FUNDAMENTAL ASTRONOMY

1. 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 thesky. 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. 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.

7. 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

8. 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. 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')

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 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

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. 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. 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. 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 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.

26. 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. 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 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.

29. 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.

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 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).

33. 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. 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. 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 => 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.

40. 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.

41. NUTATION Relative positions ofMoon, Earth and Sunvary witht => periodic additional motions (nutations); 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).

42. 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. 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. 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. 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 10-14 or 10-15 . 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 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