1. Astronomical Institute of the Romanian Academy
FUNDAMENTAL
ASTRONOMY
Magda Stavinschi
Astronomical Institute of the Romanian Academy

2. No indication
of the distance
to the objects

3. 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.

4. GEOMETRICAL EFFECTS Several geometrical phenomena affect the
transformation between
the instrument and the sky.
One is a purely geometrical transformation;
others are due to kinematic properties
of the ensemble Earth-celestial body.

5. FIELD-TO-FOCUS TRANSFORMATION
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.

6. The equatorial coordinates
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 and Δδ into linear coordinates.

7. differential coordinates => standard coordinates
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
gnomonic or central projection

8. apparent displacement of a star on the celestial sphere
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.

9. 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.

10. 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.:
OE, EB, BP

11. OP = OE(t) + EB(t) + BP(t')
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 =
diurnal or geocentric parallax
(observation performed from an artificial satellite)
EB: Earth center – SS barycenter
at the time t (given by ephemerides)
BP: SS barycenter - 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')

12. 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 α and δ
α0,δ0 of the star are given for a date t0
=> the coordinates at time t are:
α = α0 + (t - t0) μα
δ = δ0 + (t - t0) μδ

13. OPTICAL EFFECTS They are produced by various properties of light:
       finite velocity,
       non-linear propagation in gravity fields,
       its ondulatory nature.

14. ABERRATION 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)

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

16. 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.

17. 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.

18. 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.

19. REFERENCE
SYSTEMS & FRAMES

20. which is a theoretical concept
In astronomy is a
reference system (R.S.),
which is a theoretical concept or
reference frame (R.F.),
a practical realization of a R.S., which provides a means of assigning coordinates to an object.

21. REFERENCE SYSTEM 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.

22. The ensemble of fiducial points and algorithms
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

23. IDEAL REFERENCE SYSTEM
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).

24.  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.

25. REFERENCE SYSTEMS Dynamical definition
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: SS as 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.

26. = extragalactic celestial R.S.
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.

27. It is based upon numerical values of a
CONVENTIONAL REFERENCE SYSTEM
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.

28. 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 of astronomical 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.

29. International Celestial Reference System (ICRS)
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 and
the origin in this principal plane
as near as possible to the dynamical equinox of J

30. INTERMEDIARY REFERENCE SYSTEM
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).

31. CONVENTIONAL REFERENCE FRAMES
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.
Result:
reference frame
or, better,
conventional reference frame
presented in the form of
a catalogue of positions and proper motions.

32. For a dynamical definition, one has to establish
(using the conventional model)
a numerical theory of 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 = SS center 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).

33. α = T + H International Terrestrial Reference Frame ITRF
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

34. ROTATION
OF THE EARTH
TIME

35. - complicated ensemble of physical phenomena
ROTATION OF THE EARTH
- 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

36. Pole Stars are Transient
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.

37. POLAR MOTION
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.

38. 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.

39. 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
=> α and 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.

40. Earth mean figure:
ellipsoid flattened 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 torque which 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.

41. NUTATION Relative positions of Moon, Earth and Sun vary with t
=> periodic additional motions
(nutations);
their periods directly 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 as angle variations
in longitude & in obliquity.
They are elliptical. They can also be represented as the
sum of two circular nutations with the same period but
different amplitudes & directions (one prograde, one retrograde).

42. Heraclides, Aristotle (4rd century B.C.) Copernicus (16th century)
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

43. EARTH’S ROTATION VARIABILITY
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

44. Secular decrease of the rotation rate causes a LOD
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

45. Abrupt, irregular changes of
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?)

46. UNIVERSAL TIME The measurements of the Earth's rotation are
under the form of time series of the so-called
Earth Orientation Parameters (EOP)
UNIVERSAL TIME
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).

47. COORDINATES OF THE POLE 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.

48. 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 or
10-16 is expected in the near future.

49. 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

50. LEGAL SCALE TIMES LEAP SECONDS 2005 Dec 31 23h 59m 59s
based on UTC, differing from TAI
by an integer number of seconds.
LEAP SECONDS
decided by IERS:
|UTC – UT1| < 0.9 s
Now: UTC - TAI = - 32 s
LAST: 1 January 1999
NEXT:
2005 Dec 31 23h 59m 59s
2005 Dec 31 23h 59m 60s
2006 Jan 1 0h 0m 0s

51. TT = TAI + 32.184 s 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 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.

52. SPACE ASTROMETRY Advantages
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.

53. HIPPARCOS
mission

54. HIgh Precision PARallax COllecting Satellite
The principle of HIPPARCOS was invented by Lacroute in
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
Hipparchus of Rodhes BC
-calculated the length of the year to
within 6.5 min;
-discovered the
precession of the equinoxes
-first known star catalogue (1080 stars)

55. Launched: August 8, 1989
Very elongated orbit instead of the expected geostationary one.
Perigee 500 km high and an apogee close to 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

57. 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.

58. 16 printed volumes and a set of ASCII CD-Rom discs
Contents of the Hipparcos Catalogue
Published by ESA (1997):
16 printed volumes and a set of ASCII CD-Rom discs
117,955 entries for astrometry &
118,204 for the photometric results

59. 11,600 recognized or suspected variables.
Astrometric results
Positions and p.m. given in ICRS for
mean epoch of observations
Median standard uncertainty for:
star positions with Hp < 9 at epoch is
0.77 mas (in α cos δ) and 0.64 mas (in δ)
yearly p.m.: 0.88 mas/yr (in α cos δ) and 0.74 mas/yr (in δ)
parallaxes: 0.97 mas
Photometric results
median photometric uncertainty for Hp < 9 is mag.
11,600 recognized or suspected variables.

60. TYCHO CATALOGUE 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
Photometric median standard uncertainty:
0.012 mag for VT
For the entire catalogue:
25 mas for position
0.06 mag for VT photometry

61. positions and magnitudes of 2,538,913 stars, based on satellite data,
Tycho-2 Catalogue
positions and magnitudes of 2,538,913 stars,
based on satellite data,
only for an observation epoch close to
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

62. SPACE GLOBAL ASTROMETRY PROJECTS
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.

63. G A I A 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.

64. LAUNCH: Dec-2011 END:2020 OBJECTIVES:
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.

65. 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 distant quasars;
stringent new tests of general relativity and cosmology.

66. SIM PlanetQuest 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.

67. FDGBA IAU WORKING - GROUP THE FUTURE DEVELOPMENT OF
GROUND-BASED ASTROMETRY
FDGBA

68. 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

69. POSSIBLE PROGRAMS for FDGBA
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.

70. SELECTED BIBLIOGRAPHY
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