocity along the
true equator.

Anirbit (TIFR)                         Coordinates on the Cosmos   October 25, 2009   18 / 33
Closer look at the pole and the ascension origin

Deﬁnition of the origin of right ascension
By abuse of notation we shall call the origin of right ascension as just
“origin” :P

The current deﬁnition of the origin is called the Celestial Ephemeris
Origin (CEO) which is a designated point on the equator of the CIP.

The CEO was located on the true CIP equator of J2000.0 at a point
2.012mas from the ICRS prime meridian (consistent the conventional
deﬁnition of the Earth Rotation Angle), at right ascension
00h00m00s.00013416 in the ICRS.
As the true equator moves in space, the path of the CEO in space is
such that the point has no instantaneous east-west velocity along the
true equator. After 1 century, the CEO is still within 70mas of the
ICRS prime meridian, whereas the equinox has moved nearly 1.4
degrees.

Anirbit (TIFR)                         Coordinates on the Cosmos   October 25, 2009   18 / 33
Closer look at the pole and the ascension origin

Deﬁnition of the origin of right ascension
By abuse of notation we shall call the origin of right ascension as just
“origin” :P

The current deﬁnition of the origin is called the Celestial Ephemeris
Origin (CEO) which is a designated point on the equator of the CIP.

The CEO was located on the true CIP equator of J2000.0 at a point
2.012mas from the ICRS prime meridian (consistent the conventional
deﬁnition of the Earth Rotation Angle), at right ascension
00h00m00s.00013416 in the ICRS.
As the true equator moves in space, the path of the CEO in space is
such that the point has no instantaneous east-west velocity along the
true equator. After 1 century, the CEO is still within 70mas of the
ICRS prime meridian, whereas the equinox has moved nearly 1.4
degrees.

Anirbit (TIFR)                         Coordinates on the Cosmos   October 25, 2009   18 / 33
Closer look at the pole and the ascension origin

Terrestial Ephemeris Origin and Earth Rotation Angle

Anirbit (TIFR)                         Coordinates on the Cosmos   October 25, 2009   19 / 33
Closer look at the pole and the ascension origin

Terrestial Ephemeris Origin and Earth Rotation Angle

The Terrestial Ephemeris Origin (TEO) is deﬁned symmetrically with
the CEO on the true terrestrial equator perpendicular to the CIP on the
Earth.

Anirbit (TIFR)                         Coordinates on the Cosmos   October 25, 2009   19 / 33
Closer look at the pole and the ascension origin

Terrestial Ephemeris Origin and Earth Rotation Angle

The Terrestial Ephemeris Origin (TEO) is deﬁned symmetrically with
the CEO on the true terrestrial equator perpendicular to the CIP on the
Earth. TEO is the origin for the ITRS.

Anirbit (TIFR)                         Coordinates on the Cosmos   October 25, 2009   19 / 33
Closer look at the pole and the ascension origin

Terrestial Ephemeris Origin and Earth Rotation Angle

The Terrestial Ephemeris Origin (TEO) is deﬁned symmetrically with
the CEO on the true terrestrial equator perpendicular to the CIP on the
Earth. TEO is the origin for the ITRS.

Earth Rotation Angle (ERA) is the angle between the direction of CEO
and the TEO.

Anirbit (TIFR)                         Coordinates on the Cosmos   October 25, 2009   19 / 33
Closer look at the pole and the ascension origin

Terrestial Ephemeris Origin and Earth Rotation Angle

The Terrestial Ephemeris Origin (TEO) is deﬁned symmetrically with
the CEO on the true terrestrial equator perpendicular to the CIP on the
Earth. TEO is the origin for the ITRS.

Earth Rotation Angle (ERA) is the angle between the direction of CEO
and the TEO.

The notion of Universal Time (UT1){to be deﬁned later} is set to
be a linear function of the ERA.

Anirbit (TIFR)                         Coordinates on the Cosmos   October 25, 2009   19 / 33
Closer look at the pole and the ascension origin

Terrestial Ephemeris Origin and Earth Rotation Angle

The Terrestial Ephemeris Origin (TEO) is deﬁned symmetrically with
the CEO on the true terrestrial equator perpendicular to the CIP on the
Earth. TEO is the origin for the ITRS.

Earth Rotation Angle (ERA) is the angle between the direction of CEO
and the TEO.

The notion of Universal Time (UT1){to be deﬁned later} is set to
be a linear function of the ERA.
The time derivative of UT1 is deﬁned as the Earths angular velocity.

Anirbit (TIFR)                         Coordinates on the Cosmos   October 25, 2009   19 / 33
Reference frames from the text-book

Miles to go before you sleep...

1   Some basics

2   Natural markers in the sky

3   Closer look at the pole and the ascension origin

4   Reference frames from the text-book

5   Setting up the time coordinate

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   20 / 33
Reference frames from the text-book

Frames from the book

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   21 / 33
Reference frames from the text-book

Frames from the book

Now we can breeze through some of the textbook examples of reference
frames which at some point or the other was in use.

