  The radii of young pre-main-sequence (PMS) stars in the Orion Nebula Cluster
(ONC) have been estimated using their rotation periods and projected equatorial
velocities. Stars at a given effective temperature have a spread in their
geometrically estimated projected radii that is larger than can be accounted
for with a coeval model, observational uncertainties and randomly oriented
rotation axes. It is shown that the required dispersion in radius (a factor of
2-3 full width half maximum) can be modelled in terms of a spread in stellar
ages larger than the median age of the cluster, although the detailed star
formation history cannot be uniquely determined using present data. This
technique is relatively free from systematic uncertainties (binarity,
extinction, variability, distance) that have hampered previous studies of the
ONC star formation history using the conventional Hertzsprung-Russell diagram.
However, the current ONC rotational data are biased against low luminosity
objects, so the deduced dispersions in radius and inferred age are probably
underestimates. In particular, the ages of a tail of PMS stars that appear to
be >=10Myr old in the Hertzsprung-Russell diagram cannot be verified with
present data. If projected equatorial velocities were measured for these
objects it could easily be checked whether their radii are correspondingly
smaller than the bulk of the ONC population.
