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FUNDAMENTAL ASTRONOMY. Magda Stavinschi Astronomical Institute of the Romanian Academy. No indication of the distance to the objects. The astrometric information is generally NOT the direction from which the light arrives , but a quantity more directly

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Magda Stavinschi

Astronomical Institute of the Romanian Academy

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No indication

of the distance

to the objects

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The astrometric information is generally NOT the direction

from which the light arrives, but a quantity more directly

related to the geometric position of the celestial body in space

in a certain reference coordinated system.

To achieve this one we must apply a certain number of corrections

to the apparent direction in which the celestial body seems to lie.

The ensemble of these corrections

constitutes the reduction of observations.

We intend to summarize all the possible effects, since the

parameters that characterize some of them are often

unknowns in the reduction of observations.

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Several geometrical phenomena affect the

transformation between

the instrument and thesky.

One is a purely geometrical transformation;

others are due to kinematic properties

of the ensemble Earth-celestial body.

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The final objective of an astrometric observation

is to determine the position in the sky, in some C.R.F.

But, in many cases, the field of view of the instrument is limited

and one has to refer the observation to neighboring objects

which are part of the C.R.F., or link to it.

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For this, it is convenient to use a

local system of celestial coordinates

centered at a certain point A (α0,δ0).

The equatorial coordinates

of a point in the vicinity of A are

α0 + Δα , δ0+ Δδ

The image of this region of the celestial sphere

on an ideal focal surface is planar

ð one has to transform the differential coordinates

Δα andΔδ into linear coordinates.

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It is done by a

conic projection

from the center

of the unit

celestial sphere on A.

Ax,Ay are tangents to the declination small circle

=> increasing right ascensions,

along the celestial meridian, the positive direction =>N

This local system of coordinates = standard coordinates

The transformation

differential coordinates => standard coordinates

gnomonicor central projection

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Annual Parallax

apparent displacement of a star

on the celestial sphere

due to the orbital motion of the Earth.

Correcting for parallax => the direction of the star

as seen from the barycenter B of the Solar System.

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In evaluating stellar parallaxes,

we assume that the observation

is performed from the

center of the Earth.

This is no longer

the case for

bodies in the Solar System.

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Let us observing a planet P; the vector OP observer-planet

has to be considered as the sum of 3 vectors in a barycentric R.S.:


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OE: obs - Earth center at time t of observation.

It rotates around the axis of the Earth;

produces a diurnal apparent motion of the direction of the planet =

diurnalor geocentric parallax

(observation performed from an artificial satellite)

EB: Earthcenter – SS barycenter

at the time t (given by ephemerides)

BP: SSbarycenter - planet.

at t' when the light which reached the observer at t

was emitted by P.

(It takes the parallax proper, but also the planetary aberration, effect produced by the finite speed of light.)

=> direction in which the planet is visible at t is given by

OP = OE(t) + EB(t) + BP(t')

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Proper motions(p.m.)

= projection on the sky of the motion of a star

w.r.t. the SS barycenter

= combination of the actual motions of the star

and of the Sun within the Galaxy

p.m. μ in terms of yearly variations of αandδ

α0,δ0of the star are given for a date t0

=> the coordinates at time t are:

α = α0 + (t- t0) μα

δ= δ0 + (t- t0)μδ

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  • They are produced by various properties of light:

  • finite velocity,

  • non-linear propagation in gravity fields,

  • its ondulatory nature.

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due to the relative motion

of the source P and the observer

The apparent direction from

which the light is coming at t =

the direction of the point where

the light source was at t - Δt

(Δt = the time during which the light

traveled from P to the observer)

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In Newtonian space, if r (|r| = r) is the true position vector,

=> the apparent position is given by r’, such that

r' = r + r V/c

(V = velocity of the observer w.r.t. the star; c = speed of light)

V can be split in 3 components:

V = V0 + VE - VS

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VS = star velocity w.r.t. the SS barycenter

(For stars: not known; it is neglected:

the corresponding displacement is taken into account by

the p.m. of the star.

For planets: known from ephemerides)

VE= velocity of Earth center of mass w.r.t. SS barycenter

It gives rise to the annual aberration ,

in which V is replaced by VE.

Planets: the total aberration, caused by VE – VS,

is the planetary aberration.

V0= velocity of the observer w.r.t. Earth center of mass.

On the ground it is obtained from the Earth rotation parameters

=> diurnal aberration.