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   21 / 33
Reference frames from the text-book

Frames from the book

Now we can breeze through some of the textbook examples of reference
frames which at some point or the other was in use.Some of these that we
shall look at are:

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   21 / 33
Reference frames from the text-book

Frames from the book

Now we can breeze through some of the textbook examples of reference
frames which at some point or the other was in use.Some of these that we
shall look at are:
The Horizontal Frame

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   21 / 33
Reference frames from the text-book

Frames from the book

Now we can breeze through some of the textbook examples of reference
frames which at some point or the other was in use.Some of these that we
shall look at are:
The Horizontal Frame
The Hour Frame

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   21 / 33
Reference frames from the text-book

Frames from the book

Now we can breeze through some of the textbook examples of reference
frames which at some point or the other was in use.Some of these that we
shall look at are:
The Horizontal Frame
The Hour Frame
The Equatorial Frame

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   21 / 33
Reference frames from the text-book

Frames from the book

Now we can breeze through some of the textbook examples of reference
frames which at some point or the other was in use.Some of these that we
shall look at are:
The Horizontal Frame
The Hour Frame
The Equatorial Frame
The Ecliptic Frame

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   21 / 33
Reference frames from the text-book

Frames from the book

Now we can breeze through some of the textbook examples of reference
frames which at some point or the other was in use.Some of these that we
shall look at are:
The Horizontal Frame
The Hour Frame
The Equatorial Frame
The Ecliptic Frame
The Galactic Frame

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   21 / 33
Reference frames from the text-book

Frames from the book

Now we can breeze through some of the textbook examples of reference
frames which at some point or the other was in use.Some of these that we
shall look at are:
The Horizontal Frame
The Hour Frame
The Equatorial Frame
The Ecliptic Frame
The Galactic Frame

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   21 / 33
Reference frames from the text-book

Frames from the book

Now we can breeze through some of the textbook examples of reference
frames which at some point or the other was in use.Some of these that we
shall look at are:
The Horizontal Frame
The Hour Frame
The Equatorial Frame
The Ecliptic Frame
The Galactic Frame
Let us have a brief look at each of them.

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   21 / 33
Reference frames from the text-book

The Horizontal Frame

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   22 / 33
Reference frames from the text-book

The Horizontal Frame

The features of this system are the following:

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   22 / 33
Reference frames from the text-book

The Horizontal Frame

The features of this system are the following:
The origin is the position of the observer.

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   22 / 33
Reference frames from the text-book

The Horizontal Frame

The features of this system are the following:
The origin is the position of the observer.
The direction of the local vertical is called the zenith (z-axis)

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   22 / 33
Reference frames from the text-book

The Horizontal Frame

The features of this system are the following:
The origin is the position of the observer.
The direction of the local vertical is called the zenith (z-axis)
The x-axis is taken towards the southern direction.

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   22 / 33
Reference frames from the text-book

The Horizontal Frame

The features of this system are the following:
The origin is the position of the observer.
The direction of the local vertical is called the zenith (z-axis)
The x-axis is taken towards the southern direction.
The plane normal to the local vertical is called the horizon

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   22 / 33
Reference frames from the text-book

The Horizontal Frame

The features of this system are the following:
The origin is the position of the observer.
The direction of the local vertical is called the zenith (z-axis)
The x-axis is taken towards the southern direction.
The plane normal to the local vertical is called the horizon
The plane containing the local vertical and the celestial pole is called
the meridian plane

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   22 / 33
Reference frames from the text-book

The Horizontal Frame

The features of this system are the following:
The origin is the position of the observer.
The direction of the local vertical is called the zenith (z-axis)
The x-axis is taken towards the southern direction.
The plane normal to the local vertical is called the horizon
The plane containing the local vertical and the celestial pole is called
the meridian plane
The intersection of the meridian plane with the celestial sphere is
called the Local Astronomical Meridian

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   22 / 33
Reference frames from the text-book

The Hour Frame

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   23 / 33
Reference frames from the text-book

The Hour Frame

As a result of the diurnal motion the coordinates of the stars become
variable in the Horizontal Frame and hence this is probably the worst of
the lot.

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   23 / 33
Reference frames from the text-book

The Hour Frame

As a result of the diurnal motion the coordinates of the stars become
variable in the Horizontal Frame and hence this is probably the worst of
the lot. The next obvious improvement was to make the markers
independent of the earth’s rotation by the following scheme:

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   23 / 33
Reference frames from the text-book

The Hour Frame

As a result of the diurnal motion the coordinates of the stars become
variable in the Horizontal Frame and hence this is probably the worst of
the lot. The next obvious improvement was to make the markers
independent of the earth’s rotation by the following scheme:

The earth’s rotation axis direction is called the Celestial Pole.

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   23 / 33
Reference frames from the text-book

The Hour Frame

As a result of the diurnal motion the coordinates of the stars become
variable in the Horizontal Frame and hence this is probably the worst of
the lot. The next obvious improvement was to make the markers
independent of the earth’s rotation by the following scheme:

The earth’s rotation axis direction is called the Celestial Pole.
The x − y plane is taken to be the celestial equator.

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   23 / 33
Reference frames from the text-book

The Hour Frame

As a result of the diurnal motion the coordinates of the stars become
variable in the Horizontal Frame and hence this is probably the worst of
the lot. The next obvious improvement was to make the markers
independent of the earth’s rotation by the following scheme:

The earth’s rotation axis direction is called the Celestial Pole.
The x − y plane is taken to be the celestial equator.
The z-axis is taken as the direction of the celestial pole.

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   23 / 33
Reference frames from the text-book

The Hour Frame

As a result of the diurnal motion the coordinates of the stars become
variable in the Horizontal Frame and hence this is probably the worst of
the lot. The next obvious improvement was to make the markers
independent of the earth’s rotation by the following scheme:

The earth’s rotation axis direction is called the Celestial Pole.
The x − y plane is taken to be the celestial equator.
The z-axis is taken as the direction of the celestial pole.
The origin of longitudes is taken to be the intersection of the celestial
equator with local astronomical meridian.

