Details on the reasons, consequences and process regarding the IAU 2012 re-definition of
the astronomical unit (au)
1- The astronomical unit as part of the astronomical system of units
- It is convenient for astronomers to use, for certain applications, an
astronomical system of units, in which the unit of mass is equal to
the mass of the Sun, M
S, the unit of time is one day, D, and the unit
of length is the astronomical unit of length (or simply the "astronomical unit").
- The astronomical unit is a unit of length approximating the Sun-Earth
distance that it is in common use by astronomers for expressing distances.
2- The old definition of the astronomical unit
- The au was defined by a mathematical expression involving the mass of
the Sun, the length of the day and a fixed number, chosen as being a
conventional value of a constant designated as the "Gaussian gravitational constant".
- More precisely, the au was "that length for which the Gaussian
gravitational constant,
k, takes the value of 0.017 202 098 95 when
the units of measurements are the astronomical unit of length, mass and
time", or equivalently "the radius of an unperturbed circular Newtonian
orbit about the Sun of a particle having infinitesimal mass, moving with
an angular frequency of 0.017 202 098 95 radians per day".
- The practice of using the value of
k as a fixed constant which served
to define the astronomical unit was in use unofficially since the 19th
century and officially since 1938.
- The fixed number chosen for
k came from an old measurement of the
Earth's mean motion around the Sun.
- Expressing distances in astronomical unit as defined above allowed
astronomers to overcome the difficulty of measuring distances in some
physical unit (such as the meter).
- Such a practice was useful for many years because astronomers were
not able to make distance measurements in the solar system as precisely
as they could measure angles.
3- The problems encountered with the old definition
- Due to the complexity of the above definition, there have been many
incorrect descriptions of the au and wrong statements about what it was
intended to be.
- With the old definition, the length of the au in Système
International (SI) meters was determined by observations in the solar
system so that the value in fact depended on the theory of motion and
observations being used.
- The description of the old definition was based on a Newtonian concept
which was difficult to extend to the framework of General relativity,
which is the framework needed by modern dynamical astronomy.
- The value in SI units of the solar mass parameter (i.e. the product,
GM
S, of M
S by the gravitational constant G) had to
be derived from a mathematical formula and the value in meters of the au,
which did not give a direct access to that parameter.
- The accuracy of modern range measurements (i.e. uncertainty of a few
meters in a length of 150 millions of kilometers) makes the use of the practice
(described in 2-) unnecessary.
4- The new definition (IAU 2012 Resolution B2)
- The new definition is such that the au is a conventional unit of
length equal to a fixed number of SI meters.
- The conventional value (i.e. 149 597 870 700 m exactly) adopted for the
new definition has been chosen to be consistent with the best estimate
of the numerical value of the au corresponding to the old definition, which
was provided in the IAU 2009 System of astronomical constants.
- This definition of the astronomical unit is to be used with all
forms of the metrics used in General Relativity.
5- Advantages of the new definition
- It eliminates possible conflicts with SI units.
- It eliminates dependence on theories of motion.
- It eliminates requirements for additional conventions to account for
the effects of General Relativity.
- It makes it easier to deal with possible variations in the mass of
the Sun.
6- Consequences for the users of the change of definition
- The change of definition of the astronomical unit mainly concerns
those in the field of high-accuracy solar system dynamics, because there
is a change of status of that unit: its value in SI meter is now fixed
to a conventional number and has no more to be estimated by observations
as it was with the old definition.
- The new definition makes that unit more understandable to other
scientists, engineers, and software designers.
- The astronomical unit is also used in the definition of other
astronomical measurement scales. However, the relative difference
between the old and the new definitions is so small that there would be
no significant effect in changing our understanding of distances to
objects outside our solar system considering the precision with which
they are known today. The reason for that is that the numerical
value of the new definition has been chosen to be consistent with the
best estimate corresponding to the old definition.
7- Process followed for the adoption of the new definition
- The question of fixing the length of the au goes back several years,
and has been discussed at international meetings as well as within
groups of experts, especially since 2009, in particular within the IAU
Working Group on Numerical standards for fundamental astronomy.
- There were objections to the change from a few people who considered
either that the change would be difficult to implement in the solar
system ephemeredes software, or that it would induce discrepancies with
the previous practice, or because they were attached to the historical
definition. But after a few years of discussion and the concrete proof of
the possibility of changing the definition by the producers of solar system
ephemerides, all agreed on the necessity of that re-definition.
- A draft resolution proposal was submitted to the astronomical
community in September 2011 during the "Journées 2011 "Systèmes
de référence" in Vienna, which was largely discussed during that meeting and
resulted in an improved wording of the proposal.
- That revised draft was then submitted by the President of Division 1
(Fundamental Astronomy) of the International astronomical union (D.D.
McCarthy) to the relevant commissions of that Division, which resulted
in a few improvements of the wording or proposals of changes that have not all be agreed.
Minor improvements in the wording have been proposed during Joint Discussion 7 at the
General Assembly of the IAU, the day before the publication of the text of the Resolution
in the GA newspaper which was submitted to the GA.
- The Resolution (IAU 2012 Resolution B2) was voted at the final meeting
of the General assembly of the IAU (30 August).
Nicole Capitaine, Observatoire de Paris, 2012
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