On an artificial satellite, it is the orbital aberration derived from the

motion of the satellite.

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Essentially: both velocities and directions

be computed in a common reference frame.

All of these are not sufficient for accurate astrometry.

For the second order, one must make the computations

within the framework of general relativity.

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Relativistic Light Deflection

A massive body produces a

curvature of the space, and light

is deflected towards the mass

(following the geodesics of the space).

The effect is maximum in the immediate neighborhood of the Sun

(to 1.7").

Of the order of 4 mas in the perpendicular direction.

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In astronomy is a

reference system (R.S.),

which is a theoretical concept


reference frame (R.F.),

a practical realization of a R.S., which provides a means of assigning coordinates to an object.

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system of coordinates axes

built in such a way that one might qualitatively assign

numbers, which represent unequivocally

the position and the motion of material points

-        celestial reference system

for positions, motions and dynamics of celestial bodies;

-        terrestrial reference system

for positions on the Earth and its environment.

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In both cases, no physical axes or great circles

that would materialize the coordinate system.

One has to use the existing material points

(or celestial bodies) to which positions

should be referred.

Necessarily: by what procedure these ones can be used for determining the coordinates of an observed object?

The ensemble of fiducial points and algorithms

to be used in the procedure = reference frame

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Dynamical definition

The Newtonian definition, applicable

only locally in general relativity:

W.r.t. an ideal dynamical C.R.S., celestial bodies move such as

the equations of motion have no kinematic acceleration

(due to the rotation, as in Coriolis acceleration, or due to an

nonuniform linear motion).

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Kinematic definition

An ideal kynematic C.R.F. assumes that there exists

in the Universe a class of objects, which have

no global systematic motion and therefore are

not rotating in the mean.

One must admit that its physical meaning

is questionable:

non-rotating w.r.t. what?

Actually, this means that there are

no large regions

in the sky where p.m. of these objects present

a systematic behavior.

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One can proceed in both directions and

identify a physical structure

that has the property required.

At this step, one speaks of

reference systems proper.

Dynamical definition

General choice: SSas a whole,

center of coordinate axes in the SS barycenter.

Sometimes, other systems, e.g. for the motion

of the Earth-Moon system or

of artificial satellites: geocentric dynamical system.

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Kinematic definition

Quasars (& other distant extragalactic objects) are

so distant that, in practice, they have a transverse motion

of the order of the cosmological recession rate,

a very improbable situation.

The choice of a lot of

most stable such objects as fiducial points

is adequate at the level of a few 0.01"

The system obtained

= extragalactic celestial R.S.

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Choice is made => one has to associate

a quantitative model of the structure selected

It is based upon numerical values of a

number of parameters

(not known exactly, since they result from observations)

  • one has to assign them some values

  • the model is only an approximation to the ideal R.S.

  • it is called the conventional reference system.

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Dynamical definition

The conventional system adopted in the past was determined

by a choice of values of fundamental parameters:

-        masses of planets and satellites,

-        initial conditions of their motions,

some specific constants (precession and nutation,

constant of aberration; etc.).

They are part of the system ofastronomical constants

periodically revised by the IAU (1976)

This approach to C.R.F. frames is now obsolete and the

dynamical definition is abandoned in favor of a

kinematical definition.

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Kinematic definition

Not much modeling is necessary for an extragalactic R.S. =

official IAU conventional R.S., called

International Celestial Reference System (ICRS)

starting January 1, 1998

the principal plane of the new conventional C.R.S.

as near as possible to the main equator at J 2000.0 and

the origin in this principal plane

as near as possible to the dynamical equinox of J 2000.0.

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Together with the adoption of the ICRS

(axes independent of the vernal equinox)

a new definition of the intermediary R.S. was needed.

Starting 1st January 2003, the new system is defined by:

Pole = Celestial Intermediate Pole (CIP)

Its motion is specified in the Geocentric C.R.S.

by the motion of the Tisserand mean axis of the Earth

(the mean surface geographical axis) with periods > 2 days.

Origin = Celestial Ephemeris Origin (CEO)

defined on the equator of the CIP such that it is insensitive

to changes in models for precession and nutation at the arc level.

The corresponding point on the ITRS is the

Terrestrial Ephemeris Origin (TEO).

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The final step is to materialize the C.R.S. by assigning

coordinates to a certain number of fiducial points

(stars or extragalactic objects) in this system.


reference frame

or, better,

conventional reference frame

presented in the form of

a catalogue of positions and proper motions.