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   23 / 33
Reference frames from the text-book

The Hour Frame

As a result of the diurnal motion the coordinates of the stars become
variable in the Horizontal Frame and hence this is probably the worst of
the lot. The next obvious improvement was to make the markers
independent of the earth’s rotation by the following scheme:

The earth’s rotation axis direction is called the Celestial Pole.
The x − y plane is taken to be the celestial equator.
The z-axis is taken as the direction of the celestial pole.
The origin of longitudes is taken to be the intersection of the celestial
equator with local astronomical meridian.
The Hour Angle (H) is the −φ in spherical coordinates.

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   23 / 33
Reference frames from the text-book

The Hour Frame

As a result of the diurnal motion the coordinates of the stars become
variable in the Horizontal Frame and hence this is probably the worst of
the lot. The next obvious improvement was to make the markers
independent of the earth’s rotation by the following scheme:

The earth’s rotation axis direction is called the Celestial Pole.
The x − y plane is taken to be the celestial equator.
The z-axis is taken as the direction of the celestial pole.
The origin of longitudes is taken to be the intersection of the celestial
equator with local astronomical meridian.
The Hour Angle (H) is the −φ in spherical coordinates.
π
The Declination (δ) is                2   − θ in spherical coordinates.

Anirbit (TIFR)                      Coordinates on the Cosmos      October 25, 2009   23 / 33
Reference frames from the text-book

The Hour Frame

As a result of the diurnal motion the coordinates of the stars become
variable in the Horizontal Frame and hence this is probably the worst of
the lot. The next obvious improvement was to make the markers
independent of the earth’s rotation by the following scheme:

The earth’s rotation axis direction is called the Celestial Pole.
The x − y plane is taken to be the celestial equator.
The z-axis is taken as the direction of the celestial pole.
The origin of longitudes is taken to be the intersection of the celestial
equator with local astronomical meridian.
The Hour Angle (H) is the −φ in spherical coordinates.
π
The Declination (δ) is                2   − θ in spherical coordinates. .

Anirbit (TIFR)                      Coordinates on the Cosmos      October 25, 2009   23 / 33
Reference frames from the text-book

The Hour Frame

As a result of the diurnal motion the coordinates of the stars become
variable in the Horizontal Frame and hence this is probably the worst of
the lot. The next obvious improvement was to make the markers
independent of the earth’s rotation by the following scheme:

The earth’s rotation axis direction is called the Celestial Pole.
The x − y plane is taken to be the celestial equator.
The z-axis is taken as the direction of the celestial pole.
The origin of longitudes is taken to be the intersection of the celestial
equator with local astronomical meridian.
The Hour Angle (H) is the −φ in spherical coordinates.
π
The Declination (δ) is                2   − θ in spherical coordinates. .

Anirbit (TIFR)                      Coordinates on the Cosmos      October 25, 2009   23 / 33
Reference frames from the text-book

The Equatorial Frame

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   24 / 33
Reference frames from the text-book

The Equatorial Frame

The major problem with the Hour Frame is that it has reference to the
observer’s position through the use of the Local Astronomical Meridian.

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   24 / 33
Reference frames from the text-book

The Equatorial Frame

The major problem with the Hour Frame is that it has reference to the
observer’s position through the use of the Local Astronomical Meridian.
This limitation is overcome in The Equatorial Frame by using the equinox
to deﬁne the axis. The main features of this system are:

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   24 / 33
Reference frames from the text-book

The Equatorial Frame

The major problem with the Hour Frame is that it has reference to the
observer’s position through the use of the Local Astronomical Meridian.
This limitation is overcome in The Equatorial Frame by using the equinox
to deﬁne the axis. The main features of this system are:

The Celestial Pole is still deﬁned as the z-axis

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   24 / 33
Reference frames from the text-book

The Equatorial Frame

The major problem with the Hour Frame is that it has reference to the
observer’s position through the use of the Local Astronomical Meridian.
This limitation is overcome in The Equatorial Frame by using the equinox
to deﬁne the axis. The main features of this system are:

The Celestial Pole is still deﬁned as the z-axis
The longitudinal origin or the (x-axis) is deﬁned at the Vernal
Equinox γ end of the intersection of

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   24 / 33
Reference frames from the text-book

The Equatorial Frame

The major problem with the Hour Frame is that it has reference to the
observer’s position through the use of the Local Astronomical Meridian.
This limitation is overcome in The Equatorial Frame by using the equinox
to deﬁne the axis. The main features of this system are:

The Celestial Pole is still deﬁned as the z-axis
The longitudinal origin or the (x-axis) is deﬁned at the Vernal
Equinox γ end of the intersection of the mean orbital plane of the
earth and

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   24 / 33
Reference frames from the text-book

The Equatorial Frame

The major problem with the Hour Frame is that it has reference to the
observer’s position through the use of the Local Astronomical Meridian.
This limitation is overcome in The Equatorial Frame by using the equinox
to deﬁne the axis. The main features of this system are:

The Celestial Pole is still deﬁned as the z-axis
The longitudinal origin or the (x-axis) is deﬁned at the Vernal
Equinox γ end of the intersection of the mean orbital plane of the
earth and instantaneous celestial equator.

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   24 / 33
Reference frames from the text-book

The Equatorial Frame

The major problem with the Hour Frame is that it has reference to the
observer’s position through the use of the Local Astronomical Meridian.
This limitation is overcome in The Equatorial Frame by using the equinox
to deﬁne the axis. The main features of this system are:

The Celestial Pole is still deﬁned as the z-axis
The longitudinal origin or the (x-axis) is deﬁned at the Vernal
Equinox γ end of the intersection of the mean orbital plane of the
earth and instantaneous celestial equator.
The usual spherical coordinate φ is called the Right Ascension.

