  We here develop an improved way of using a rotating star as a clock, set it
using the Sun, and demonstrate that it keeps time well. This technique, called
gyrochronology, permits the derivation of ages for solar- and late-type main
sequence stars using only their rotation periods and colors. The technique is
clarified and developed here, and used to derive ages for illustrative groups
of nearby, late-type field stars with measured rotation periods. We first
demonstrate the reality of the interface sequence, the unifying feature of the
rotational observations of cluster and field stars that makes the technique
possible, and extends it beyond the proposal of Skumanich by specifying the
mass dependence of rotation for these stars. We delineate which stars it cannot
currently be used on. We then calibrate the age dependence using the Sun. The
errors are propagated to understand their dependence on color and period.
Representative age errors associated with the technique are estimated at ~15%
(plus possible systematic errors) for late-F, G, K, & early-M stars. Ages
derived via gyrochronology for the Mt. Wilson stars are shown to be in good
agreement with chromospheric ages for all but the bluest stars, and probably
superior. Gyro ages are then calculated for each of the active main sequence
field stars studied by Strassmeier and collaborators where other ages are not
available. These are shown to be mostly younger than 1Gyr, with a median age of
365Myr. The sample of single, late-type main sequence field stars assembled by
Pizzolato and collaborators is then assessed, and shown to have gyro ages
ranging from under 100Myr to several Gyr, and a median age of 1.2Gyr. Finally,
we demonstrate that the individual components of the three wide binaries
XiBooAB, 61CygAB, & AlphaCenAB yield substantially the same gyro ages.