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For a dynamical definition, one has to establish

(using the conventional model)

a numerical theoryof the motion of planets,

and the position of reference stars are determined w.r.t.

the observed positions of planets.

=> R.F. is realized by a fundamental star catalogue.

The last such catalogue is the FK5

The kinematic extragalactic R.S. is realized by ICRF =

a catalogue of positions of

212 quasars and other extragalactic radiosources

built from a combination of observations by VLBI

ICRS origin = SScenter of mass (barycenter)

(the only point of the SS, whose motion in the Galaxy is

not perturbed by the presence of planets, satellites and the Sun).

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International Terrestrial Reference Frame


positions and motions (due to plate motions)

of a certain number of points on the surface of the Earth

To obtain the celestial equatorial coordinates

rather than the hour angle H at the International Meridian,

we note that α is related to H by

α = T + H

T = Greenwich sidereal time

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- complicated ensemble of physical phenomena

- resulting motion is a complex function of time

It could be divided in 2 groups:

- precession and nutation, which describe the

motion of the Earth's rotation axis in the C.R.S.

- Earth's rotation proper together with the polar motion

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The Earth's rotation axis is not fixed in space.

Like a rotating toy top, the direction of the rotation axis

executes a slow precession with a period of 26,000 years.

Pole Stars are Transient

Due to the precession of the rotation axis:

- Polaris will not always be the

Pole Star or North Star.

- in 13,000 years, Vega (Lyra)

= North Celestial Pole.

- in 26,000 more years, Polaris will

once again be the Pole Star.

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Euler (1758):

rotation axis moves w.r.t. an Earth-fixed R.F.

Chandler (1891):

determination from observations of the geographical

latitudes of astronomical observatories.

Chandler period (435 days) different from the

Euler period (304 days) because of the non-rigidity and the

inhomogeneous mass distribution of the Earth.

The radius of the Chandler wobble of the rotation pole

is about 6 m.

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1899 - ILS (International Latitude Service)

1962: IPMS (International Polar Motion Service)

1988: IERS (International Earth Rotation Service)

  • Polar motions caused by:

  • gravitational forces of Sun and Moon

  • geophysical processes within atmosphere, oceans and

  • interior of the Earth.

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Precession of the Equinoxes

  • Rotation axis is precessing in space

  • => orientation of the Celestial Equator precesses too,

  • with the same period

  • position of the equinoxes changing slowly

    w.r.t. background stars

    Precession of the equinoxes

    => αand δ change very slowly over a 26,000 year period.

    This effect is negligibly small for casual observing,

    but is an important correction for precise observations.

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  • Earth mean figure:

  • ellipsoidflattened at its poles

  • (equatorial radius is about

  • 21 km > polar radius).

  • There is thus an equatorial bulge

  • on which the luni-solar attraction

  • induces a torquewhich tends to rock

  • the equator towards the ecliptic.

  • Because of its rotation, exactly as a top,

  • the Earth is animated by a

  • precessional motion:

  • the rotation axis is doing a

    large motion around the

  • perpendicular to the ecliptic

  • in about 25,600 years.

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Relative positions ofMoon, Earth and Sunvary witht

=> periodic additional motions


theirperiodsdirectly related to the periods of the

orbital motions of the planets around the Sun and

of the Moon around the Earth.

Main nutation periods:

13.66 days, ½ year, 1 year, 9.3 years, 18.6 years.

Nutational motions in space, represented asangle variations

in longitude & in obliquity.

They areelliptical. They can also be represented as the

sum of two circular nutationswith thesame periodbut

different amplitudes & directions (one prograde, one retrograde).

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Babylonians & Greeks: Earth rests at the center of the universe!

= = = = = = = = = = = =

!!! Earth itself rotated on its axis !!!

Heraclides, Aristotle (4rd century B.C.)

= = = = = = = = = = = =

?! Ptolemy (2nd century A.D.) ?!

'proved' that the Earth could not move

= = = = = = = = = = = =

Copernicus (16th century)

convincing arguments for the motion

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Its variability relative to the body of the planet

or in inertial space is caused by the:

- gravitational torque exerted by the Moon, Sun and planets,

- displacements of matter in different parts of the planet and

- other excitation mechanisms.