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   24 / 33
Reference frames from the text-book

The Equatorial Frame

The major problem with the Hour Frame is that it has reference to the
observer’s position through the use of the Local Astronomical Meridian.
This limitation is overcome in The Equatorial Frame by using the equinox
to deﬁne the axis. The main features of this system are:

The Celestial Pole is still deﬁned as the z-axis
The longitudinal origin or the (x-axis) is deﬁned at the Vernal
Equinox γ end of the intersection of the mean orbital plane of the
earth and instantaneous celestial equator.
The usual spherical coordinate φ is called the Right Ascension. It is
measured as usual anticlockwise when seen from the celestial pole

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   24 / 33
Reference frames from the text-book

The Equatorial Frame

The major problem with the Hour Frame is that it has reference to the
observer’s position through the use of the Local Astronomical Meridian.
This limitation is overcome in The Equatorial Frame by using the equinox
to deﬁne the axis. The main features of this system are:

The Celestial Pole is still deﬁned as the z-axis
The longitudinal origin or the (x-axis) is deﬁned at the Vernal
Equinox γ end of the intersection of the mean orbital plane of the
earth and instantaneous celestial equator.
The usual spherical coordinate φ is called the Right Ascension. It is
measured as usual anticlockwise when seen from the celestial pole
The usual spherical coordinate θ is called the Latitude

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   24 / 33
Reference frames from the text-book

The Equatorial Frame

The major problem with the Hour Frame is that it has reference to the
observer’s position through the use of the Local Astronomical Meridian.
This limitation is overcome in The Equatorial Frame by using the equinox
to deﬁne the axis. The main features of this system are:

The Celestial Pole is still deﬁned as the z-axis
The longitudinal origin or the (x-axis) is deﬁned at the Vernal
Equinox γ end of the intersection of the mean orbital plane of the
earth and instantaneous celestial equator.
The usual spherical coordinate φ is called the Right Ascension. It is
measured as usual anticlockwise when seen from the celestial pole
The usual spherical coordinate θ is called the Latitude

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   24 / 33
Reference frames from the text-book

The Ecliptic Frame

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   25 / 33
Reference frames from the text-book

The Ecliptic Frame

The essential problem with The Equatorial Frame is that due to precession
and nutation the celestial pole keeps changing and and this chance is of
the order of 50 annually.

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   25 / 33
Reference frames from the text-book

The Ecliptic Frame

The essential problem with The Equatorial Frame is that due to precession
and nutation the celestial pole keeps changing and and this chance is of
the order of 50 annually. Also we need more precise speciﬁcation of the
averaging technique to specify the “mean” orbital planes etc. These are
taken care of by the following features of the Ecliptic Frame,

This system has the same deﬁnitions of the x,y and z axis as The
Equatorial Frame.

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   25 / 33
Reference frames from the text-book

The Ecliptic Frame

The essential problem with The Equatorial Frame is that due to precession
and nutation the celestial pole keeps changing and and this chance is of
the order of 50 annually. Also we need more precise speciﬁcation of the
averaging technique to specify the “mean” orbital planes etc. These are
taken care of by the following features of the Ecliptic Frame,

This system has the same deﬁnitions of the x,y and z axis as The
Equatorial Frame. But this time we take extra eﬀorts to specify the
variations of the ecliptic and the equatorial plane.
The ecliptic plane oscillates with an amplitude of 1 about a mean
plane on a time scale of several years.

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   25 / 33
Reference frames from the text-book

The Ecliptic Frame

The essential problem with The Equatorial Frame is that due to precession
and nutation the celestial pole keeps changing and and this chance is of
the order of 50 annually. Also we need more precise speciﬁcation of the
averaging technique to specify the “mean” orbital planes etc. These are
taken care of by the following features of the Ecliptic Frame,

This system has the same deﬁnitions of the x,y and z axis as The
Equatorial Frame. But this time we take extra eﬀorts to specify the
variations of the ecliptic and the equatorial plane.
The ecliptic plane oscillates with an amplitude of 1 about a mean
plane on a time scale of several years. A further slow evolution of
amplitude by ±1.3◦ on a time scale of 100000 years is superposed.

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   25 / 33
Reference frames from the text-book

The Ecliptic Frame

The essential problem with The Equatorial Frame is that due to precession
and nutation the celestial pole keeps changing and and this chance is of
the order of 50 annually. Also we need more precise speciﬁcation of the
averaging technique to specify the “mean” orbital planes etc. These are
taken care of by the following features of the Ecliptic Frame,

This system has the same deﬁnitions of the x,y and z axis as The
Equatorial Frame. But this time we take extra eﬀorts to specify the
variations of the ecliptic and the equatorial plane.
The ecliptic plane oscillates with an amplitude of 1 about a mean
plane on a time scale of several years. A further slow evolution of
amplitude by ±1.3◦ on a time scale of 100000 years is superposed. It
further rotates by 47 per century relative to an inertial frame.

