11 Regarding the re-definition of the astronomical unit of length (AU) E.V. Pitjeva Institute of Applied Astronomy, Russian Academy of Sciences Workshop on Precision Physics and Fundamental Physical Constants (FFK 2013)

22 The advent of the Astronomical Unit The Astronomical Unit is one of the most basic units of astronomy: It determined the scale of the solar system. Classical measurements in the solar system were angle and periods (P) or mean motion (n): 2π/P. Astronomical System (AS) of units: · solar mass (M), · mean solar day (d), · gravitational constant (k 2 ), where the Gaussian constant k = For a (massless) particle at 1 AU from the Sun in keplerian motion, we have a=1, M=1, so the mean motion is n=k and the period P= 2π/k = known as a Gaussian year, which is an old measurement of the Earth's mean motion. In 1976, the International Astronomical Union adopted the definition of the AU: "The astronomical unit of length is that length (A) for which the Gaussian gravitational constant (k) takes the value of when the units of measurements are the astronomical unit of length, mass and time.“

33 Distance to any celestial object in AU can be obtained from annual parallax (angular displacement). What is the AU value in metrical units? Historical determinations of AU  III century BC, the first attempt to estimate the AU value in metrical units was made by Aristarchus of Samos. His estimate was based on the angle between the Moon and the Sun when the Moon was judged to be exactly half illuminated.  1672, Domenico Cassini: the reasonable accuracy 10% of AU by measuring the parallax of Mars from two locations on the Earth.  1800's:, the accurate 2% was obtained by observing the transit of Venus.  The latter 1800's: 0.1% from asteroid parallaxes.  1950, Rabe: the accurate 0.05% (65000 km) from the close approach of Eros.

44 Modern determinations of AU Since the beginning Venus radar echoes in 1961 the value of the Astronomical Unit, has been determined exclusively from ranging data of planets and spacecraft: τ [μs] ≈ 2 ∙ R ∙ AU/c, where R – distance between the Earth and the observable body, c – velocity of light. 1961, first successful ranging to Venus was permitted at MIT, JPL (USA), Institute of Radioengineering and Electronics (USSR) and Jodrell Bank (England), the accurate 2000 km to 130 km. Typical uncertainties in the value of AU have decreased from many tens of thousands of kilometers to the present level of a few meters.

5 We have proposed to the NSFA WG ( Pitjeva, Standish, Cel.Mech. Dynam.Astr.,2009, 103, ) the value AU = (3) m obtained while fitting DE and EPM ephemerides that was accepted by XXVII GA IAU as the current best estimation (Luzum et al., Pitjeva, Standish, Cel.Mech. Dynam.Astr.,2011, 110, ).

66 Connection between AU and heliocentric gravitation constant GM Sun The unit distance AU (the value of the astronomical unit in meters) can be expressed in a term of other astronomical constants by its definition: GM Sun [m 3 s -2 ]=k 2 AU[m] 3 /86400[s] 2. This equation was used for the connection between the systems of units SI and astronomical. The value GM Sun in the physical system of units may be estimated from fitting ephemerides to observations. However, this value usually it has been calculated from an entirely equivalent process - that of adjusting the AU value, obtained in meters while fitting planet ephemerides. The value AU = (3) m is consistent with the value GM Sun = (10) ·10 20 [m 3 s -2 ] proposed by W. Folkner and accepted by XXVII GA IAU.

77 Motives of the re-definition of the astronomical unit Although the Astronomical System of units is necessary: The two systems (with SI units and astronomical units) are equivalent for use in dynamical astronomy; anybody can use either of these two systems, which ever he prefers. The astronomical system is convenient for dynamical astronomy in the Solar system. The AU is a convenient unit of length, as are the units of days or Julian centuries instead of SI seconds. It is the astronomical system that is now used by the majority of users of planetary ephemerides (other than navigation) and all Almanacs. However: P reference of a self-consistent set of units and numerical standards (SI) for use in modern dynamical astronomy. The wrong understanding the previous definition of AU, considering that AU is the major axle of the Earth orbit. But AU is just “large meter”. The change of the heliocentric gravitational GM Sun obtained from modern observations must correspond to the change of AU in accord the previous definition of AU, however it is inconvenient to have a variable astronomical unit of length.

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11 RESOLUTION B2 on the re-definition of the astronomical unit of length. Proposed by the IAU Division I Working Group Numerical Standards and supported by Division I The XXVIII General Assembly of International Astronomical Union recommends  1) that the astronomical unit be re-defined to be a conventional unit of length equal to m exactly, in agreement with the value adopted in IAU 2009 res. B2,  2) that this definition of the astronomical unit be used with all time scales such as TCB, TDB, TCG, TT, etc.,  3) that the Gaussian gravitational constant k be deleted from the system of astronomical constants,  4) that the value of the solar mass parameter, GM , be determined observationally in SI units,  5) that the unique symbol “au” be used for the astronomical unit.

12 What has changed for users? For practical goals, there are not any changes. One can use or the SI system or Solar system units for calculation own tasks. The value AU has been fixed on the magnitude AU = m that was adopted as the current best value at the XXVII GA IAU in 2009, and this value was recommended for using. The the connection between the systems of units SI and astronomical one has changed. The value AU and GM Sun are not coupled.

13 The scale of interstellar distances is based on the astronomical unit AU.. 1 parsec is the distance corresponding to a parallax of one arcsecond, i.e. the line equal 1 AU is seen as the 1" angle. Then, this scale spreads on galactic and intergalactic distances: 1 kpc = 1000 pc, 1 Mpc = 10 6 pc. For the value AU = m 1 pc = ∙ m. Usually only several significant numbers is used for the value in pc.

14 Thanks !