The observed oscillations can be interpreted in terms of:

- mantle elasticity,

- Earth flattening,

- structure and properties of the core-mantle boundary,

- rheology of the core,

- underground water,

- oceanic variability,

- atmospheric variability on time scales of weather or climate

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Period of rotation of the Earth (LOD)

assumed constant

until the 20th century,

apart from a secular change

Kant (1754) predicted that friction

with the tidal forces on Earth

would cause a deceleration

of the Earth's rotation.

Ferrel and Delaunay (19th century) confirmed this effect.

Secular decrease of the rotation rate causes a LOD

increase of about 2 ms/century

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1936 (N. Stoyko): seasonal irregularities

Days in March about 1 ms longer than days in July.

Abrupt,irregular changes of

thousandths of a second

(interactions between motions in the

Earth's outer layers and core?)

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The measurements of the Earth's rotation are

under the form of time series of the so-called

Earth Orientation Parameters (EOP)


UT1 = time of the Earth clock (one revolution in about 24h).

Practically proportional to the sidereal time.

Excess revolution time = length of day (LOD)

Greenwich Mean Sideral Time (GMST) = angle computed

from the UT1 referred to the instantaneous position of the

axis of rotation of the Earth (instantaneous pole).

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x , y: Celestial Ephemeris Pole (CEP),

relative to IRP (IERS Reference Pole).

CEP differs from the instantaneous rotation axis by quasi-diurnal

terms with amplitudes under 0.01".

x-axis: in the direction of IRM (IERS Reference Meridian)

y-axis: in the direction 90° West longitude.

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Timing techniques

A class of astrometric techniques

is not based upon analyses of

electromagnetic waves received from space,

but on measurement of

time intervals between events

one of which, at least, originates

from space or is connected with it.

Accuracies of the order of 10-14 or 10-15 .

10-16 is expected in the near future.

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International Atomic Time (TAI):

time reference established by the BIH (now BIPM)

on the basis of atomic clocks operating in various

establishments in accordance with the definition

of the second, the unit of time of SI

TAI is a coordinate time scale defined in a

geocentric R.F. whose scale unit is the SI second,

realized on the rotating geoid

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based on UTC, differing from TAI

by an integer number of seconds.


decided by IERS:

|UTC – UT1| < 0.9 s

Now: UTC - TAI = - 32 s

LAST: 1 January 1999


2005 Dec 31 23h 59m 59s

2005 Dec 31 23h 59m 60s

2006 Jan 1 0h 0m 0s

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For astronomy: terrestrial time TT,

ideal form of TAI,

it extends without discontinuity the old

Ephemeris Time (TE) in a geocentric R.F.

TT = TAI + 32.184 s

The theoretical basis for TE is wholly non-relativistic.

1984: ET replaced by the two relativistic timescales

Barycentric Dynamical Time (TDB)

Terrestrial Dynamical Time (TDT).

In practice,

the length of the TE second =

= the length of the TDB or TDT second.

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Absence of atmospheric refraction and turbulence

( image is a fixed diffraction pattern, which is much more

accurate than on the Earth).

Quasi-absence of mechanical torques

modifying the position of the image of the center

of the field when the instrument changes orientation.

Possibility to observe the entire sky with a single instrument.

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The principle of HIPPARCOS was invented by Lacroute in 1966 .

More than 10 years elapsed before space technology allowed

serious consideration of its development.

Later E. Hog added the concept of scientific use of the star-mapper

with 2 color channels and the Tycho experiment.

HIgh Precision PARallax COllecting Satellite

Hipparchusof Rodhes

190-120 BC

-calculated the length of the year to

within 6.5 min;

-discovered the

precession of the equinoxes

-first known star catalogue (1080 stars)

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Launched: August 8, 1989

Very elongated orbit instead of the expected geostationary one.

Perigee 500 km high and an apogee close to 36500 km.

Period = 10h 40min.

Last observation: March 1993.

General principle of HIPPARCOS

  • - global astrometry instrument

  • conceived to measure, or in due cause to determine,

  • large angles on the sky

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HIPPARCOS Final Catalogue

Two catalogues were produced independently.

The most detailed and updated reduction is presented in Vol. 1 & 3

of the published catalogue (ESA, 1997).

The resulting astrometric parameters obtained by each consortium

were not identical.

For obtaining a unique consistent catalogue,

a merging of the two was performed.

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Contents of the Hipparcos Catalogue

Published by ESA (1997):

16 printed volumes and a set of ASCII CD-Rom discs

117,955entries for astrometry &

118,204for the photometric results

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Astrometric results

Positions and p.m. given in ICRS for

mean epoch of observations 1991.25.