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   25 / 33
Reference frames from the text-book

The Ecliptic Frame

The essential problem with The Equatorial Frame is that due to precession
and nutation the celestial pole keeps changing and and this chance is of
the order of 50 annually. Also we need more precise speciﬁcation of the
averaging technique to specify the “mean” orbital planes etc. These are
taken care of by the following features of the Ecliptic Frame,

This system has the same deﬁnitions of the x,y and z axis as The
Equatorial Frame. But this time we take extra eﬀorts to specify the
variations of the ecliptic and the equatorial plane.
The ecliptic plane oscillates with an amplitude of 1 about a mean
plane on a time scale of several years. A further slow evolution of
amplitude by ±1.3◦ on a time scale of 100000 years is superposed. It
further rotates by 47 per century relative to an inertial frame.
The reference ecliptic is taken at J2000.0 and T is time measured in
Julian Centuries (36525 days) from J2000.0.
Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   25 / 33
Reference frames from the text-book

The Ecliptic Frame

The essential problem with The Equatorial Frame is that due to precession
and nutation the celestial pole keeps changing and and this chance is of
the order of 50 annually. Also we need more precise speciﬁcation of the
averaging technique to specify the “mean” orbital planes etc. These are
taken care of by the following features of the Ecliptic Frame,

This system has the same deﬁnitions of the x,y and z axis as The
Equatorial Frame. But this time we take extra eﬀorts to specify the
variations of the ecliptic and the equatorial plane.
The ecliptic plane oscillates with an amplitude of 1 about a mean
plane on a time scale of several years. A further slow evolution of
amplitude by ±1.3◦ on a time scale of 100000 years is superposed. It
further rotates by 47 per century relative to an inertial frame.
The reference ecliptic is taken at J2000.0 and T is time measured in
Julian Centuries (36525 days) from J2000.0.
Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   25 / 33
Reference frames from the text-book

Specifying variations of the plane

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   26 / 33
Reference frames from the text-book

Specifying variations of the plane

Then the minimal model for the plane variations specify 2 parameters:

π = angle between mean ecliptic at T and reference ecliptic at J2000.0

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   26 / 33
Reference frames from the text-book

Specifying variations of the plane

Then the minimal model for the plane variations specify 2 parameters:

π = angle between mean ecliptic at T and reference ecliptic at J2000.0
= inclination of the ecliptic at T w.r.t the celestial equator at J2000.0

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   26 / 33
Reference frames from the text-book

Specifying variations of the plane

Then the minimal model for the plane variations specify 2 parameters:

π = angle between mean ecliptic at T and reference ecliptic at J2000.0
= inclination of the ecliptic at T w.r.t the celestial equator at J2000.0
The minimal model variations are:
π = 47.0029 T − 0.033 T 2

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   26 / 33
Reference frames from the text-book

Specifying variations of the plane

Then the minimal model for the plane variations specify 2 parameters:

π = angle between mean ecliptic at T and reference ecliptic at J2000.0
= inclination of the ecliptic at T w.r.t the celestial equator at J2000.0
The minimal model variations are:
π = 47.0029 T − 0.033 T 2
= 23.439291 − 46.815 T

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   26 / 33
Reference frames from the text-book

Specifying variations of the plane

Then the minimal model for the plane variations specify 2 parameters:

π = angle between mean ecliptic at T and reference ecliptic at J2000.0
= inclination of the ecliptic at T w.r.t the celestial equator at J2000.0
The minimal model variations are:
π = 47.0029 T − 0.033 T 2
= 23.439291 − 46.815 T
Among the many other variations that are superimposed on this, the
other prominent one is the nutation of the earth’s axis with a period
of 18.6 years with an amplitude of 9.20 .

Anirbit (TIFR)                      Coordinates on the Cosmos   October 25, 2009   26 / 33
Setting up the time coordinate

Miles to go before you sleep...

1   Some basics

2   Natural markers in the sky

3   Closer look at the pole and the ascension origin

4   Reference frames from the text-book

5   Setting up the time coordinate

Anirbit (TIFR)                     Coordinates on the Cosmos   October 25, 2009   27 / 33
Setting up the time coordinate

The TAI time scales

Anirbit (TIFR)                     Coordinates on the Cosmos   October 25, 2009   28 / 33
Setting up the time coordinate

The TAI time scales

The second is deﬁned as 9192631770 periods of radiation
corresponding to the transition from the J + S = 4 to J + S = 3
(J = 2 and S = 1 for the outer electron of Cs) of Cs 133 on the
7
2
geoid of the earth.

Anirbit (TIFR)                     Coordinates on the Cosmos   October 25, 2009   28 / 33
Setting up the time coordinate

The TAI time scales

The second is deﬁned as 9192631770 periods of radiation
corresponding to the transition from the J + S = 4 to J + S = 3
(J = 2 and S = 1 for the outer electron of Cs) of Cs 133 on the
7
2
geoid of the earth.
The current standard of time is called the International Atomic
Time (TAI) which coordinates between about 150 such atomic clocks
at speciﬁc laboratories and hence also improves the statistical errors.

Anirbit (TIFR)                     Coordinates on the Cosmos   October 25, 2009   28 / 33
Setting up the time coordinate

The TAI time scales

The second is deﬁned as 9192631770 periods of radiation
corresponding to the transition from the J + S = 4 to J + S = 3
(J = 2 and S = 1 for the outer electron of Cs) of Cs 133 on the
7
2
geoid of the earth.
The current standard of time is called the International Atomic
Time (TAI) which coordinates between about 150 such atomic clocks
at speciﬁc laboratories and hence also improves the statistical errors.
The stability of the TAI is 1 − 5 × 10−14 sec over periods of 1-month
to several years.

