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 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.
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.
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.
For this, it is convenient to use a local system of celestial coordinates centered at a certain point A (α 0, δ 0 ). The equatorial coordinates of a point in the vicinity of A are α 0 + α, δ 0 + δ The image of this region of the celestial sphere on an ideal focal surface is planar one has to transform the differential coordinates α and δ into linear 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
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.
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.
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
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')
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 α 0, δ 0 of the star are given for a date t 0 => the coordinates at time t are: α = α 0 + (t - t 0 ) µ α δ = δ 0 + (t - t 0 )µ δ
OPTICAL EFFECTS They are produced by various properties of light: finite velocity, non-linear propagation in gravity fields, its ondulatory nature.
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 - t ( t = the time during which the light traveled from P to the observer)
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 = V 0 + V E - V S
V S = 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) V E = velocity of Earth center of mass w.r.t. SS barycenter It gives rise to the annual aberration, in which V is replaced by V E. Planets: the total aberration, caused by V E V S, is the planetary aberration. V 0 = 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.
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.
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.
REFERENCE SYSTEMS & FRAMES
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.
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.
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
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).
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.
REFERENCE SYSTEMS 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.
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.
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.
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.
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.
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 1 st 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 µarc level. The corresponding point on the ITRS is the Terrestrial Ephemeris Origin (TEO).
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.
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).
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 T = Greenwich sidereal time α = T + H
ROTATION OF THE EARTH TIME
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
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 ax -Polariswill 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.
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.
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.
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.
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.
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).
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
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: 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
Period of rotation of the Earth (LOD( LOD) assumed constant until the 20th century, apart from a 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 (19 th century) confirmed this effect. Secular decrease of the rotation rate causes a LOD increase of about 2 ms/century
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?)
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).
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.
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.
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
LEGAL SCALE TIMES 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
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 relativistic. 1984: ET replaced by the two relativistic timescales Barycentric Dynamical Time (TDB) In practice, Terrestrial Dynamical Time (TDT). the length of the TE second = = the length of the TDB or TDT second.
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.
HIPPARCOS mission
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 Hipparchus of Rodhes 190-120 120 BC -calculated the length of the year to within 6.5 min; -discovered the precession of the equinoxes -first known star catalogue (1080 stars)
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
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.
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
Astrometric results Positions and p.m. given in ICRS for mean epoch of observations 1991.25. Median standard uncertainty for: star positions with H p < 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 H p < 9 is 0.0015 mag. 11,600 recognized or suspected variables.
TYCHO CATALOGUE 1,058,332 entries, < V T ~10.5 mag (limiting magnitude V T ~11.5 mag) Median astrometric standard uncertainty (V T < 9 mag) 7 mas for position at 1991.25 Photometric median standard uncertainty: 0.012 mag for V T For the entire catalogue: 25 mas for position 0.06 mag for V T photometry
Tycho-2 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 (V T < 9): 7 mas, for all stars: 60 mas. Mean standard uncertainty in p.m. is 2.5 mas/yr
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.
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 L 2 of the Earth-Sun system.
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.
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.
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.
IAU WORKING - GROUP THE FUTURE DEVELOPMENT OF GROUND-BASED ASTROMETRY FDGBA
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 http://www.astro.ro/wg
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.
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 http://www.iers.org/ http://scienceworld.wolfram.com/astronomy/time.html http://cdsweb.u-strasbg.fr/hipparcos.html http://sci.esa.int/science-e/www/area/index.cfm?fareaid=26 http://aira.astro.ro/wg/