  Fitting spectral distributions of total fluxes or image intensities are two
standard methods for estimating the masses of starless cores and protostellar
envelopes. These mass estimates, which are the main source and basis of our
knowledge of the origin and evolution of self-gravitating cores and protostars,
are uncertain. In this model-based study, a grid of radiative transfer models
of starless cores and protostellar envelopes was computed and their total
fluxes and image intensities were fitted to derive the model masses. To
investigate intrinsic effects related to the physical objects, all
observational complications were explicitly ignored. Known true values of the
numerical models allow us to assess the qualities of the methods and fitting
models, as well as the effects of nonuniform temperatures, far-infrared opacity
slope, selected subsets of wavelengths, background subtraction, and angular
resolutions. The method of fitting image intensities gives more accurate masses
for more resolved objects than the method of fitting total fluxes. With the
latter, a fitting model that assumes optically thin emission gives much better
results than the one allowing substantial optical depths. Temperature excesses
within the objects above the mass-averaged values skew their spectral shapes
towards shorter wavelengths, leading to masses underestimated typically by
factors 2-5. With a fixed opacity slope deviating from the true value by a
factor of 1.2, derived masses are inaccurate within a factor of 2. The most
accurate masses of the models are estimated by fitting just two or three
longest-wavelength fluxes. Conventional algorithm of background subtraction is
a likely source of large systematic errors. The absolute values of masses of
the unresolved or poorly resolved objects in star-forming regions are uncertain
to within at least a factor of 2-3.