Anirbit (TIFR)                     Coordinates on the Cosmos   October 25, 2009   28 / 33
Setting up the time coordinate

The TAI time scales

The second is deﬁned as 9192631770 periods of radiation
corresponding to the transition from the J + S = 4 to J + S = 3
(J = 2 and S = 1 for the outer electron of Cs) of Cs 133 on the
7
2
geoid of the earth.
The current standard of time is called the International Atomic
Time (TAI) which coordinates between about 150 such atomic clocks
at speciﬁc laboratories and hence also improves the statistical errors.
The stability of the TAI is 1 − 5 × 10−14 sec over periods of 1-month
to several years.
The TAI second is coherent with the SI second at the level of
2 × 10−14 sec.

Anirbit (TIFR)                     Coordinates on the Cosmos   October 25, 2009   28 / 33
Setting up the time coordinate

The TAI time scales

The second is deﬁned as 9192631770 periods of radiation
corresponding to the transition from the J + S = 4 to J + S = 3
(J = 2 and S = 1 for the outer electron of Cs) of Cs 133 on the
7
2
geoid of the earth.
The current standard of time is called the International Atomic
Time (TAI) which coordinates between about 150 such atomic clocks
at speciﬁc laboratories and hence also improves the statistical errors.
The stability of the TAI is 1 − 5 × 10−14 sec over periods of 1-month
to several years.
The TAI second is coherent with the SI second at the level of
2 × 10−14 sec.

Anirbit (TIFR)                     Coordinates on the Cosmos   October 25, 2009   28 / 33
Setting up the time coordinate

The UTC time scale

Anirbit (TIFR)                     Coordinates on the Cosmos   October 25, 2009   29 / 33
Setting up the time coordinate

The UTC time scale

It was not possible to shift all astronomical data into TAI time-scale and
hence people instituted the Coordinated Universal Time (UTC) which
sort of interpolates between the irregular deﬁnition of second as derived
from earth’s rotation and the TAI second.

Anirbit (TIFR)                     Coordinates on the Cosmos   October 25, 2009   29 / 33
Setting up the time coordinate

The UTC time scale

It was not possible to shift all astronomical data into TAI time-scale and
hence people instituted the Coordinated Universal Time (UTC) which
sort of interpolates between the irregular deﬁnition of second as derived
from earth’s rotation and the TAI second.
This interpolation requires intermittent insertion of leap seconds at the
end of December or June by convention. These insertions ensure that
TAI − UTC = δAT is an integral number of seconds.

Anirbit (TIFR)                     Coordinates on the Cosmos   October 25, 2009   29 / 33
Setting up the time coordinate

The UTC time scale

It was not possible to shift all astronomical data into TAI time-scale and
hence people instituted the Coordinated Universal Time (UTC) which
sort of interpolates between the irregular deﬁnition of second as derived
from earth’s rotation and the TAI second.
This interpolation requires intermittent insertion of leap seconds at the
end of December or June by convention. These insertions ensure that
TAI − UTC = δAT is an integral number of seconds.
The UTC is also bounded by other pre-existing convention of time called
Universal Time (UT1) as |UT 1 − UTC | = |δUT | ≤ 0.9s which deﬁned
second using the mean solar time and deﬁned midnight as the 0h. UT1
obviously was plagued by the irregularities of the earth’s rotation.

Anirbit (TIFR)                     Coordinates on the Cosmos   October 25, 2009   29 / 33
Setting up the time coordinate

The UTC time scale

It was not possible to shift all astronomical data into TAI time-scale and
hence people instituted the Coordinated Universal Time (UTC) which
sort of interpolates between the irregular deﬁnition of second as derived
from earth’s rotation and the TAI second.
This interpolation requires intermittent insertion of leap seconds at the
end of December or June by convention. These insertions ensure that
TAI − UTC = δAT is an integral number of seconds.
The UTC is also bounded by other pre-existing convention of time called
Universal Time (UT1) as |UT 1 − UTC | = |δUT | ≤ 0.9s which deﬁned
second using the mean solar time and deﬁned midnight as the 0h. UT1
obviously was plagued by the irregularities of the earth’s rotation.

Anirbit (TIFR)                     Coordinates on the Cosmos   October 25, 2009   29 / 33
Setting up the time coordinate

Some other time-scales

Anirbit (TIFR)                     Coordinates on the Cosmos   October 25, 2009   30 / 33
Setting up the time coordinate

Some other time-scales

Just for the sake of completeness I am enlisting here some of the other
time-scales that are also used

Anirbit (TIFR)                     Coordinates on the Cosmos   October 25, 2009   30 / 33
Setting up the time coordinate

Some other time-scales

Just for the sake of completeness I am enlisting here some of the other
time-scales that are also used
Barycentric Dynamical Time (TDB) is used as the time-scale for
the ephemerides, referred to the barycentre of the solar system

Anirbit (TIFR)                     Coordinates on the Cosmos   October 25, 2009   30 / 33
Setting up the time coordinate

Some other time-scales

Just for the sake of completeness I am enlisting here some of the other
time-scales that are also used
Barycentric Dynamical Time (TDB) is used as the time-scale for
the ephemerides, referred to the barycentre of the solar system This is
also denoted as Teph in the ephemerides

Anirbit (TIFR)                     Coordinates on the Cosmos   October 25, 2009   30 / 33
Setting up the time coordinate

Some other time-scales

Just for the sake of completeness I am enlisting here some of the other
time-scales that are also used
Barycentric Dynamical Time (TDB) is used as the time-scale for
the ephemerides, referred to the barycentre of the solar system This is
also denoted as Teph in the ephemerides
Terrestial Time (TT) is used as a time-scale of ephemerides for
observations from the geoid and the general conversion is
TT = TAI + 32.184s

