  Astrophysical models of planet formation require accurate radiometric dating
of meteoritic components by short-lived (Al-Mg, Mn-Cr, Hf-W) and long-lived
(Pb-Pb) chronometers, to develop a timeline of such events in the solar nebula
as formation of Ca-rich, Al-rich Inclusions (CAIs), chondrules, planetesimals,
etc. CAIs formed mostly around a time ("t=0") when the short-lived radionuclide
26Al (t1/2 = 0.72 Myr) was present and presumably homogeneously distributed at
a known level we define as (26Al/27Al)SS = 5.23 x10^-5. The time of formation
after t=0 of another object can be found by determining its initial
(26Al/27Al)0 ratio and comparing it to (26Al/27Al)SS. Dating of meteoritic
objects using the Mn-Cr or Hf-W systems is hindered because the abundances
(53Mn/55Mn)SS and (182Hf/180Hf)SS at t=0 are not known precisely. To constrain
these quantities, we compile literature Al-Mg, Mn-Cr, Hf-W and Pb-Pb data for
14 achondrites and use novel statistical techniques to minimize the
discrepancies between their times of formation across these systems. We find
that for (53Mn/55Mn)SS = (8.09+/-0.65)x10^-6, (182Hf/180Hf)SS =
(10.42+/-0.25)x10^-5, tSS = 4568.36+/-0.20 Myr, and a 53Mn half-life of
3.80+/-0.23 Myr, these four free parameters make concordant 37 formation times
recorded by the different systems in 14 achondrites. These parameters also make
concordant the ages derived for chondrules from CB/CH achondrites, formed
simultaneously in an impact, and are apparently concordant with the I-Xe
chronometer as well. Our findings provide very strong support for homogeneity
of 26Al, 53Mn, and 182Hf in the solar nebula, and our approach offers a
framework for more precise chronometry.