Median standard uncertainty for:

star positions with Hp< 9at epoch is

0.77 mas (in α cos δ)and0.64 mas (in δ)

yearly p.m.:0.88 mas/yr (in α cos δ)and0.74mas/yr (in δ)

parallaxes: 0.97 mas

Photometric results

median photometric uncertainty for Hp < 9 is 0.0015 mag.

11,600 recognized or suspected variables.

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1,058,332 entries, < VT ~10.5 mag

(limiting magnitude VT ~11.5 mag)

Median astrometric standard uncertainty

(VT < 9 mag) 7 mas

for position at 1991.25

Photometric median standard uncertainty:

0.012 mag for VT

For the entire catalogue:

25 mas for position

0.06 mag for VT photometry

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Tycho-2 Catalogue

positions and magnitudes of 2,538,913 stars,

based on satellite data,

only for an observation epoch close to 1992.5

Median uncertainty - the same as for the Tycho

for bright stars (VT< 9): 7 mas,

for all stars: 60 mas.

Mean standard uncertainty in p.m. is 2.5 mas/yr

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Ground-based astrometry precision will always

remain limited by the atmosphere.

0.01 mas (or better) required by the many astrophysical

problems cannot generally be met from the Earth

=>only space astrometry can satisfy it.

The main principles of Hipparcos, namely the

double field of view, slow rotation of the satellite,

and a specific sky scanning law proved to be

inescapable basics that are present in all projects.

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Global Astrometry Instrument for Astrophysics

Based upon HIPPARCOS main principles

with two fields of view separated by 106°.

It is intended to be placed on a

Lissajous-type eclipse-free orbit

around the Lagrange point L2

of the Earth-Sun system.

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LAUNCH: Dec-2011   END:2020


The largest and most precise three-dimensional chart

of our Galaxy by providing unprecedented

positional and radial velocity measurements

for about one billion stars

in our Galaxy and throughout the Local Group.

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This will amount to about 1% of the Galactic stellar population.

Combined with astrophysical information for each star, provided

by on-board multi-color photometry, will have the precision

necessary to quantify the early formation, and subsequent

dynamical, chemical and star formation evolution

of the Milky Way Galaxy.

  • Additional scientific products:

  • detection and orbital classification of tens of thousands of

  • extra-solar planetary systems;

  • a comprehensive survey of objects ranging from huge numbers

  • of minor bodies in our SS, through galaxies in the nearby

  • Universe, to some 500000 distant quasars;

  • stringent new tests of general relativity and cosmology.

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Scheduled for launch in 2011:

positions and distances of stars

several hundred times more accurately

than any previous program.

This accuracy will allow it to determine

the distances to stars throughout the galaxy

and to probe nearby stars for Earth-sized planets.

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As the Newsletter No.1 of the IAU 2000, Commission 8 announced

The post-Hipparcos era has brought an element of uncertainty

as to the goals and future programs for all of ground-based astrometry

The WG has to identify scientifically

important programs that can be

realized using GBA or related observations,

and to study what kind of modifications,

upgrades or additions to the existing

instruments should be performed in order

to provide useful astronomical information

with necessary accuracy, keeping in mind

what the future astrometric satellites

will contribute

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  • astrometric observations of some natural satellites, asteroids

  • & comets with small or medium-sized telescopes - monitoring selected asteroids approaching the Earth - observations of artificial objects and space events and other natural

  • phenomena generating hazards in the vicinity of the Earth - improving double star orbits - astrometric re-reduction of old observations of bright main belt

  • asteroids obtained at Golosiiv in the system of modern

  • catalogues such as Tycho-2 to improve asteroid orbits - astrometric observations of the areas around extragalactic radiosources

  • to extend Hipparcos system to the faint stars - rediscovering of recently discovered asteroids with the help of digital

  • plate archive that we are creating now as a part of the work

  • on the integration of our plate archive into national and

  • international virtual observatories.

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Kovalevsky, J.,

Modern Astrometry, Springer-Verlag, 1994, 2002

Danjon, A.,

Astronomie Générale, 1980, Librairie Blanchard, Paris

Soffel, M.H.,

Relativity in Astrometry, Celestial Mechanics and Geodesy,

Springer -Verlag, Berlin, Heidelberg, 1989

Woolard, E.W. and Clemence, G.M.

Spherical Astronomy, Academic Press, New York, 1966