Anirbit (TIFR)                     Coordinates on the Cosmos   October 25, 2009   30 / 33
Setting up the time coordinate

Some other time-scales

Just for the sake of completeness I am enlisting here some of the other
time-scales that are also used
Barycentric Dynamical Time (TDB) is used as the time-scale for
the ephemerides, referred to the barycentre of the solar system This is
also denoted as Teph in the ephemerides
Terrestial Time (TT) is used as a time-scale of ephemerides for
observations from the geoid and the general conversion is
TT = TAI + 32.184s From 1984 − 2000 the TT was called Terrestial
Dynamical Time (TDT)

Anirbit (TIFR)                     Coordinates on the Cosmos   October 25, 2009   30 / 33
Setting up the time coordinate

Some other time-scales

Just for the sake of completeness I am enlisting here some of the other
time-scales that are also used
Barycentric Dynamical Time (TDB) is used as the time-scale for
the ephemerides, referred to the barycentre of the solar system This is
also denoted as Teph in the ephemerides
Terrestial Time (TT) is used as a time-scale of ephemerides for
observations from the geoid and the general conversion is
TT = TAI + 32.184s From 1984 − 2000 the TT was called Terrestial
Dynamical Time (TDT)

Anirbit (TIFR)                     Coordinates on the Cosmos   October 25, 2009   30 / 33
Setting up the time coordinate

Dates

Anirbit (TIFR)                     Coordinates on the Cosmos   October 25, 2009   31 / 33
Setting up the time coordinate

Dates

I shall not explain how a day and year is deﬁned :)

Anirbit (TIFR)                     Coordinates on the Cosmos   October 25, 2009   31 / 33
Setting up the time coordinate

Dates

I shall not explain how a day and year is deﬁned :)
A Julian Year is deﬁned to have 365.25 days.

Anirbit (TIFR)                     Coordinates on the Cosmos   October 25, 2009   31 / 33
Setting up the time coordinate

Dates

I shall not explain how a day and year is deﬁned :)
A Julian Year is deﬁned to have 365.25 days.
Every day has been given a number called the Julian Day Number
starting the count from 1st January 4713BC .

Anirbit (TIFR)                     Coordinates on the Cosmos   October 25, 2009   31 / 33
Setting up the time coordinate

Dates

I shall not explain how a day and year is deﬁned :)
A Julian Year is deﬁned to have 365.25 days.
Every day has been given a number called the Julian Day Number
starting the count from 1st January 4713BC .
Time is measured from the mean noon of 1st January , 4713BC and
hence in the The Astronomical Almanac one gets a Julian Date
(JD) for every day of the year.

Anirbit (TIFR)                     Coordinates on the Cosmos   October 25, 2009   31 / 33
Setting up the time coordinate

Dates

I shall not explain how a day and year is deﬁned :)
A Julian Year is deﬁned to have 365.25 days.
Every day has been given a number called the Julian Day Number
starting the count from 1st January 4713BC .
Time is measured from the mean noon of 1st January , 4713BC and
hence in the The Astronomical Almanac one gets a Julian Date
(JD) for every day of the year.
For example the Julian Date for 24th June, 2000 is 2451719.5 when
June 24th begins. As another example we have that 18th UT of
24th June, 2000 is JD2451720.25.

Anirbit (TIFR)                     Coordinates on the Cosmos   October 25, 2009   31 / 33
Setting up the time coordinate

Dates

I shall not explain how a day and year is deﬁned :)
A Julian Year is deﬁned to have 365.25 days.
Every day has been given a number called the Julian Day Number
starting the count from 1st January 4713BC .
Time is measured from the mean noon of 1st January , 4713BC and
hence in the The Astronomical Almanac one gets a Julian Date
(JD) for every day of the year.
For example the Julian Date for 24th June, 2000 is 2451719.5 when
June 24th begins. As another example we have that 18th UT of
24th June, 2000 is JD2451720.25.
A Julian Century contains 36525 days.

Anirbit (TIFR)                     Coordinates on the Cosmos   October 25, 2009   31 / 33
Setting up the time coordinate

Dates

I shall not explain how a day and year is deﬁned :)
A Julian Year is deﬁned to have 365.25 days.
Every day has been given a number called the Julian Day Number
starting the count from 1st January 4713BC .
Time is measured from the mean noon of 1st January , 4713BC and
hence in the The Astronomical Almanac one gets a Julian Date
(JD) for every day of the year.
For example the Julian Date for 24th June, 2000 is 2451719.5 when
June 24th begins. As another example we have that 18th UT of
24th June, 2000 is JD2451720.25.
A Julian Century contains 36525 days.

Anirbit (TIFR)                     Coordinates on the Cosmos   October 25, 2009   31 / 33
Setting up the time coordinate

More dates

Anirbit (TIFR)                     Coordinates on the Cosmos   October 25, 2009   32 / 33
Setting up the time coordinate

More dates

I list here two more conventions of counting dates that have speciﬁc uses,

Anirbit (TIFR)                     Coordinates on the Cosmos   October 25, 2009   32 / 33
Setting up the time coordinate

More dates

I list here two more conventions of counting dates that have speciﬁc uses,
Orbital data for earth satellites is often expressed using Modiﬁed
Julian Date Numbers (MJD) which is counted from the
17th November , 1858 and hence we have MJD = JD − 2400000.5days

Anirbit (TIFR)                     Coordinates on the Cosmos   October 25, 2009   32 / 33
Setting up the time coordinate

More dates

I list here two more conventions of counting dates that have speciﬁc uses,
Orbital data for earth satellites is often expressed using Modiﬁed
Julian Date Numbers (MJD) which is counted from the
17th November , 1858 and hence we have MJD = JD − 2400000.5days
If a star is lying close to the ecliptic then there can be a delay of
about 16 minutes between signals from there reaching the earth at the
ends of the orbit. These are taken into account by a dating system
centered at the sun called the Heliocentric Julian Date (HJD)

Anirbit (TIFR)                     Coordinates on the Cosmos   October 25, 2009   32 / 33
Setting up the time coordinate

Generalized Julian Dates and epochs

Anirbit (TIFR)                     Coordinates on the Cosmos   October 25, 2009   33 / 33
Setting up the time coordinate

Generalized Julian Dates and epochs
There are Julian Dates deﬁned for other time scales as well and in 2009
the deﬁnitions are,
JDUT 1 =2454831.5+dayoftheyear +fractionofdayfrom0h UT 1.

Anirbit (TIFR)                     Coordinates on the Cosmos   October 25, 2009   33 / 33
Setting up the time coordinate

Generalized Julian Dates and epochs
There are Julian Dates deﬁned for other time scales as well and in 2009
the deﬁnitions are,
JDUT 1 =2454831.5+dayoftheyear +fractionofdayfrom0h UT 1.
JDTT =2454831.5+dayoftheyear +fractionofdayfrom0h TT .

Anirbit (TIFR)                     Coordinates on the Cosmos   October 25, 2009   33 / 33
Setting up the time coordinate

Generalized Julian Dates and epochs
There are Julian Dates deﬁned for other time scales as well and in 2009
the deﬁnitions are,
JDUT 1 =2454831.5+dayoftheyear +fractionofdayfrom0h UT 1.
JDTT =2454831.5+dayoftheyear +fractionofdayfrom0h TT .

The Astronomical Almanac lists out Julian Dates for calendar date for
other various years.

Anirbit (TIFR)                     Coordinates on the Cosmos   October 25, 2009   33 / 33
Setting up the time coordinate

Generalized Julian Dates and epochs
There are Julian Dates deﬁned for other time scales as well and in 2009
the deﬁnitions are,
JDUT 1 =2454831.5+dayoftheyear +fractionofdayfrom0h UT 1.
JDTT =2454831.5+dayoftheyear +fractionofdayfrom0h TT .

The Astronomical Almanac lists out Julian Dates for calendar date for
other various years.
The Modiﬁed Julian Date in any time-scale is deﬁned as
MJD = 54831.0 + day of year + fraction of day from 0h
. (0h as deﬁned in the time-scale being used).
Years are measured in units of epochs and they are of two kinds,

Anirbit (TIFR)                     Coordinates on the Cosmos   October 25, 2009   33 / 33
Setting up the time coordinate

Generalized Julian Dates and epochs
There are Julian Dates deﬁned for other time scales as well and in 2009
the deﬁnitions are,
JDUT 1 =2454831.5+dayoftheyear +fractionofdayfrom0h UT 1.
JDTT =2454831.5+dayoftheyear +fractionofdayfrom0h TT .

The Astronomical Almanac lists out Julian Dates for calendar date for
other various years.
The Modiﬁed Julian Date in any time-scale is deﬁned as
MJD = 54831.0 + day of year + fraction of day from 0h
. (0h as deﬁned in the time-scale being used).
Years are measured in units of epochs and they are of two kinds,
Julian Epoch = J[2000.0 + (JDTT − 2451545.0)/365.25]

Anirbit (TIFR)                     Coordinates on the Cosmos   October 25, 2009   33 / 33
Setting up the time coordinate

Generalized Julian Dates and epochs
There are Julian Dates deﬁned for other time scales as well and in 2009
the deﬁnitions are,
JDUT 1 =2454831.5+dayoftheyear +fractionofdayfrom0h UT 1.
JDTT =2454831.5+dayoftheyear +fractionofdayfrom0h TT .

The Astronomical Almanac lists out Julian Dates for calendar date for
other various years.
The Modiﬁed Julian Date in any time-scale is deﬁned as
MJD = 54831.0 + day of year + fraction of day from 0h
. (0h as deﬁned in the time-scale being used).
Years are measured in units of epochs and they are of two kinds,
Julian Epoch = J[2000.0 + (JDTT − 2451545.0)/365.25]
Besselian Epoch
= B[1900.0 + (JDTT − 2415020.31352)/365.242198781]

Anirbit (TIFR)                     Coordinates on the Cosmos   October 25, 2009   33 / 33
Setting up the time coordinate

Generalized Julian Dates and epochs
There are Julian Dates deﬁned for other time scales as well and in 2009
the deﬁnitions are,
JDUT 1 =2454831.5+dayoftheyear +fractionofdayfrom0h UT 1.
JDTT =2454831.5+dayoftheyear +fractionofdayfrom0h TT .

The Astronomical Almanac lists out Julian Dates for calendar date for
other various years.
The Modiﬁed Julian Date in any time-scale is deﬁned as
MJD = 54831.0 + day of year + fraction of day from 0h
. (0h as deﬁned in the time-scale being used).
Years are measured in units of epochs and they are of two kinds,
Julian Epoch = J[2000.0 + (JDTT − 2451545.0)/365.25]
Besselian Epoch
= B[1900.0 + (JDTT − 2415020.31352)/365.242198781]
Many pulsars are dated in the Besselian system.
Anirbit (TIFR)                     Coordinates on the Cosmos   October 25, 2009   33 / 33

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